# Systems Of Particles And Rotational Motion Questions

We provide systems of particles and rotational motion practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on systems of particles and rotational motion skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of systems of particles and rotational motion Questions

Question NoQuestionsClass
1The displacement of centre of mass of
( A_{B} ) system till the string becomes
vertical is:
A. zero
B. ( L(1-cos theta) )
c. ( frac{L}{2}(1-cos theta) )
D. None of these
11
2A metal bar of ( 70 mathrm{cm} ) long and ( 4 mathrm{kg} ) in mass supported on two knife edges placed ( 20 mathrm{cm} ) from each end. A ( 6 mathrm{kg} ) load is suspended at ( 30 mathrm{cm} ) from on end.
Find the normal reaction at the knife-
edge. (assume it to be of uniform cross
section and homogeneous)
( A cdot 55 mathrm{N} ) at ( K_{1} ) and ( 33 mathrm{N} ) at ( K_{2} )
B. ( 45 mathrm{N} ) at ( K_{1} ) and ( 53 mathrm{N} ) at ( K_{2} )
c. ( 55 mathrm{N} ) at ( K_{1} ) and ( 43 mathrm{N} ) at ( K_{2} )
D. 43 N at ( K_{1} ) and ( 55 mathrm{N} ) at ( K_{2} )
11
3If ( vec{a}=hat{i}+hat{j}+hat{k} & vec{b}=hat{j}-hat{k}, ) then the
vector ( vec{c} ) such that ( vec{a} . vec{c}=3 & vec{a} times vec{c}=vec{b} )
is
A ( cdot frac{1}{3}(3 hat{i}-2 hat{j}+5 hat{k}) )
B・( _{frac{1}{3}}(5 hat{i}+2 hat{j}+2 hat{k}) )
c ( cdot frac{1}{3}(hat{i}+2 hat{j}-5 hat{k}) )
D ( cdot frac{1}{3}(3 hat{i}+2 hat{j}+hat{k}) )
11
4A body of mass ( m ) moving with a
velocity ( v ) strikes a stationary body of
mass ( m ) and sticks to it. What is the
speed of the system
A ( .2 v )
B.
c. ( frac{v}{2} )
D. ( frac{v}{3} )
11
5The principle involved in the working of a beam balance is :
A. principle of moments
B. principle of inertia
c. principle of superposition
D. principle of velocity
11
6The point through which the total weight appears to act for any orientation of the object is
A. centre of gravity
B. centre of momentum
c. centre of force
D. none of the above
11
7If ( vec{r}=2 hat{i}+hat{j} mathrm{m} ) and ( vec{F}=hat{i}+2 hat{j} N . ) Then
the magnitude and direction of torque ( tau )
is :
A ( cdot 4 N m ) along ( 45^{circ} ) with ( x ) -axis or ( y ) -axis
B. 3Nm along 45 ( ^{circ} ) with ( x ) -axis or ( y ) -axis.
c. ( 4 N m ) along ( z ) -axis
D. ( 3 N m ) along ( z ) -axis
11
8When tall buildings are constructed on earth, the duration of day night
A. slightly increases
B. slightly decreases
c. has no change
D. none of these
11
9A sphere is projected up an inclined
plane with a velocity ( v_{0} ) and zero angular velocity as shown. The coefficient of friction between the
sphere and the plane is ( mu=tan theta . ) If
the total time of rise of the sphere is
( frac{boldsymbol{x} boldsymbol{v}_{0}}{boldsymbol{g} sin theta}, ) find the value of ( boldsymbol{2} boldsymbol{x} )
11
10Assertion
To unscrew a rusted nut, we need a
wrench with longer arm.
Reason
Wrench with longer arm reduces the
torque of the arm.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
11The moment of inertia of a circular disc
of radius ( 2 m ) and mass ( 1 k g ) about an
axis passing through its centre of mass
and perpendicular to plane is ( 2 k g-m^{2} )
Its moment of inertia about an axis
parallel to this axis and passing through its edge in ( k g-m^{2} ) is
A . 10
B. 8
( c cdot 6 )
D. 4
11
12A cylindrical disc of a gyroscope of ( operatorname{mass} boldsymbol{m}=15 k g ) and radius ( boldsymbol{r}=mathbf{5 . 0} boldsymbol{c m} )
spins with an angular velocity ( omega= ) 330 rad/s.The distance between the
bearings in which the axle of the disc is mounted is equal to ( l=15 mathrm{cm} ). The
axle is forced to oscillate about a
horizontal axis with a period ( boldsymbol{T}=mathbf{1 . 0} boldsymbol{s} )
and amplitude ( varphi_{m}=20^{circ} . ) Find the
maximum value of the gyroscopic forces exerted by the axle on the bearings in ( boldsymbol{N} )
11
13rotating in the horizontal plane with
constant angular speed ( omega, ) as shown in
the figure. At time ( t=0, ) a small insect
starts from ( O ) and moves with constant
speed ( v ) with respect to the rod towards
the other end. It reaches the end of the
rod at ( t=T ) and stops. The angular
speed of the system remains ( omega )
throughout. The magnitude of the torque ( |vec{tau}| ) on the system about ( boldsymbol{O}, ) as a function of time is best represented by
which plot?
( A cdot A )
B. B
( c cdot c )
D.
11
14Let ( I_{A} ) and ( I_{B} ) be moments of inertia of ( a )
body about two axes ( A ) and ( B )
respectively. The axis ( A ) passes through
the centre of mass of the body but ( B )
does not
A ( cdot I_{A}<I_{B} )
B. If ( I_{A}<I_{B} )
C. If the axes are parallel, ( I_{A}<I_{B} )
D. If the axes are not parallel, then ( I geq I_{B} )
11
15Torque/moment of inertia equals to:
A . angular velocity
B. angular acceleration
c. angular momentum
D. force
11
16Two particles ( A ) and ( B ) initially at rest move towards each other under a
mutual force of attraction. The speed of
center of mass at the instant when the
speed of ( A ) is ( v ) and the speed of ( B ) is ( 2 v ) is
( A )
B. Zero
c. ( 2 v )
D. ( frac{3 v}{2} )
11
17The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height ( h ) from rest
without sliding is
A ( cdot sqrt{left(frac{g}{5}right) g h} )
в. ( sqrt{g h} )
c. ( sqrt{left(frac{4}{3}right) g h} )
D. ( sqrt{left(frac{10}{7}right) g h} )
11
18Name and state the law which is kept in
mind while balancing equations.
11
19A Diwali rocket is ejecting 0.05 kg of gases per second at a velocity of ( 400 m s^{-1} . ) The accelerating force on the rocket is equal to :
A. 20 dyne
B. 20 newton
c. ( 20 mathrm{kg} ) wt
D. sufficient data not giver
11
20A man turns on rotating table with an
angular speed ( omega . ) He is holding two equal masses at arms length. Without moving his arms, he just drops the two masses. How will his angular speed change?
A. less than ( omega )
B. more than ( omega )
c. it will be equal to
D. it will be more than ( omega ) if the dropped mass is more than ( 9.8 mathrm{Kg} ) and it will be less than ( omega ) if the mass dropped is less than ( 9.8 mathrm{Kg} )
11
21Two blocks of masses ( 2 k g ) and ( 1 k g )
respectively are tied to the ends of a
strings which passes over a light
frictionless pulley. The masses are held
at rest at the same horizontal level and
then released. The distance traversed by
centre of mass in 2 seconds is: ( (g= )
( left.10 m / s^{2}right) )
A ( .1 .42 m )
B. ( 2.22 m )
c. ( 3.12 m )
D. ( 3.33 m )
11
22Mass per unit of a semicircular disc of
total mass m radius R varies linearly
with radial distance from the point 0 (base centre). Find the height of centre of mass from 0
A ( cdot frac{2 R}{pi} )
в. ( frac{3 R}{2 pi} )
c. ( frac{4 R}{3 pi} )
D. ( frac{3 R}{8} )
11
23Find out the velocity of the centre of mass of two ( 1 k g ) masses moving toward
each other, one mass with velocity ( boldsymbol{v}_{1}= )
( mathbf{1 0 m} / boldsymbol{s}, ) the other with velocity ( boldsymbol{v}_{mathbf{2}}= )
( 20 m / s )
A. ( 0 m / s )
B. ( 5 m / s ) to the left
c. ( 10 m / s ) to the left
D. ( 15 mathrm{m} / mathrm{s} ) to the left
E . ( 20 mathrm{m} / mathrm{s} ) to the left
11
24A man weighing 100 kg carries a load of
( 10 mathrm{kg} ) on his head. He jumps from a tower with the load on his head. What
will be the weight of the load as experienced by the man?
A. zero
в. ( 10 mathrm{kg} )
c. slightly more than ( 10 mathrm{kg} )
D. ( 110 mathrm{kg} )
11
25There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration ( bar{a} ).
Acceleration of center of mass is :
A . zero
в. ( frac{1}{2} bar{a} )
( c cdot bar{a} )
D. centre of mass for such a system can not be defined
11
26Assuming that the earth’s orbit round
the sun be circular, find the linear
velocity of its motion and the period of revolution about the sun. Given ( G= )
( 6.67 times 10^{-11} ) S.I. units, mass of the
( operatorname{sun}=1.99 times 10^{30} k g, ) mean distance
between the sun and the earth ( = )
( 1.497 times 10^{-11} m )
11
27The steel balls ( A ) and ( B ) have a mass of
( 500 g ) each and are rotating about the
vertical axis with an angular velocity of
4 rad/s at a distance of ( 15 C M ) from
the axis. Collar ( C ) is now forced down
until the balls are at a distance of
( 5 C M ) from the axis. How much work
must be done to move the collar down?
11
28The centre of mass of the shaded
portion of the disc is (The mass is
portion):
( A cdot frac{R}{20} ) to the left of ( A )
B. ( frac{R}{12} ) to the left of ( A )
C. ( frac{R}{40} ) to the right of ( A )
D. ( frac{R}{12} ) to the right of ( A )
11
29Two thin uniform rods ( boldsymbol{A}(boldsymbol{M}, boldsymbol{L}) ) and
( B(3 M, 3 L) ) are joined as shown. Find
the ( M I ) about an axis passing through
the centre of mass of system of rods and perpendicular to the length.
11
30Three similar spheres of mass ( mathrm{m} ) and
radius r are moving down along three
inclined planes ( A, B ) and ( C ) of similar
dimensions. Sphere on inclined plane ( A ) rolls down in pure rolling, on B it partially
rolls and partially slides down the plane
whereas on plane ( mathrm{C} ) it slides down
without rolling, then at the bottom of
planes
A. Velocities of all sphere are same.
B. Velocities on A and C are same whereas that on B is less
C. Velocities of sphere on ( A ) is least and that on ( C ) is maximum
D. Velocities of sphere A is maximum
11
31Two painters are working from a wooden board ( 5 mathrm{m} ) long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of 1040
N. Painter A of mass ( 80 mathrm{kg} ) is working at
a distance of ( 1 mathrm{m} ) from one end. Painter
B of mass ( 60 mathrm{kg} ) is working at a
distance of ( x ) m from the centre of mass
of the board on the other side. Take
mass of the board as ( 20 mathrm{kg} ) and ( g= )
( 10 m s^{-2} . ) The range of ( x ) so that both the
painters can work safely is :
A ( cdot frac{1}{3}<x<frac{11}{6} )
в. ( 0<x<frac{11}{6} )
c. ( _{0<x}<frac{10}{3} )
D. ( frac{1}{3}<x<2 )
11
32Two uniform solid spheres of equal radii
( R, ) but mass ( M ) and ( 4 M ) have a centre
to centre separation ( 6 R ), as shown in Figure. The two spheres are held fixed. A projectile of mass ( m ) is projected from
the surface of the sphere of mass ( M )
directly towards the centre of the second sphere. Obtain an expression for the minimum speed ( v ) of the projectile
so that it reaches the surface of the
second sphere.
11
33Two points ( A ) and ( B ) on a disc have
velocities ( v_{1} ) and ( v_{2} ) at some moment.
Their directions make angles ( 60^{circ} ) and
( 30^{circ} ) respectively with the line of
separation as shown in figure. The
angular velocity of disc is not given by :
A ( cdot frac{v_{1}}{sqrt{3} d} )
B. ( frac{v_{2}}{d} )
( ^{mathbf{c}} cdotleft(frac{sqrt{3} v_{1}-v_{2}}{2 d}right) )
D. None of these
11
34If the resultant of all the external forces
acting on a system of particles is zero, then from an inertial frame,one can
surely say that :
A. linear momentum of the system does not change in time
B. kinetic energy of the system does not change in time
c. angular momentum of the system does not change in time
D. potential energy of the system does not change in time
11
35Two particles ( A ) and ( B ), initially at rest, moves towards each other under a
mutual force of attraction. At the instant
when the speed of ( A ) is ( u ) and the speed of
( mathrm{B} ) is ( 2 u, ) the speed of centre of mass is
A. zero
в. ( u )
( c .1 .5 u )
D. ( 3 u )
11
36Calculate the moment about the points ( mathrm{C}(1,1,1) ) of a force ( 5 mathrm{N} ). acting along the line ( underset{A B}{text { where } A, B text { are the points }(2,3,4)} ) (3,5,6) respectively the distance being measured in ( mathrm{m} )
( mathbf{A} cdot 5(-2 i+j) )
B . ( 7(-2 i+j) )
c. ( frac{5}{3}(-2 i+j) )
D. ( frac{5}{3}(j) )
11
37If a rigid body acted upon by a system of coplanar parallel forces is to be in
equilibrium, then :
A. vector sum of the forces must be zero
B. vector sum of the moments of the forces taken about a point in their plane must be zero
c. one of the conditions
(A) or
(B) must be satisfied
D. Both the conditions (A) and
(B) must be satisfied
11
38The following motion is based on the
law of conservation of angular
momentum
A) rotation of top
B) diving of a diver
C) rotation of ballet dancer on smooth
horizontal surface
D) a solid sphere that rolls down on an inclined plane Identify the wrong statement:
A. In rotating a top, angular momentum is conserved.
B. When a diver dives using a board, angular momentum is conserved.
c. In rotation of a ballet dancer on a smooth horizontal surface, angular momentum is conserved
D. When a solid sphere rolls down an inclined plane angular momentum is conserved.
11
39A block of mass ( 2 k g ) is moving with a velocity of ( 2 hat{i}-hat{j}+3 hat{k} m / s . ) Find the
magnitude and direction of momentum of the block with the ( x- ) axis.
A ( cdot_{2 sqrt{14}} operatorname{kg} m / s, tan ^{-1}(sqrt{frac{5}{7}}) )
B. ( _{2 sqrt{7}} k g m / s, tan ^{-1}(sqrt{frac{2}{7}}) )
c. ( _{2 sqrt{14}} k g m / s, tan ^{-1}(sqrt{frac{2}{7}}) )
D. ( 2 sqrt{9} ) kg ( m / s, tan ^{-1}(sqrt{frac{3}{7}}) )
11
40A steering wheel of diameter ( 0.5 mathrm{m} ) is rotated anticlockwise by applying two forces each of magnitude 5 N. Draw a diagram to show the application of
forces and calculate the moment of
couple applied.
11
41One can lean further to one side or the
other without creating enough turning force to tip him over. This is because
A. The person has low centre of gravity
B. The person has no centre of gravity
c. The person has high centre of gravity
D. None of the above
11
42Two rings have their ( M . I ) in the ratio 2
1, If their diameters are in ratio of 2: 1
then the ratio of their masses will be:
( mathbf{A} cdot 2: 1 )
B. 1: 1
c. 1: 2
( mathbf{D} cdot 1: 4 )
11
43In a two step pulley arrangement meant
for a load ( mathrm{W} ), the ratio between force ( mathrm{P} )
and ( W ) in equilibrium position, when
radii of pulleys are ( r_{1} ) and ( r_{2} )
A ( cdot frac{r_{2}}{r_{1}-r_{2}} )
B. ( frac{r_{1}-r_{2}}{r_{2}} )
c. ( frac{r_{1}}{r_{2}-r_{1}} )
D. ( frac{r_{2}-r_{1}}{r_{1}} )
11
44An automobile moves on a road with a
speed of ( 54 k m h^{-1} . ) The radius of its
wheel is ( 0.45 m ) and the moment of
inertia of the wheel about its axis of
rotation is ( 3 mathrm{kgm}^{2} ). If the vehicle is
brought to rest in ( 15 s ), the magnitude of average torque transmitted by its brakes to the wheels is:
A . ( 2.86 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-2} )
B. ( 6.66 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-2} )
c. ( 8.58 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-2} )
D. ( 10.86 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-2} )
11
45One solid sphere and disc of same
radius are falling along an inclined plane without slipping. One reaches
earlier than the other due to
B. Different sizes
c. Different friction
D. Different moment of inertia
11
46Assertion
The center of mass of a body may lie where there is no mass.
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
47The moment of inertia of a thin square
plate ( A B C D ) of uniform thickness about
an axis passing through the centre 0
and perpendicular to the plane of the
plate is :
This question has multiple correct options
A ( cdot I_{1}+I_{2} )
B ( cdot I_{3}+I_{4} )
( mathbf{c} cdot I_{1}+I_{3} )
( mathbf{D} cdot I_{1}+I_{2}+I_{3}+I_{4} )
11
48A man is standing on a boat in still water. If he walks towards the shore the
boat will
A. Move away from the shore
B. Remain stationary
c. Move towards the shore
D. sink
11
49In the arrangement shown in figure
above, a weight ( A ) possesses mass ( m ), a
pulley ( B ) possesses mass ( M ). Also
known are the moment of inertia ( I ) of
the pulley relative to its axis and the
radii of the pulley ( R ) and ( 2 R ) The mass
of the threads is negligible. If the acceleration of the weight ( boldsymbol{A} ) after the
system is set free is ( boldsymbol{w}= )
find the value of ( b )
11
50A uniform rod is suspended horizontally from its mid-point. A piece of metal whose weight is ( boldsymbol{w} ) is suspended at a
distance ( l ) from the mid-point. Another
weight ( W_{1} ) is suspended on the other
side at a distance ( l_{1} ) from the mid-point to bring the rod to a horizontal position. When ( boldsymbol{w} ) is completely immersed in
water, ( boldsymbol{w}_{1} ) needs to be kept at a distance
( l_{2} ) from the mid-point to get the rod
back into horizontal position. The specific gravity of the metal piece is
A ( cdot frac{w}{w_{1}} )
в. ( frac{w l_{1}}{w l-w_{1} l_{2}} )
c. ( frac{l_{1}}{l_{1}-l_{2}} )
D. ( frac{l_{1}}{l_{2}} )
11
51In Figure a spherical part of radius ( frac{R}{2} ) is
removed from a bigger solid sphere of
radius ( R . ) Assuming uniform mass
distribution, a shift in the centre of
mass will be:
( A cdot frac{-R}{6} )
B. ( -frac{R}{14} )
( mathbf{c} cdot frac{R}{9} )
D. ( frac{R}{3} )
11
52A body at rest starts sliding from top of a smooth inclined plane and requires 4 seconds to reach bottom. How much
time does it take, starting from rest at top, to cover one-fourth of a distance?
A. 1 second
B. 2 seconds
c. 3 seconds
D. 4 seconds
11
53Two block masses ( m_{1} ) and ( m_{2} ) are
connected with the help of a spring of spring constant ( k ) initially the spring in its natural length as shown. A sharp
impulse is given to mass ( m_{2} ) so that it
acquires a velocity ( v_{0} ) towards right. If the system is kept on smooth floor then find:
(a) the velocity of the centre of mass
(b) the maximum elongation that the spring will suffer?
11
54A solid sphere is rolling purely on a rough horizontal surface with speed of
center ( u=12 mathrm{m} / mathrm{s} . ) It collides
inelastically with a smooth vertical wall at a certain moment, the coefficient of restitution being ( frac{1}{2} . ) How long (in sec) after the collision, the sphere will begin
pure rolling? [coefficient of friction between the
sphere and the ground is ( frac{3}{35} )
A . 16
B . 12
( c .6 )
D. 13
11
55A wheel moves in the xy plane such that
the location of its center is given by
equations
( mathbf{x}_{mathbf{0}}=mathbf{1 2 t}^{3}, mathbf{y}_{mathbf{0}}=mathbf{R}=mathbf{2}, ) where ( mathbf{x}_{o} ) and ( mathbf{y}_{o} )
are measured in metre and ( t ) in
seconds.
The angular displacement of a radial
line measured from a vertical reference
line is ( Theta=8 t^{4}, ) where ( Theta ) is in radians
(given ( v_{o} ) is the velocity of center of
wheel
11
56When we jump on a heap of sand, we
didn’t get hurted but on the floor of concrete, we get hurted. Explain.
11
57A gardener waters a lawn with a hose ejecting ( 250 mathrm{cc} ) of water per second through an orifice of area ( 2.5 mathrm{sqcm} )
Find the backward force on the
gardener.
A . ( 0.15 N )
B. ( 1.25 N )
c. ( 0.20 N )
D. ( 0.25 N )
11
58ILLUSTRATION 9.24 A cylindrical drum, pushed along by a
board rolls forward on the ground. There is no slipping at any
contact. Find the distance moved by
the man who is pushing the board,
when axis of the cylinder covers a
distance L.
exis of the cylinder covers a
11
59The ratio of angular velocity of rotation of minute hand of a clock with the
angular velocity of rotation of the earth
A ( cdot 12 )
B. 6
( c cdot 24 )
D. none of these
11
60A Proton of mass ( 1.6 times 10^{-27} ) kg goes
round in a circular orbit of radius ( 0 . )
metre under a centripetal force of ( 6 times )
( 10^{-14} N ) then the frequency of revolution
A . ( 1.25 times 10^{6} mathrm{rps} )
в. ( 2.50 times 10^{6} )rps
c. ( 3.75 times 10^{r} r p s )
D. ( 5 times 10^{6} r p s )
11
61A long-jumper runs before jumping in
order to :
A. cover a greater distance
B. maintain momentum conservation
c. gain energy by running
D. gain momentum
11
62Four particles of equal masses are
placed on the vertices of a square and
are rotated with a uniform angular
velocity about one of the edges ( (A) ) as
shown in the figure. Which particle will
have a larger angular momentum
( A cdot A )
B. B
( c . c )
11
63A cylinder is rolling without sliding over
two horizontal planks (surfaces) 1 and 2
If the velocities of the surfaces ( A ) and ( B )
are ( -boldsymbol{v} hat{boldsymbol{i}} ) and ( 2 boldsymbol{v} hat{boldsymbol{i}} ) respectively. Then
This question has multiple correct options
A ( cdot ) position of instantaneous axis of rotation is ( frac{2 R}{3} )
B. position of instantaneous axis of rotation is ( frac{4 R}{3} )
c. angular velocity of the cylinder is ( 5 v / 2 R )
D. angular velocity of the cylinder is ( 3 v / 2 R )
11
64A particle of mass ( M, ) charge ( q>0 ) and
initial kinetic energy ( K ) is projected from infinity towards a heavy nucleus of charge ( Q ) assumed to have a fixed
position.
(a) If the aim is perfect, how close to the center of the nucleus is the particle when it comes instantaneously to rest?
(b) With a particular imperfect aim, the particle’s closest approach to nucleus is twice the distance determined in (a)
Determine speed of particle at the closest distance of approach.
11
65Assertion
A rigid body can be elastic.
Reason
If a force is applied on the rigid body, its
dimensions may change.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
66A disc is rotating with an angular speed of ( omega . ) If a child sits on it which of the
following is conserved?
A. Kinetic energy
B. Potential energy
c. Linear momentum
D. Angular momentum
11
67Two particles are shown in the figure. at ( boldsymbol{t}=mathbf{0} ) a constant force ( boldsymbol{F}=mathbf{6} boldsymbol{N} ) starts
acting on the ( 3 k g ) man. Find the velocity of the center of mass of these particles
at ( t=5 s )
( A cdot 5 m / s )
B. ( 4 m / s )
( c cdot 6 m / s )
D. ( 3 m / s )
11
68Suppose the resulting torque on a body is
(i) zero
(ii) not zero. What is the effect
of the acting torques on the body in the two cases?
11
69What work should be done in order to
squeeze all water from a horizontally located cylinder (figure shown above) during the time ( t ) by means of a constant force acting on the piston? The volume of water in the cylinder is equal
to ( V ), the cross-sectional area of the
orifice to ( s, ) with ( s ) being considerably less than the piston area. The friction
and viscosity are negligibly small
( A=frac{1}{2} rho frac{V^{3}}{(S t)^{2}} )
B. ( A=frac{3}{2} rho frac{V^{3}}{(S t)^{2}} )
( c )
D. None of thes
11
70A jar filled with two non mixing liquids
1 and 2 having densities ( rho_{1} ) and ( rho_{2} ) respectively. A solid ball, made of a
material of density ( rho_{3}, ) is dropped in the jar. It comes to equilibrium in the
position shown in the figure
A ( cdot rho_{3}<rho_{1}<rho_{2} )
B . ( rho_{1}<rho_{3}<rho_{2} )
( mathbf{c} cdot rho_{1}<rho_{2}<rho_{3} )
D. ( rho_{3}<rho_{2}<rho_{1} )
11
71From the figure
[
F_{1} sqrt{longleftarrow} d_{1} longrightarrow d_{2} longrightarrow
]
( mathbf{A} cdot frac{f_{1}}{d_{1}}=frac{f_{2}}{d_{2}} )
( mathbf{B} cdot f_{1} times d_{2}=f_{2} times d_{1} )
( mathbf{C} cdot f_{1} times d_{1}=f_{2} times d_{2} )
D. All
11
72A circular disc is rotating about its own
axis, the direction of its angular momentum is:
B. along the axis of rotation
c. along the tangent
D. perpendicular to the direction of angular velocity
11
73Two identical blocks ( A ) and ( B ) of mass
( m ) joined together with a massless
spring as shown in the figure are placed on a smooth surface. If the block ( mathbf{A} )
moves with an acceleration ( a_{0} ), then the
acceleration of the block ( B ) is
A ( cdot a_{0} )
в. ( -a_{0} )
( c )
[
frac{f}{m}-a_{0}
]
D. ( frac{f}{m} )
11
74The vector perpendicular to ( hat{mathbf{i}}+hat{mathbf{j}}+hat{mathbf{k}} ) is
( mathbf{A} cdot hat{i}-hat{j}+hat{k} )
B. ( hat{i}-hat{j}-hat{k} )
c. ( -hat{i}-hat{j}-hat{k} )
D. ( 3 hat{i}+2 hat{j}-5 hat{k} )
11
75A solid ball is placed on a rough horizontal surface with initial velocity
of its ( C O M ) as ( v_{0} ) and initial angular
velocity ( omega_{0} ) as shown and given in List 1
11
76Three identical cylinders of radius R are
in contact. Each cylinder is rotating
with angular velocity ( omega . A ) thin belt is
moving without sliding on the cylinders
Calculate the magnitude of velocity of
point ( P ) with respect to ( Q . P ) and ( Q ) are two points of belt which are in contact
with the cylinder.
11
77The centre of mass of a system of two particles divides. The distance between them is
A. In inverse ratio of square of masses of particles
B. In direct ratio of square of masses of particles
c. In inverse ratio of masses of particles
D. In direct ratio of masses of particles.
11
78A thin circular ring of mass ( M ) and
radius ( r ) is rotating about its axis with constant angular velocity ( omega . ) Two objects each of mass ( mathrm{m} ) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
A ( cdot frac{(M+2 m) omega}{2 m} )
в. ( frac{2 M omega}{M+2 m} )
c. ( frac{(M+2 m) omega}{M} )
D. ( frac{M omega}{M+2 m} )
11
79Two persons of masses ( 55 k g ) and ( 65 k g )
respectively, are at the opposite ends of a boat. The length of the boat is ( 3.0 m )
and weights 100kg. The 55kg man
walks up to the ( 65 k g ) man and sits with
him. If the boat is in still water the
centre of mass of the system shifts by:
A. zero
B. ( 0.75 m )
( c .3 .0 m )
D. ( 2.3 m )
11
80Six identical particles each of mass ( boldsymbol{m} )
are arranged at the corners of a regular hexagon of side length ( L ). If the mass of one of the particle is doubled, the shift in the centre of mass is:
A.
в. ( frac{6 mathrm{L}}{7} )
( c cdot frac{L}{7} )
D. ( frac{mathrm{L}}{sqrt{3}} )
11
81The area of the parallelogram whose adjacent sides are ( overline{boldsymbol{P}}=mathbf{3} overline{boldsymbol{i}}+mathbf{4} overline{boldsymbol{j}}, overline{boldsymbol{Q}}= )
( -5 bar{i}+7 bar{j} ) is (in sq. units)
A . 20.
B. 82
( c cdot 4 )
D. 46
11
82Derive an expression for moment of inertia about its tangent perpendicular to the plane.11
83A particle moves on a given line with a constant speed v. At a certain time it is
at a point ( P ) on its straight line path. 0 is fixed point. Show that ( (overrightarrow{O P} times vec{v}) ) is independent of the position P.
11
84Two block of mass ( m_{1} ) and ( m_{2} ) are
connected with the help of a spring
constant ( k ) initially the spring in its natural length as shown. A sharp
impulse is given to mass ( m_{2} ) so that it
acquires a velocity ( v_{0} ) towards right. If the system is kept on smooth floor then find
(a) the velocity of the centre of
mass,
(b) the maximum elongation that the spring will suffer?
11
85A diatomic molecule is formed by two
atoms which may be treated as mass
points ( m_{1}, ) and ( m_{2} ) joined by a massless rod of length r. Then, the moment of inertia of the molecule about an axis
passing through the centre of mass and perpendicular to rod is :
A. zero
B. ( left(m_{1}+m_{2}right) r^{2} )
c. ( frac{left(m_{1}+m_{2}right)}{m_{1} m_{2}} r^{2} )
D. ( left(frac{m_{1} m_{2}}{m_{1}+m_{2}}right) r^{2} )
11
86A projectile is projected at a speed u at an angle with the horizontal. At the highest point projectile split into two fragments comming to rest Then.11
87A rod hinged at one end is made to rotate freely in influence of gravity with initial position being horizontal(angular velocity =0) has
A. acceleration of free end making some acute angle with rod
B. acceleration of free end making some no angle with rod
c. some finite velocity of one end
D. none of these
11
88A bullet hits and gets embedded in a
solid block resting on a frictionless surface. In this process which one of the following is correct?
A. Only momentum is conserved
B. Only kinetic energy is conserved
c. Neither momentum nor kinetic energy is conserved
D. Both momentum and kinetic energy are conserveç
11
89A solid cylinder rolls down an inclined
plane. Its mass is ( 2 k g ) and radius ( 0.1 m )
If the height of the inclined plane is ( 4 m ) its rotational kinetic energy, when it reaches the foot of the plane is:
A . ( 78.4 mathrm{J} )
B. ( 39.2 J )
c. ( frac{78.4}{3} )
D. 19.6 ( J )
11
having track, is ( M=1 k g ) and rests
over a smooth horizontal floor. ( A )
cylinder of radius ( r=10 mathrm{cm} ) and mass
( m=0.5 k g ) is hanging by thread such
that axes of cylinder and track are in
same level and surface of cylinder is in contact with the track as shown in
figure. When the thread is burnt cylinder starts to move down the track.
Sufficient friction exists between
surface of cylinder and track, so that cylinder does not slip.Calculate velocity of axis of cylinder and velocity of the block when it reaches bottom of the
track. Also find force applied by block on
the floor at that moment ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
11
91A circular loop of mass ( mathrm{m} ) and ( mathrm{R} ) rests
flat on a horizontal frictionless
surface.A bullet also of mass ( mathrm{m} ), and
moving with a velocity v, strikes the loop and gets embedded in it. The thickness of the hoop is much smaller than R. The anguler velocity with system rotates after the bullet strikes the hoop is
11
92On a horizontal frictionless frozen lake,
a girl ( (36 mathrm{kg}) ) and a box ( (9 mathrm{kg}) ) are connected to each other by means of a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl traveled when she meets the box?
A . 10
B. since there is no friction, the girl will not move
( c cdot 16 m )
D. ( 4 mathrm{m} )
11
93Under the action of a central force, there
is a conservation of
A. Angular momentum only
B. Mechanical energy only
C. Angular momentum and mechanical energy
D. Neither angular momentum nor mechanical energy
11
94If the extension of the spring is ( x_{0} ) at time ( t, ) then the displacement of the second block at this instant is :
( ^{mathrm{A}} cdot frac{F t^{2}}{2 m}-x_{0} )
( ^{text {В }} cdot frac{1}{2}left(frac{F t^{2}}{2 m}+x_{0}right) )
c. ( frac{1}{2}left(frac{2 F t^{2}}{m}-x_{0}right) )
( frac{1}{2}left(frac{F t^{2}}{2 m}-x_{0}right) )
11
95Neglecting the mass of the thread, find the time dependence of the
instantaneous power developed by the
gravitational force :
( ^{mathbf{A}} cdot P=frac{2}{3} m g^{2} t )
B. ( P=frac{3}{2} m g^{2} t )
( ^{mathbf{C}} P=2 frac{2}{3} m g^{2} t )
D. ( P=2 frac{3}{2} m g^{2} t )
11
96Assertion
The size and shape of the rigid body remains unaffected under the effect of
external forces.
Reason
The distance between two particles remains constant in a rigid body
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
97Moment of inertia of a uniform circular
disc about a diameter is ( I ). Its moment
of in axis perpendicular to its plane and passing through a point on its rim will be:
A . ( 5 I )
B. ( 6 I )
( c .3 I )
D. ( 4 I )
11
98Moment of inertia of a disc about the
tangent parallel to its plane is ( I ). The moment of inertia of the disc tangent and perpendicular to its plane is
( ^{mathrm{A}} cdot frac{3 I}{4} )
в. ( frac{3 I}{2} )
c. ( frac{5 I}{6} )
D. ( frac{6 I}{5} )
11
99A man, sitting firmly over a rotating stool has his arms stretched. If he folds
his arms, the work done by the man is :
A. zero
B. positive
c. negative
D. may be positive or negative
11
100The length of seconds hand of watch is
( 1.5 mathrm{cm} ) and its mass is ( 7 times 10^{-3} mathrm{g} ). Its
angular momentum is,
A ( cdot 1.1 times 10^{-11} mathrm{kgm}^{2} mathrm{s}^{-1} )
B . ( 5.5 times 10^{-11} mathrm{kgm}^{2} mathrm{s}^{-1} )
C. ( 1.1 times 10^{-12} mathrm{kgm}^{2} mathrm{s}^{-1} )
D. ( 5.5 times 10^{-13} k g m^{2} s^{-1} )
11
101A system of identical cylinder and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. The velocity of lower and the upper plates are ( v ) and ( 2 v ) respectively, as shown. Then the ratio of angular speeds of the upper cylinders to lower cylinder is:
A ( cdot frac{1}{3} )
в.
( c )
D. None of these
11
102The direction of ( boldsymbol{tau} ) is :
( mathbf{A} cdot ) parallel to the plane of ( bar{r} ) and ( bar{F} )
B. perpendicular to the plane of ( bar{r} ) and ( bar{F} ).
C. parallel to the plane of ( bar{r} ) and ( bar{P} ).
D. perpendicular to the plane of ( bar{r} ) and ( bar{P} ).
11
103Find the moment of inertia of a solid
cylinder of mass ( M ) and radius ( R ) about a line parallel to the axis of the cylinder
and on the surface of the cylinder.
11
104Four identical solid spheres each of
mass ( M ) and radius ( R ) are fixed at four
corners of a light square frame of side length ( 4 R ) such that centres of spheres coincide with corners of square.
The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is:
A ( cdot frac{21 M R^{2}}{5} )
в. ( frac{42 M R^{2}}{5} )
c. ( frac{84 M R^{2}}{5} )
D. ( frac{168 M R^{2}}{5} )
11
105A uniform scale is kept in equilibrium
when supported at the ( 60 mathrm{cm} ) mark and
a mass ( M ) is suspended from the
( 90 mathrm{cm} ) mark as shown in the figure.
State with reasons whether the weight
of the scale is greater than, less than or
equal to mass ( M )
( mathbf{A} cdot 3 M )
в. ( 4 M )
( c .5 M )
D. ( M )
11
106The end ( B ) of uniform rod ( A B ) which
makes angle ( theta ) with the floor is being
pulled with a velocity ( v_{0} ) as shown
Taking the length of rod as ( l ), calculate
the following at the instant when ( boldsymbol{theta}= )
( 37^{circ} )
(a) The velocity of end ( boldsymbol{A} )
(b) The angular velocity of rod
(c) Velocity of ( C M ) of the rod.
11
107A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular
velocity of 20 rad/s. When the stretches
her arms fully, the spinning speed decreases in 10 rad/s/. If ( I ) is the
initial moment of inertia of the dancer
the new moment of inertia is
( mathbf{A} cdot 21 )
B. 31
c. ( I / 2 )
D. ( I / 3 )
11
108topp
( Q ) Type your question
wrench, and the length of the wrench ?
( operatorname{cockw} )
11
109A uniform disc of mass M and radius R
is mounted on an axle supported in friction less bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is:
( ^{A} cdot frac{M R}{2 T} )
в. ( frac{2 T}{M R} )
c. ( frac{T}{M R} )
D. ( frac{M R}{T} )
11
110What is the order of magnitude of the
seconds present in a day?
11
111What is the position of centre of gravity of a rectangular lamina?
A. At the mid point of longer side
B. At the mid point of shorter side
c. At the point of intersection of its diagonals
D. At one of the corners
11
112In the figure shown, plank is
being pulled to the right with a constant
speed v. If the cylinder does not slip then
This question has multiple correct options
A. the speed of the centre of mass of the cylinder is ( 2 v )
B. the speed of the centre of mass of the cylinder is zero
c. the angular velocity of the cylinder is ( v / R )
D. the angular velocity of the cylinder is zero
11
113At rotational equilibrium, the sum of
clockwise moments equals to the sum
of anti-clockwise moments.
A. True
B. False
11
114In a rectangle ( A B C D(B C=2 A B) )
the moment of inertia along axis will be
minimum through:
( A . B C )
B. ( B D )
( c . H F )
D. ( E G )
11
115The angular velocity of a rotating body is ( vec{omega}=4 hat{i}+hat{j}-2 hat{k} . ) The linear velocity of the body whose position vector is ( 2 hat{i}+ ) ( mathbf{3} hat{boldsymbol{j}}-mathbf{3} hat{boldsymbol{k}} ) is:
A ( .5 hat{i}+8 hat{j}+14 hat{k} )
B . ( 3 hat{i}+8 hat{j}+10 hat{k} )
c. ( 8 hat{i}-3 hat{j}+2 hat{k} )
D . ( -8 hat{i}+3 hat{j}+2 hat{k} )
11
116The moment of inertia of a fly-wheel is ( 4 k g m^{2} . ) A torque of 10 Newton-meter is
applied on it. The angular acceleration produced will be :
A .25 radians ( / mathrm{sec}^{2} )
B. 0.25 radians ( / ) sec ( ^{2} )
c. 2.5 radians ( / ) sec ( ^{2} )
D. Zero
11
117A shell fired from a gun at an angle to the horizontal explodes in mid air. Then
the centre of mass of the shell
fragments will move
A. vertically down
B. horizontally
c. along the same parabolic path along which the ‘intact shell was moving
D. along the tangent to the parabolic path of the ‘intact shell, at the point of explosion.
11
118A rod is hinged at centre and rotated by applying the torque starting from rest , the power developed by the torque with respect to time is of
A. cubic nature
c. linear nature
D. sinusoidal nature
11
119Show that the vector is parallel to a vector ( vec{A}=hat{i}-hat{j}+2 hat{k} ) is parallel to a vector ( vec{B}=3 hat{i}-3 hat{j}+6 hat{k} )
A ( cdot frac{1}{3} ) times the magnitude of ( vec{B} )
B. ( frac{1}{4} ) times the magnitude of ( vec{B} ).
C ( cdot frac{1}{2} ) times the magnitude of ( vec{B} )
D. None of these
11
120A false balance has equal arms. An
object weights ( boldsymbol{w}_{1} ) when placed in one
pan and ( w_{2} ) when placed in the other
pan. Then weight ( boldsymbol{w} ) of the object is :
A ( cdot sqrt{w_{1} w_{2}} )
в. ( frac{w_{1}+w_{2}}{2} )
c. ( left(frac{w_{1}^{2}+w_{2}^{2}}{2}right)-1 )
D. ( sqrt{w_{1}^{2}+w_{2}^{2}} )
11
121A thin metal rod of length ( 0.6 m ) is in
vertical straight position on horizontal floor. This rod is falling freely to a side without slipping. The angular velocity of rod when its top end touches floor, is :
11
122The moment of inertia of a uniform
semi circular disc about an axis
passing through its centre of mass and perpendicular to its plane is (Mass of this disc is ( M ) and radius is ( R ) )
( ^{mathbf{A}} cdot frac{M R^{2}}{2}+Mleft(frac{4 R}{3 pi}right)^{2} )
( ^{text {В }} cdot frac{M R^{2}}{2}-Mleft(frac{4 R}{3 pi}right)^{2} )
( ^{mathrm{c}} cdot frac{M R^{2}}{2}-Mleft(frac{2 R}{pi}right)^{2} )
( ^{mathrm{D}} cdot frac{M R^{2}}{2}+Mleft(frac{2 R}{pi}right)^{2} )
11
123Two particles of mass ( 1 mathrm{kg} ) and ( 2 mathrm{kg} ) are located at ( x=0 ) and ( x=3 ) m. Find the position of their center of mass.
( A cdot 4 m )
B. 2 ( m )
( c cdot 6 m )
D. 8 m
11
124One end of a uniform rod having mass ( mathrm{m} ) and length ( l ) is hinged. The rod is
placed on a smooth horizontal surface and rotates on it about the hinged end
at a uniform angular velocity ( omega . ) The
force exerted by the hinge on the rod has a horizontal component equal to:
( mathbf{A} cdot m omega^{2} l )
B. Zero
( mathrm{c} cdot mathrm{mg} )
D ( cdot frac{1}{2} m omega^{2} )
11
125If ( vec{A}=hat{i}+2 hat{j}+3 hat{k} & vec{B}=3 hat{i}-2 hat{j}+hat{k} )
then the area of parallelogram formed with ( vec{A} ) and ( vec{B} ) as the sides of the
parallelogram is :
A. ( sqrt{3} )
B. ( 8 sqrt{3} )
( c cdot 64 )
D.
11
126A catapult with a basket of mass ( 50 mathrm{kg} ) launches a ( 200 mathrm{kg} ) rock by swinging around from a horizontal to a
vertical position with an angular velocity of 2.0 rad/s. Assuming the rest of the catapult is massless and the catapult arm is ( 10 mathrm{m} ) long, what is the velocity of the rock as it leaves the catapult?
( A cdot 10 mathrm{m} / mathrm{s} )
B. 20 ( mathrm{m} / mathrm{s} )
( c cdot 25 m / s )
D. ( 50 mathrm{m} / mathrm{s} )
E. ( 100 mathrm{m} / mathrm{s} )
11
127The volume of the ( y= ) tethradron formed by the coterminous edges ( bar{a}, bar{b}, bar{c} ) is 3 Then the volume of the parallelepiped
formed by the coterminous edges ( overline{boldsymbol{a}}+ ) ( bar{b}, bar{b}+bar{c}, bar{c}+bar{a} ) is
( mathbf{A} cdot mathbf{6} )
B. 18
( c .36 )
D.
11
128A solid cylinder of mass ( mathrm{m} ) and radius ( mathrm{r} ) is rolling on a rough inclined plane of inclination ( theta . ) The coefficient of friction
between the cylinder and incline is ( mu ) Then:
This question has multiple correct options
A. frictional force is always ( mu ) mg ( cos theta )
B. friction is a dissipative force.
c. by decreasing ( theta ), frictional force decreases
D. friction opposes translation and supports rotation
11
129A body moves along circular path of radius ( 10 mathrm{m} ) and the coefficient of friction is ( 0.5 . ) What should be its
angular velocity in rad/s if it is not to
slip from the surface? ( left(boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2}right) )
A . 0.7
B. 0.28
c. 0.27
D. 2.7
11
130A solid sphere is rotating freely about
its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?
A. Rotational kinetic energy
B. Angular velocity
c. Angular momentum
D. Moment of inertia
11
131A bomb of mass 2 kg which is at rest
explodes into three fragments of equal
masses. Two of the fragments are found to move with a speed of ( 1 mathrm{m} / mathrm{s} ) each in mutually perpendicular direction. The total energy released during explosion is then
A . 1.5
B. 2 J
c. 4 J
D. 5 J
11
132Two horizontal circular discs of
their central axes. One disc is given
some angular velocity and the other is
stationary. Their rims are now brought
in contact. There is friction between the
rims. Correct statement from the
following is:
A. Force of friction between the rims will disappear when the discs rotate with same angular speed
B. Force of friction between the rims will disappear when they have equal linear velocities
C. Angular Momentum of the system is conserved
D. Rotational Kinetic Energy of the system is conserved.
11
133In the shown figure the magnitude of
acceleration of centre of mass of the
system is ( left(boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-mathbf{2}}right) )
A ( cdot 4 m s^{-2} )
B. ( 10 mathrm{ms}^{-2} )
c. ( 2 sqrt{2} mathrm{ms}^{-2} )
( D cdot 5 m s^{-2} )
11
134Two homogeneous spheres ( A ) and ( B ) masses ( mathrm{m} ) and ( 2 mathrm{m} ) having radii ( 2 mathrm{a} ) and a respectively are placed in touch. The distance of centre of mass from first
sphere is:
( A )
B. 2a
c. 3a
D. None of these
11
135A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad ( s^{-1} ). The radius of the cylinder is ( 0.25 mathrm{m} . ) What is the kinetic energy
associated with the rotation of the
cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
11
136Four point masses are placed at the
corners of a square of side ( 2 m ) as shown
in the figure. Find the center of mass of
the system w.r.t center of square.
11
137At a given instant of time the position vector of a particle moving in a circle with a velocity ( 3 hat{i}-4 hat{j}+5 hat{k} ) is ( hat{i}+9 hat{j}- )
8 ( hat{k} ). It’s angular velocity at that time is
A ( cdot frac{(13 hat{i}-29 hat{j}-31 hat{k})}{sqrt{146}} )
B. ( frac{(13 hat{i}-29 hat{j}-31 hat{k})}{146} )
( frac{(13 hat{i}+29 hat{j}-31 hat{k})}{sqrt{146}} )
D. ( frac{(13 hat{i}+29 hat{j}+31 hat{k})}{146} )
11
138Find the velocities of the point ( boldsymbol{B} )
A. ( 7.1 mathrm{cm} / mathrm{s} )
B. ( 10 mathrm{cm} / mathrm{s} )
( c cdot 5 c m / s )
D. ( 0 mathrm{cm} / mathrm{s} )
11
139As shown in the figure, a bob of mass ( m )
is tied by a massless string whose other
end portion is wound on a fly whee
(disc) of radius ( r ) and mass ( m . ) When
released from rest the bob starts falling
vertically. When it has covered a
distance of ( h, ) the angular speed of the
wheel will be:
( mathbf{A} cdot r sqrt{frac{3}{4 g h}} )
B. ( frac{1}{r} sqrt{frac{4 g h}{3}} )
( c cdot r sqrt{frac{3}{2 g h}} )
D. ( frac{1}{r} sqrt{frac{2 g h}{3}} )
11
140Given that ( P ) is a point on a wheel rolling on a horizontal ground. The radius of the wheel is ( R ). Initially if the point ( P ) is
in contact with the ground, the wheel rolls through half revolution. What is the displacement of point ( P ? )
B. ( R sqrt{pi^{2}+4} )
( c . pi R )
D. ( 2 pi R )
11
141A cord is wound round the
circumference of a solid cylinder of
radius ( R ) and mass ( M . ) The axis of the
cylinder is horizontal. A weight ( m g ) is
attached to the end of the cord and falls
from rest. After falling through a
distance ( h )
The angular velocity of the cylinder will
be :
A ( cdot frac{2 m g}{M+2 m} )
в. ( sqrt{frac{2 g h}{R^{2}}} )
c. ( sqrt{frac{4 m g h}{(M+2 m) R^{2}}} )
11
142State whether true or false.
The position of the centre of gravity of the pot before filling it with water will be at its base.
A. True
B. False
11
143The center of gravity of a hollow cone of height ( h ) is at distance ( x ) from its vertex
where the value of ( x ) is.
11
144Three bricks each of length ( L ) and mass
( M ) are arranged as shown from the wall.
The distance of the centre of mass of
the system from the wall is?
A ( frac{11}{12} L )
в. ( frac{7}{8} L )
c. ( frac{1}{12} L )
D. ( frac{15}{1} L )
11
145A fan of moment of inertia ( I ) is set into
rotation at time ( t=0 ) with constant
power ( P . ) Then
A. The angular speed of the fan is proportional to ( t )
B. The angular acceleration of the fan remains constant
c. The magnitude of the angular displacement is proportional to ( t^{2} )
D. The magnitude of the torque is proportional to ( t^{-1 / 2} / 2 ) –
11
146A uniform disc of radius ( R ) is put over
another uniform disc of radius ( 2 R ) of
the same thickness and density. The peripheries of the two discs touch each other. Locate the centre of mass of
the system from the centre of large disc
11
147A constant power is supplied to a rotating disc. The relationship between the angular velocity ( (omega) ) of the disc and
number of rotations ( n ) made by the disc
is governed by:
A. ( quad_{omega} propto n^{frac{1}{3}} )
в. ( quad_{omega} propto n^{frac{2}{3}} )
c. ( quad_{omega} propto n^{frac{3}{2}} )
D. ( omega propto n^{2} )
11
148If the scalar and vector products of two vector are ( 4 sqrt{3} ) and 144 respectively, what is the angle between the two
vectors?
A ( cdot tan ^{-1}(12 sqrt{3}) )
B ( cdot tan ^{-1}left(frac{38}{sqrt{3}}right) )
c. ( tan ^{-1}left(frac{sqrt{3}}{12}right) )
D. ( tan ^{-1}(36) )
11
149Two blocks of masses ( 6 mathrm{kg} ) and ( 4 mathrm{kg} ) are attached to the two ends of a massless
string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the
system will be :
A . g, vertical downwards
B. g/5, vertical downwards
c. g/25, vertical downwards
D. zero
11
150( 200 g ) ball is tied to one end of a string of length ( 20 mathrm{cm} . ) It is revolved in a
horizantal circle at an angular frequency of 6 rpm. Then, angular velocity & linear velocities of the ball respectively are
rads ( ^{-1} ) and ( m s^{-1}: )
A. 0.7284,0.1257
7
в. 0.6284,0.1257
c. 0.6284,0.1457
D. 0.7284,0.1457
11
151In the figure shown, a ring A is initially
rolling without sliding with a velocity ( mathbf{v} ) on the horizontal surface of the body B
(of same mass as ( A ) ). All surfaces are
smooth. B has no initial velocity. The
maximum height reached by A on B is ( frac{v^{2}}{x g} . ) Find ( x )
11
152Masses of ( 1 g, 2 g, 3 g ldots .100 g )
are suspended from the ( 1 mathrm{cm}, 2 mathrm{cm}, 3 mathrm{cm} ) ( ldots .100 mathrm{cm} ) marks of a light metre scale. The system will be supported in equilibrium at :
( mathbf{A} cdot 60 mathrm{cm} )
в. ( 67 mathrm{cm} )
( mathrm{c} .55 mathrm{cm} )
D. ( 72 mathrm{cm} )
11
153Two point size bodies of masses ( 20 g )
( 30 g ) are fixed at two ends of a light rod
of length ( 1.5 m . ) The moment of inertia of these two bodies about an axis
perpendicular to the length of rod and
passing through their center of mass is:
A. ( 1.8 times 10^{-2} k g m^{2} )
В. ( 2.7 times 10^{-2} k g m^{2} )
c. ( 4.5 times 10^{-2} k g m^{2} )
D. ( 6 times 10^{-2} k g m^{2} )
11
154Two blocks of masses ( 10 mathrm{kg} ) and ( 30 mathrm{kg} ) are placed along a vertical line. If the first block is raised through a height of 7 cm by what distance should the second mass be moved to raise the
center of mass by ( 1 mathrm{cm} )
A. ( 1 mathrm{cm} ) up
B. ( 1 mathrm{cm} ) down
c. ( 2 mathrm{cm} ) down
D. ( 2 mathrm{cm} ) up
11
155What is the momentum of a ( 6.0 k g )
bowling ball with a velocity of ( 2.2 m / s ? )
A . 11.2
B. 17.2
c. 15.2
D. 13.2
11
156A man standing on a platform holds
weights in his outstretched arms. The
system rotates freely about a central
vertical axis. If he now draws the
weights inwards close to his body,
This question has multiple correct options
A. the angular velocity of the system will increase.
B. the angular momentum of the system will decrease.
C. the kinetic energy of the system will increase.
D. he will have to expend some energy to draw the weights in.
11
157A non-zero external force acts on a
system of particles. The velocity and acceleration of the centre of mass are
found to be ( v_{0} ) and ( a_{C} ) respectively at
any instant ( t . ) It is possible that
(i) ( boldsymbol{v}_{mathbf{0}}=mathbf{0}, boldsymbol{a}_{boldsymbol{C}}=mathbf{0} )
(ii) ( boldsymbol{v}_{0} neq mathbf{0}, boldsymbol{a}_{C}=mathbf{0} )
(iii) ( boldsymbol{v}_{0}=mathbf{0}, boldsymbol{a}_{C} neq mathbf{0} ;(text { iv }) boldsymbol{v}_{mathbf{0}} neq mathbf{0}, boldsymbol{a}_{C} neq mathbf{0} )
Then
A. (iii) and (iv) are true
B. (i) and (ii) are true
( c . ) (i) and (iii) are true
D. (i), (iii) and (iv) are true
11
158Consider a disc rolling without slipping
on a horizontal surface at a linear speed
Vas shown in figure:
This question has multiple correct options
A. the speed of the particle A is ( 2 v )
B. the speed of B, C and D are all equal to v.
C. the speed of ( C ) is zero
D. the speed of 0 is less than the speed of ( B )
11
159The minimum coefficient of friction
( mu_{min } ) between a thin homogeneous rod
and a floor at which a person can slowly lift the rod from the floor without
slippage to the vertical position, applying to it a force perpendicular to it is ( frac{1}{x sqrt{x}} . ) Find the value of ( x )
11
160A cylinder of mass ( m ) and radius ( R ) rolls
down an incline plane of inclination ( theta ) The linear acceleration of the axis of the
cylinder is given as ( a=frac{x}{3} g sin theta . ) Find ( x )
11
161If the force applied on a particle is zero then the quantities which are conserved are
A. Only momentum
c. Momentum and angular momentum
D. only potential energy
11
162The advantages of being short and stocky is that you’re less likely to get knocked over. This is because
A. The short and stocky person has a lower center of gravity
B. The short and stocky person has a larger center of gravity
c. They have less height and less weight
D. None of the above
11
163A rubber ball of mass ( 10 g m ) and volume
( 15 c m^{3} ) dipped in water to a depth of
10m. Assuming density of water
uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take ( g= )
( 980 mathrm{cm} / mathrm{s}^{2} )
(b) ( 2.02 sec )
B . (a) ( 4.9 mathrm{m} / mathrm{s}^{2} )
(b) ( 2.02 sec )
c. (a) ( 4.9 mathrm{m} / mathrm{s}^{2} )
(b) ( 12.02 mathrm{sec} )
D. (a) ( 8.9 m / s^{2} )
(b) ( 2.02 sec )
11
164Two unequal masses are tied together
with a cord with a compressed spring in
between
Which one is correct?
A. Both masses will have equal KE.
B. Lighter block will have greater KE.
C . Heavier block will have greater KE.
D. None of above answers is correct.
11
165A uniform wire of length I and mass ( mathrm{M} ) bented in the shape of semicircle of
radius ( r ) as shown in figure.Calculate moment of inertia about ( X X^{prime} )
A ( cdot frac{M l^{2}}{2 pi^{2}} )
в. ( frac{4 M l^{2}}{pi^{2}} )
c. ( frac{4 M l^{2}}{4 pi^{2}} )
D. None of the above
11
166A non-uniform bar of weight ( W ) is
suspended at rest by two strings of
negligible weight as shown in fig. The angles made by the strings with the
vertical are ( 36.9^{circ} ) and ( 53.1^{circ} )
respectively. The bar is ( 2 m ) long.
Calculate the distance d of the center of
gravity of the bar from its left end
11
167Analogue of mass in rotational motion
is
A. Moment of inertia
B. Angular momentum
c. Gyration
D. None of these
11
168Two blocks are resting on ground with masses ( 5 k g ) and ( 7 k g . ) A string
connected them which goes over a massless pulley A. There is no friction between pulley an d string A. force ( boldsymbol{F}= )
( 124 N ) is applied on pulley A.Find
acceleration of centre of mass of the
system of two masses ( left(operatorname{in} m / s^{2}right) )
11
169A vector ( vec{A} ) points vertically upward and ( vec{B} ) points towards south. Then the vector product ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}} ) is:
A. along west
B. along east
c. along north
D. vertically downward
11
170When slightly different weights are placed on the two pans of a beam balance, the beam comes to rest at an
angle with the horizontal. The beam is supported at a single point ( P ) by a pivot. Then which of the following statement(s) is/are true?
nonzero at the equilibrium position
B. The whole system does not continue to rotate about ( P ) because it has a large moment of inertia
c. The centre of mass of the system lies below P.
D. The centre of mass of the system lies above P.
11
171A body of mass ( m ) slides down an incline and reaches the bottom with a
velocity ( v ). If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been:
( A )
B . ( (sqrt{2}) v )
c. ( frac{v}{sqrt{2}} )
D. ( (sqrt{frac{2}{5}}) )
11
172( (n-1) ) equal point masses each of
mass ( m ) are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass
A ( cdot-frac{a}{n-1} )
в. ( -frac{a^{2}}{n-1} )
c. ( -frac{a}{(n-1)^{2}} )
D. ( -frac{3 a}{2 n-1} )
11
173A vehicle is moving on a track with
constant speed as shown in figure. The apparent weight of the vehicle is
A. Maximum at ( A )
B. Maximum at ( B )
c. Maximum at ( C )
D. Maximum at ( A, B ) and ( C )
11
174A solid sphere, solid cylinder, hollow sphere, hollow cylinder of same mass and same radii are rolling down freely on an inclined plane. The body with maximum acceleration is:
A. Solid sphere
B. Solid cylinder
c. Hollow sphere
D. Hollow cylinder
11
175A string breaks if its tension exceeds 10 newtons ( A ) stone of mass 250 gm tied to
this string length ( 10 mathrm{cm} ) is rotated in a horizontal circle The maximum angular velocity of rotation can be.
11
176A constant external torque ( tau ) acts for a
very brief period ( Delta t ) on a rotating
system having moment of inertia ( boldsymbol{I} )
then
This question has multiple correct options
A. the angular momentum of the system will change by ( tau Delta t )
B. the angular velocity of the system will change by ( tau Delta t / I )
c. if the system was initially at rest, it will acquire rotational kinetic energy ( (tau Delta t)^{2} / 2 I )
D. the kinetic energy of the system will change by ( (tau Delta t)^{2} / 2 I )
11
177A pulley fixed to the ceiling carries a string with bodies of masses ( mathrm{m} ) and ( 3 mathrm{m} ) attached to its ends. The masses of the
pulley and the string are negligible, friction is absent. The acceleration of
the centre of mass of the system is
( mathbf{A} cdot-g / 4 )
в. ( g / 4 )
c. ( g / 5 )
( mathbf{D} cdot-g / 5 )
11
178A grind-stone starts revoiving from rest,
it its angular acceleration is 4.0 rad / sec ( ^{2} ) (uniform) then after 4 sec.
What is its angular displacement & angular velocity respectively –
11
179Derive an expression for angular
momentum
11
180A bullet leaves the rifle of mass one kg and the rifle recoils thereby with a velocity of ( 30 mathrm{cm} / mathrm{s} ). If the mass of bullet is ( 3 g, ) find the velocity of the bullet.
( mathbf{A} cdot 10 m / s )
в. ( 100 mathrm{m} / mathrm{s} )
c. ( 200 m / s )
D. ( 50 m / s )
11
181A wheel is rotating with an angular speed 20 rad ( / ) s. It is stopped to rest by applying constant torque in ( 4 s ). If the moment of inertia of the wheel about is
axis is ( 0.20 k g / m^{2}, ) then the work done
by the torque in two seconds will be :
A . ( 10 J )
B. ( 20 J )
c. ( 30 J )
D. ( 40 J )
11
182What is the torque on the bar?11
183A uniform disc is acted by two equal forces of magnitude ( F . ) One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface is nF. If ( r ) be the radius of
the disc, then the value of n would be?
(in ( N) )
( mathbf{A} cdot mathbf{0} )
в. 1.2
c. 2.0
D. 3.2
11
184A bomb at rest explodes into three fragments. Two fragments fly off at right angles to each other.These two
A ( .14 mathrm{m} / mathrm{s} )
B. ( 15 mathrm{m} / mathrm{s} )
( c cdot 18 m / s )
D. ( 16 mathrm{m} / mathrm{s} )
11
185A uniform solid cylindrical roller of mass ‘m’ is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is ‘a’ and it
is rolling without slipping then the
value of ‘F’ is:
( A cdot 2 mathrm{ma} )
B cdot ( frac{3}{2} mathrm{ma} )
( c . ) ma
D・言ma
11
186A uniform rod of mass ( m ) and length ( l )
hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinged when the rod becomes vertical is
A ( cdot frac{m g}{4} )
B. 5 ( frac{-m g}{2} )
c. ( frac{m g}{6} )
( stackrel{mathrm{D}}{-}_{2}^{7} m g )
11
187us
and radius ( 0.5 mathrm{m} ) is initially at rest on a
horizontal frictionless surface. Three
forces of equal magnitude ( 0.5 N ) are
applied simultaneously along the three
sides of an equilateral triangle ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z} )
with its vertices on the perimeter of the
disc (see figure). One second after applying the forces, the angular speed
of the disc in ( r a d s^{-1} ) is:
( A cdot 2 )
B. 4
( c .5 )
( D )
11
188If the two handles of an hydraulic jack are balanced by two masses in the ratio ( 1: 2, ) then the respective areas are in
the ratio of:
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4
11
189A book is lying on a table, what is the angle between the book on the table and
the weight of the book?
A ( cdot 0^{circ} )
B . ( 45^{circ} )
( c .90^{circ} )
D. ( 180^{circ} )
11
190Which of the following is/are the
properties of moment of a couple?
This question has multiple correct options
A. It tends to produce pure rotation.
B. It is different about any point in the plane of lines of action of the forces.
C. It can be replaced by any other couple of the same moment
D. The resultant of set of two or more couples is equal to the sum of the moments of the individual couples.
11
191In a rotational motion of a rigid body, all
particles move with
A. same linear velocity and same angular velocity
B. same linear velocity and different angular velocity
C. different linear velocities and same angular velocities
D. different linear velocities and different angular velocities
11
192The kinetic energy of a moving body is given by ( K=2 v^{2}, K ) being injoules
and ( v ) in ( mathrm{m} / mathrm{s} ). Its momentum when
traveling with a velocity of ( 2 m s^{-1} ) will
be :
A ( .16 mathrm{kgms}^{-1} )
в. ( 4 mathrm{kgms}^{-1} )
c. 8 kgms( ^{-1} )
D. 2 kgms ( ^{-1} )
11
193A small body ( A ) is fixed to the inside of ( a )
thin rigid hoop of radius ( R ) and mass
equal to that of the body ( A ). The hoop rolls without slipping over a horizontal plane; at the moments when the body ( A )
gets into the lower position, the centre
of the hoop moves with velocity ( v_{0} ) figure shown above). If the hoop moves without bouncing for ( v_{0}=sqrt{x g R} ), then
find the value of ( x )
11
194Three bodies a ring ( (R), ) a solid cylinder
( (C) ) and a solid sphere ( (S) ) having same
mass and same radius roll down the
inclined plane without slipping. They
start from rest, if ( v_{R}, v_{C} ) and ( v_{S} ) are
velocities of respective bodies on reaching the bottom of the plane, then:
A ( cdot v_{R}=v_{C}=v_{S} )
в. ( v_{R}>v_{C}>v_{S} )
c. ( v_{R}<v_{C}v_{S} )
11
195A rod ( 0.5 mathrm{m} ) long has two masses each
of 20 gram stuck at its ends. If the
masses are treated as point masses and if the mass of the rod is neglected, then the moment of inertia of the
system about a transverse axis passing
through the centre is
A ( cdot 1.25 times 10^{-3} mathrm{kg}-mathrm{m}^{2} )
B . ( 2.5 times 10^{-3} mathrm{kg}-mathrm{m}^{2} )
C ( cdot 4 times 10^{-3} mathrm{kg}-mathrm{m}^{2} )
D. ( 5 times 10^{-3} mathrm{kg}-mathrm{m}^{2} )
11
196Let ( F ) be the force acting on a particle
having position vector ( r ) and ( tau ) be the torque of this force about the origin.
Then
A. ( r . tau=0 ) and ( F . tau neq 0 )
B. ( r . tau neq 0 ) and ( F . tau=0 )
c. ( r . tau neq 0 ) and ( F . tau neq 0 )
D. r. ( tau= ) O and ( F . tau=0 )
11
197A circular loop of radius ( 0.3 mathrm{cm} ) lies
parallel to a much bigger circular loop of radius ( 20 mathrm{cm} . ) The centre of the
smaller loop is on the axis of the bigger drop. The distance between their
centres is ( 15 mathrm{cm} . ) If a current of ( 10 mathrm{A} )
flows through the bigger loop, then the flux linked with smaller loop is
A. ( 9.1 times 10^{-11} mathrm{Wb} )
B. ( 6 times 10^{-11} mathrm{Wb} )
c. ( 3.3 times 10^{-11} W b )
D. ( 6.6 times 10^{-11} mathrm{Wb} )
11
198A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
The plank is pulled to the right by a constant force ( F ). If the sphere does not
slip over the plank, then This question has multiple correct options
A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force ( F )
11
199A swimmer while jumping into water
from a height easily forms a loop in air, if
A. He pulls his arms and leg in
B. He spreads legs and his arms
C . He keeps himself straight
D. His body is so formed
11
200Derive the conservation of linear
momentum
11
201A counterclockwise couple ( C(theta) ) acts on
a uniform ( 1.5 mathrm{kg} ) bar ( mathrm{AB} ) as shown in Fig.
1. Given two cases:
Case (a) ( C(theta)=5.4 sin theta mathrm{N}-mathrm{m} )
Case (b) ( C(theta) ) varies as shown in Fig. 2
The total work done on the bar as it
rotates in the vertical plane about ( mathbf{A} )
from ( theta=0^{circ} ) to ( theta=180^{circ} ) in the above two
cases are ( W_{a} ) and ( W_{b} ) respectively.
Then,
(Take ( left.boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
This question has multiple correct options
( A cdot W_{a}=3.22 mathrm{N}-mathrm{m} )
B. ( W_{a}=4.2 mathrm{N}-mathrm{m} )
C ( . W_{b}=4.2 mathrm{N}-mathrm{m} )
D. ( W_{b}=1.86 mathrm{N}-mathrm{m} )
11
202Consider the following two statements A and B and identify the correct choice
A) The torques produced by two forces of couple are opposite to each other
B) The direction of torque is always perpendicular to plane of rotation of body
A. A is true but B is false
B. A is false but B is true
c. Both A and B are true
D. Both A and B are false
11
203A solid cylinder and a hollow cylinder of the same mass and radius, both
initially at rest, roll down the same inclined plane without slipping. Choose the correct options. This question has multiple correct options
A. The hollow cylinder reaches the bottom first
B. The solid cylinder reaches the bottom first
c. The two cylinder reach the bottom together
D. Their kinetic energies at the bottom are equal.
11
204Can the centre of gravity be situated outside the material of the body?
A. Yes
B. No
c. can’t say
D. None
11
205A light spring of force constant ( boldsymbol{K} ) is
held between two blocks of masses ( m )
and ( 2 m . ) The two blocks and the spring system rests on a smooth horizontal
floor. Now the blocks are moved towards
each other compressing the spring by ( x ) and then they are suddenly released. The relative velocity between the blocks when the spring attains its natural length will be
( ^{mathrm{A}} cdot(sqrt{frac{3 K}{2 m}}) x )
( ^{mathrm{B}} cdot(sqrt{frac{2 K}{3 m}}) x )
( ^{c cdot}(sqrt{frac{K}{3 m}}) x )
( ^{mathrm{D} cdot}(sqrt{frac{K}{2 m}}) x )
11
206Angular speed and angular frequency
use the same variable ( omega . ) Are there any
differences in their interpretation. Explain
11
207A body weighs ( 250 mathrm{N} ) on the surface of the earth. How much will it weigh half way down to the centre of the earth.?
( A cdot 125 N )
B. 150 N
c. ( 175 mathrm{N} )
D. 250 N.
11
208A sphere is rolled on a rough horizontal
surface. It gradually slows down and stops. The force of friction tends to:
This question has multiple correct options
A. decrease linear velocity
B. increase linear momentum
c. decrease angular velocity
D. increase angular velocity
11
209A disc of moment of inertia ( ^{prime} I_{1}^{prime} ) is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant
angular speed ‘ ( omega_{1}^{prime} ). Another disc of
moment of inertia ( ^{prime} I_{2}^{prime} ) having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed
( omega_{2}^{prime} . ) The energy lost by the initial rotating disc is
( ^{A} cdot frac{1}{2}left[frac{I_{1}+I_{2}}{I_{1} I_{2}}right] omega_{1}^{2} )
в. ( frac{1}{2}left[frac{I_{1} I_{2}}{I_{1}-I_{2}}right] omega_{1}^{2} )
c. ( frac{1}{2}left[frac{I_{1}-I_{2}}{I_{1} I_{2}}right] omega_{1}^{2} )
D. ( frac{1}{2}left[frac{I_{1} I_{2}}{I_{1}+I_{2}}right] omega_{1}^{2} )
11
210A cylinder of radius ( R ) is to roll without
slipping between two planks as shown in the figure, Then
This question has multiple correct options
A. angular velocity of the cylinder is ( frac{v}{R} ) counter clockwise
B. angular velocity of the cylinder is ( frac{2 v}{R} ) clockwise
c. velocity of centre of mass of the cylinder is v towards left
D. velocity of centre of mass of the cylinder is ( 2 v ) towards right
11
211A uniform rod of mass ( M ) and length ( L ) hinged at centre is rotating in
horizontal plane with angular speed ( omega_{0} )
Now two objects each of mass ( m ) are kept on rod near the hinge on both sides. They starts sliding towards ends.
Find ( omega ) of rod finally.
A ( frac{M omega_{0}}{6 M+m} )
в. ( frac{M omega_{0}}{M+6 m} )
c. ( frac{6 M omega_{0}}{M+m} )
D. ( frac{M omega_{0}}{M+2 m} )
11
212A thin ring has mass ( 0.25 mathrm{kg} ) and radius
( 0.5 m . ) Its moment of inertia about an
axis passing through its centre and perpendicular to its plane is
A ( cdot 0.0625 mathrm{kgm}^{2} )
B. ( 0.625 mathrm{kgm}^{2} )
c. ( 6.25 mathrm{kgm}^{2} )
D. ( 62.5 mathrm{kgm}^{2} )
11
213Two balls of masses ( 2 g ) and ( 6 g ) moving with ( K E ) in the ratio of ( 3: 1, ) What is the
ratio of their linear momenta?
A . 1: 1
B . 2: 1
( c cdot 1: 2 )
D. None of these
11
214Moment of inertia of a solid about its geometrical axis is given by ( l=frac{2}{5} M R^{2} )
where ( M ) is mass ( & R ) is radius. Find
out the rate by which its moment of inertia is changing keeping density constant at the moment ( boldsymbol{R}= )
( mathbf{1} boldsymbol{m}, boldsymbol{M}=mathbf{1} boldsymbol{k} boldsymbol{g} ) & rate of change of
radius w.r.t. time ( 2 m s^{-1} )
A. ( 4 mathrm{kg} mathrm{ms}^{-1} )
B. 2 ( k g m^{2} s^{-1} )
c. ( 4 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-1} )
D. None of these
11
215A body weighing ( 8 g ) when placed in one pan and ( 18 g ) when placed on the other pan of a false balance. If the beam is horizontal when both the pans are
empty, then the true weight of the body is
A . ( 13 g )
в. ( 9 g )
c. ( 22 g )
D. ( 12 g )
11
216Moment of inertia of a bar magnet of mass ( m ) length ( l ) breath ( n ) is ( I ). then moment of inertia of another bar
magnet of mass ( 2 m ) length ( 2 l ) breath ( 2 b ) would be
( A cdot 81 )
B. 4 1
c. 21
D.
11
217A mass ( m ) is moving with a constant velocity along a line parallel to x-axis. Its angular momentum with respect to origin on z-axis is
A. zero
B. Remain constant
c. Goes on increasing
D. Goes on decreasing
11
218A boy is standing at the center of a boat
which is free to move on water. The
distance of the boy from the shore is
100m. If mass of the boy and boat are
( 40 K g ) and ( 60 K g ) respectively and boy
moves with a velocity ( 1 m / )sec towards
the shore, what is the distance of the
boy from the shore at the end of 5 th second?
11
219In the figure shown ( A B C ) is a uniform
wire. If centre of mass of wire lies vertically below point ( A, ) then ( frac{B C}{A B} ) is
close to:
This question has multiple correct options
( mathbf{A} cdot 1.85 )
B. 1.5
c. 1.37
D. 3
11
220Which of the following is/are correct?
This question has multiple correct options
A. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must be moving.
B. If centre of mass remains at rest, then net work done
by the forces acting on the system must be zero.
C. If centre of mass remains at rest, then the net external force must be zero.
D. If speed of centre of mass is changing, then there must be some net work being done on the system from outside.
11
221If rotational inertial parameter of a body rolling down a rough inclined plane (of inclination ( theta ) and height ( h ) ) without slipping is given by ( beta=frac{I_{c m}}{M R^{2}}, ) then the time taken by the body to reach the bottom of the inclined plane is given by
( ^{mathrm{A}} t=frac{1}{sin theta} sqrt{(1+beta) frac{h}{2 g}} )
в. ( t=frac{1}{sin theta} sqrt{(1+beta) frac{2 h}{g}} )
( ^{c} t=frac{1}{sin theta} sqrt{(1-beta) frac{h}{2 g}} )
D ( t=frac{1}{sin theta} sqrt{(1+beta) frac{h}{g}} )
11
222What will be the loss in potential energy
of chain (mass ( m ) ) when half of its
length is grounded.
11
223The moment of inertia and rotational
kinetic energy of a fly wheel are ( 20 k g-m^{2} ) and 1000 joule
respectively. Its angular frequency per minute would be
A. ( frac{600}{pi} )
B. ( frac{25}{pi^{2}} )
c. ( frac{5}{pi} )
D. ( frac{300}{pi} )
11
fixed to a mount B of mass ( m_{2}(text { fig }) . ) A
constant horizontal force ( F ) is applied to
the end ( mathrm{K} ) of a light thread tightly wound on the cylinder. The friction between the
mount and the supporting horizontal plane is assumed to be absent. Find:
(a) the acceleration of the point ( K )
(b) the kinetic energy of this system
seconds after the beginning of motion.
( ^{mathbf{A}} cdot_{a_{k}}=frac{Fleft(3 m_{1}+2 m_{2}right)}{2 m_{1}left(m_{1}+m_{2}right)} ; K cdot E=frac{1}{2} frac{F^{2}left(3 m_{1}+m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} t^{2} )
B. ( a_{k}=frac{Fleft(3 m_{1}+2 m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} ; K cdot E=frac{1}{2} frac{F^{2}left(3 m_{1}+2 m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} t^{2} )
( a_{k}=frac{Fleft(3 m_{1}+2 m_{2}right)}{2 m_{1}left(m_{1}+m_{2}right)} ; K cdot E=frac{1}{2} frac{F^{2}left(3 m_{1}+2 m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} t^{2} )
( ^{mathrm{D}} a_{k}=frac{Fleft(3 m_{1}+2 m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} ; K cdot E=frac{1}{2} frac{F^{2}left(3 m_{1}+m_{2}right)}{m_{1}left(m_{1}+m_{2}right)} t^{2} )
11
225A ball of mass 100 g is moving with a velocity of ( 10 . ) The ball is stopped by the boy in ( 0.2 m s . ) Find the force of the ball?11
226Find out the average angular speed and
angular speed of the second hand of
clock.
11
227The moment of inertia of a uniform thin
sheet of mass ( M ) of the given shape
about the specified axis is (axis and
sheet both are in the same plane):
A ( cdot frac{7}{12} M a^{2} )
B ( cdot frac{5}{12} M a^{2} )
c. ( frac{1}{3} M a^{2} )
D. ( frac{1}{12} M a^{2} )
11
228A tall, cylindrical chimney falls over when its base is ruptured. Treat the
chimney as a thin rod of length ( 55.0 mathrm{m} )
At the instant it makes an angle of
( 35.0^{circ} ) with the vertical as it falls, what
are
(a) the radial acceleration of the top,
and
(b) the tangential acceleration of the top. (Hint : Use energy considerations, not a torque.)
(c) At
what angle ( theta ) is the tangential acceleration equal to g?
11
229A ( 2.5 k g ) ball is dropped onto a concrete floor. It strikes the floor with a
momentum of ( 20 k g m / s ) and bounces away from the floor with a momentum
of ( 16 k g m / s . ) What is the magnitude of
change of momentum of the ball?
A. ( 4 k g . m / s )
в. ( 8 k g m / s )
c. ( 32 k g m / s )
D. ( 36 k g m / s )
E . ( 40 mathrm{kgm} / mathrm{s} )
11
230A disk of mass ( M, ) radius ( R ) and
thickness ( frac{R}{6} ) has a moment of intertia ( I ) about an axis passing through the centre and perpendicular to the disk. The disk is recasted to form a sphere.
Obtain the moment of inertia of the
11
231The center of gravity of an object
A. can never exist at a point where there is no mass.
B. can exist at a point where there is no mass.
C. may exist or may not exist.
D. none of the above
11
232Light with energy flux of ( 24 W m^{-2} ) is incident on a well polished disc of radius ( 3.5 mathrm{cm} ) for one hour. The
momentum transferred to the disc is
A ( cdot 1.1 mu mathrm{kgms}^{-1} )
B. 2.2 ( mu mathrm{kgms}^{-1} )
c. ( 3.3 mu mathrm{kgms}^{-1} )
D. ( 4.4 mu mathrm{kgms}^{-1} )
11
233Two identical rods each of moment of
inertia ( ^{prime} I^{prime} ) about a normal axis through
centre are arranged in the from of a cross. The ( M . I . ) of the system about an
axis through centre and perpendicular
to the plane of system is:
A . ( 2 I )
B. ( I )
c. 2.5
D. ( 6 I )
11
234A billiard ball, initially at rest, is given a
sharp impulse by cue. The cue is held
horizontally at a distance ( h ) above the
central line as shown in the figure. The
ball leaves the cue with a speed ( boldsymbol{v}_{mathbf{0}} . ) It
rolls and slides while moving forward
and eventually acquires a final speed
( (9 / 7) v_{0} . ) If ( R ) is the radius of the ball,
then ( h ) is
( A cdot frac{2 R}{5} )
B. ( frac{3 R}{5} )
c. ( frac{4 R}{5} )
D. ( frac{R}{5} )
11
235Two identical blocks ( A ) and ( B ) are
connected by a spring as shown in figure. Block ( A ) is not connected to the wall parallel to y-axis. B is compressed from the natural length of spring and
then left. Neglect friction. Match the following two columns.
11
236A solid cylinder of mass, ( m ), and radius,
( r, ) is rotating at an angular velocity, ( omega )
when a non-rotating hoop of equal mass and radius drops onto the cylinder. In terms of its initial angular velocity, ( omega )
what is its new angular velocity, ( omega^{prime} ? )
A ( cdot omega^{prime}=frac{omega}{3} )
B. ( omega^{prime}=frac{3 omega}{4} )
( mathbf{C} cdot omega^{prime}=omega )
( mathbf{D} cdot omega^{prime}=3 omega )
E ( cdot omega^{prime}=frac{2 omega}{3} )
11
237A kid enjoying the rotatory ride which is
rotating with angular speed equals to
3.14 rad/s. Find out the period of
revolution for this ride?
( A )
B ( cdot frac{1}{2} s )
c. 2 rev / ( s )
D. 2s
E. 4 s
11
238Center of mass of 3 particle ( 10 k g, 20 k g ) and ( 30 k g ) is at ( (0,0,0,) . ) Where shoud a
particle of mass ( 40 k g ) be placed so that the combination centre of mass will be at
(3,3,3)
A. (0,0,0)
)
в. (7.5,7.5,7.5)
c. (1,2,3)
D. (4,4,4)
11
239A uniform wire of length ( l ) is bent into
the shape of ( V ) as shown. The distance
of its centre of mass from the vertex ( boldsymbol{A} )
is
A ( . l / 2 )
B. ( frac{1 sqrt{3}}{1} )
( frac{1 sqrt{3}}{8} )
D. None of these
11
240A body of mass ( m ) slides down an
incline and reaches the bottom with a
velocity ( V ). If the same mass were in the form of a ring which rolls down the same incline, the velocity of its centre of
mass at bottom of the plane is:
A. ( V )
B. ( sqrt{2} V )
c. ( frac{V}{sqrt{2}} )
D. ( frac{V}{2} )
11
241As a matter of convention, an
anticlockwise moment is taken as
and a clockwise moment is
taken as
11
242A wheel has a constant angular acceleration of ( 3.0 mathrm{rad} / mathrm{s}^{2}, ) During a
certain ( 4.0 s ) interval, it turns through an angle of 120 rad. Assuming that. ( a t=0 )
angular speed ( omega_{0}=3 r a d / s ) how long is
motion at the start of this 4.0 second
interval?
( mathbf{A} cdot 7 s )
B. ( 9 s )
c. ( 4 s )
D. ( 10 s )
11
243A system consists of mass ( M ) and ( m )
The centre of mass of the system is:
A. nearer to ( m )
B. at the position of large mass.
c. nearer to ( M )
D. at the middle
11
244Light is incident normally on a completely absorbing surface with an energy flux of ( 25 W c m^{-2} ). if the surface
has an area of ( 25 mathrm{cm}^{-2} ), the momentum
transferred to the surface in 40 min
time duration will be :
A ( .5 .0 times 10^{-3} mathrm{Ns} )
s
B . ( 3.5 times 10^{-6} N s )
c. ( 1.4 times 10^{-6} N s )
D. ( 6.3 times 10^{-4} N s )
11
245Consider a ring rolling down a smooth inclined plane of vertical height ‘h’ and inclination ( theta . ) Then the true statement
in the following is?
A. Acceleration along the plane is ( g sin theta ) and the potential energy at the topmost point is mgh
B. Acceleration along the plane is g and the potential energy at the top most point is mgh
c. Acceleration along the plane is ( g sin theta ) and the potential energy at the top most point as mgh sin ( theta )
D. None of these
11
246The centre of mass of a body:
A. lies always at the geometrical centre
B. lies always inside the body
C. lies always outside the body
D. may lie within or outside the body
11
247The angular momentum of a particle rotating with an angular velocity ( omega ) distant ( r ) from a given origin is I. If the origin is shifted by ( 2 r, ) then the new angular momentum of the particle with same angular velocity will be
A . 2
в. 9
( c cdot 4 )
( D cdot 3 )
11
248A force of ( – ) Fk acts on ( mathrm{O} ), the origin of the coordinate system. The torque about the point (1,-1) is :
( mathbf{A} cdot-mathrm{F}(hat{mathrm{i}}-hat{mathrm{j}}) )
B. ( mathrm{F}(hat{mathrm{i}}-hat{mathrm{j}}) )
( mathbf{c} .-mathrm{F}(hat{mathbf{i}}+hat{mathbf{j}}) )
D. F(í+j)
11
249A spot light ( S ) rotates in a horizontal
plane with a constant angular velocity of ( 0.1 mathrm{rad} / mathrm{s} ). The spot of light ( boldsymbol{P} ) moves
along the wall at a distance ( 3 m ). What is
the velocity of the spot ( boldsymbol{P} ) when ( boldsymbol{theta}=mathbf{4 5}^{o} ) ?
A. ( 0.6 mathrm{m} / mathrm{s} )
B. ( 0.5 mathrm{m} / mathrm{s} )
( c .0 .4 m / s )
D. ( 0.3 mathrm{m} / mathrm{s} )
11
250A sphere of diameter ( r ) is cut from a solid sphere of radius r such that the centre of mass of remaining part be at maximum distance from original centre, then this distance is :11
251A particle of mass ( M ) is moving in a
horizontal circle of radius ( boldsymbol{R} ) with
uniform speed ( V . ) When it moves from one point to a diametrically opposite point, its
A
B. momentum does not change
c. momentum changes by ( 2 M V )
D. kinetic energy changes by ( M V^{2} )
11
252A metallic rod falls under gravity with
its ends pointing east and west. Then
A. an emf is induced in it as it cuts the magnetic lines of force
B. no emf is induced at all
C. two emf of equal nut opposite signs are induced, giving no emf is
D. its acceleration is equal to the product of ( g ) and the radius of the rod.
11
253Two circular rings of equal mass ( (boldsymbol{m}) ) and radius ( (r) ) are placed side by side, touching each other. The moment of inertia of the system about tangential axis in the plane of system passing through point of contact of the rings is:
A ( cdot frac{3}{2} m r^{2} )
B. ( 6 m r^{2} )
c. ( frac{5}{2} m r^{2} )
( D cdot 3 m r^{2} )
11
254( I ) is the moment of inertia of a thin
circular plate about an axis of rotation perpendicular to the plane of plate and
passing through its centre. The moment of inertia of same plate about an axis passing through its diameter is :
( mathbf{A} cdot 2 I )
B. ( sqrt{2} I )
c. ( frac{I}{sqrt{2}} )
D. ( frac{1}{2} )
11
255A bullet gets embedded in a solid block resting on a frictionless surface. In this
process:
A. momentum is conserved
B. kinetic energy is conserved
c. potential energy is conserved
D. both (a) and (b)
11
256Three particles of masses ( 1 mathrm{kg}, 2 mathrm{kg} ) and ( 3 mathrm{kg} ) are situated at the corners of the equilateral triangle move at speed ( 6 mathrm{ms} ) ( -1,3 mathrm{ms}^{-1} ) and ( 2 mathrm{ms}^{-1} ) respectively
Each particle maintains a direction
towards the particle at the next corner symmetrically. Find velocity of COM of the system at this instant:
( mathbf{A} cdot 3 m s^{-1} )
B. ( 5 m s^{-1} )
( mathrm{c} cdot 6 mathrm{ms}^{-1} )
D. zero
11
257The apparent weight of a body is :
This question has multiple correct options
A. may be positive
B. may be negative
c. may be zero
D. is always positive
11
258( A ) 2kg body and 3kg body are moving along the X-axis. At a particular instant the ( 2 mathrm{kg} ) body is ( 1 mathrm{m} ) from the origin and
has the velocity of ( 3 m s^{-1} ) and ( 3 k g ) body is ( 2 mathrm{m} ) from the origin and has a velocity
of ( -1 m s^{-1} . ) The position of the center of mass of the system is:
( A cdot 1 m )
B. 1.6m
c. ( 2.2 mathrm{m} )
D.
11
259A constant torque of ( 31.4 mathrm{Nm} ) is exerted on a pivoted wheel. If the angular acceleration of the wheel is ( 4 pi r a d / s e c^{2}, ) then the moment of
inertia will be
A ( cdot 5.8 mathrm{kg}-mathrm{m}^{2} )
в. ( 4.5 mathrm{kg}-mathrm{m}^{2} )
c. ( 5.6 mathrm{kg}-mathrm{m}^{2} )
D. ( 2.5 mathrm{kg}-mathrm{m}^{2} )
11
260Find the elastic deformation energy (in
J) of a steel rod whose one end is fixed
and the other is twisted through an
angle ( varphi=6.0^{circ} . ) The length of the rod is
equal to ( l=1.0 m, ) and the radius to
( boldsymbol{r}=mathbf{1 0} boldsymbol{m m} cdot(mathrm{G}=77.2 mathrm{GPa}) )
11
261Choose the correct alternatives.
This question has multiple correct options
A. For a general rotational motion, angular momentum ( L ) and angular velocity ( omega ) need not be parallel
B. For a rotational motion about a fixed axis, angular momentum ( L ) and angular velocity ( omega ) are always parallel
C. For a general translational motion, momentum ( p ) and velocity ( v ) are always parallel
D. For a general translational motion, acceleration ( a ) and velocity ( v ) are always parallel
11
262A vector ( vec{A} ) has magnitude of 3 units and it points towards east while another vector ( vec{B} ) has magnitude of 4 units and it points towards north.The ratio between ( vec{A} cdot vec{B} ) and ( |vec{A} times vec{B}| ) is:
A . 1:
B. 1:
c. 0: 12
D. 12:0
11
263A round uniform body of radius ( R ), mass ( M ) and moment of inertia ( I, ) rolls down
(without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is :
A. ( frac{g sin theta}{1+I / M R^{2}} )
B. ( frac{g sin theta}{1+M R^{2} / I} )
c. ( frac{g sin theta}{1-I / M R^{2}} )
D. ( frac{g sin theta}{1-M R^{2} / I} )
11
264How should the mass of a rotating body
of radius r be distributed so as to
maximize its angular velocity?
A. The mass should be concentrated at the outer edge of the body
B. The mass should be evenly distributed throughout the body
C. The mass should be concentrated at the axis of
rotation
D. The mass should be concentrated at a point midway between the axis of rotation and the outer edge of the body
E. Mass distribution has no impact on angular velocity
11
265When there is no external torque acting on a body moving in an elliptical path, which of the following quantities remains constant?
A. Kinetic energy
B. potential energy
c. Linear momentum
D. Angular momentum
11
266The ratio of the moment of inertia of
circular ring & circular disc having the same mass ( & ) radii about an axis
passing the ( c . m & ) perpendicular to plane is
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1
11
267Force applied by a lady is ( 2 mathrm{N} ) and moment of force is ( 16 mathrm{Nm} ), distance of pivot from effort would be
A. 32
B. 8 m
( c cdot 14 m )
D. 18
11
268A smooth washer impinges at a velocity v on a group of three smooth identical
blocks resting.
on a smooth horizontal surface as
shown in fig. The mass of each block is
equal to the washer. The diameter of the
washer and its height are equal to the edge of the block.
Determine the velocities of all the
bodies after the impact
11
269Assertion
A disc rotates along the clockwise
direction and direction of angular velocity is upwards
Reason
The linear velocity of points on the disc
are directed towards the centre
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
270Portion AB of the wedge shown in figure is rough and BC is smooth, A solid cylinder rolls without slipping from ( A ) to
B. The ratio of transnational kinetic
energy to rotational kinetic energy. when the cylinder reaches point ( C ) is
( A cdot 3 / 4 )
B.
( c cdot 7 / 5 )
( 0.8 / 3 )
11
271If a raw egg and a boiled egg are spinned together with same angular velocity on the horizontal surface then
which one will stops first?
A. boiled egg
B. raw egg
c. Both egg will stop simultaneously
D. Cannot be ascertained
11
272A rigid body is rotating about a vertical
axis at ( n ) rotations per minute. If the
axis slowly becomes horizontal in ( t )
seconds and the body keeps on rotating
at ( n ) rotations per minute then the
torque acting on the body will be, if the moment of inertia of the body about axis of rotation is ( boldsymbol{I} )
A. Zero
В. ( frac{2 pi n I}{60 t} )
c. ( frac{2 sqrt{2} pi n I}{60 t} )
D. ( frac{4 pi n I}{60 t} )
11
273A carpet of mass ( M ) made of inextensible material is along its length
in the form of a cylinder of radius ( R ) and
is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. If the horizontal velocity of the axis of the cylindrical part of the
carpet when its radius reduces to ( boldsymbol{R} / mathbf{2} ) is ( sqrt{frac{x}{3} g R}, ) find the value of ( x )
11
274A rigid massless rod of length 3 l has two masses attached art each end as
shown in the figure. The rod is pivoted at point ( P ) on the horizontal position, its instantaneous angular acceleration will
be:
A ( cdot frac{g}{2 l} )
в. ( frac{7 g}{3 l} )
c. ( frac{g}{13 l} )
D. ( frac{g}{3 l} )
11
275A ring takes time ( t_{1} ) in slipping down an inclined plane of length ( L ), whereas it
takes time ( t_{2} ) in rolling down the same
plane. The ratio of ( t_{1} ) and ( t_{2} ) is :
B . ( 1: 2^{frac{1}{2}} )
( c cdot 1: 2 )
D. ( 1: 2^{frac{1}{7}} )
11
276State whether given statement is True or False.

Centre of gravity of a freely suspended body always lies vertically below the point of suspension.
A. True
B. False

11
277Find the velocities of the point ( boldsymbol{A} )
A. ( 10.0 mathrm{cm} / mathrm{s} )
в. ( 7.21 mathrm{cm} / mathrm{s} )
( c cdot 5 c m / s )
D. ( 0 mathrm{cm} / mathrm{s} )
11
The diagram shows the ride (yellow) and the girl (red) as viewed from above at the instant the ride is stopped. The
curved arrow shows the direction of the
rotation of the ride before it was
stopped.
Which arrow shows the direction of the
girl’s velocity at the instant she flies off
the ride?
( A )
B.
( c )
D.
11
279A small disc of radius ( 2 mathrm{cm} ) is cut from
a disc of radius ( 6 mathrm{cm} ). If the distance
between their centres is ( 3.2 mathrm{cm}, ) what is
the shift in the centre of mass of the
disc?
A. ( 0.4 mathrm{cm} )
B. 2.4 ( mathrm{cm} )
c. ( 1.8 mathrm{cm} )
D. ( 1.2 mathrm{cm} )
11
280A body of mass ( M ) and radius ( R ) is
rolling on a horizontal plane with speed
v. It then rolls up an inclined plane upto a height ( h=frac{v^{2}}{g} . ) What is the nature of
the body?
A. Ring
B. Solid sphere
c. spherical shell
D. Cylinder
11
281A ring of mass ( 3 k g ) is rolling without
slipping with linear velocity ( 1 mathrm{ms}^{-1} ) on a smooth horizontal surface. A rod of
same mass is fitted along its one
diameter. Find total kinetic energy of the system (in ( J ) ).
11
282A uniform thin rod of length Lis hinged
about one of its end and is free to rotate
about the hinge without friction. Neglect the effect of gravity. A force F is
applied at a distance ( x ) from the hinge on the rod such that force is always
perpendicular to the rod. Find the normal reaction at the hinge as
function of ‘x’, at the initial instant
when the angular velocity of rod is zero.
11
283Which of the following are the advantages of having low centre of gravity? This question has multiple correct options
A. It can corner at high speed,
B. Much less risk of toppling over
c. It requires enough turning force to tip you over
D. None of the above
11
284Moment of any force is equal to the algebraic sum of the components of that force. This is known as:
A. Principle of moments
B. Principle of combination
c. Law of inflution
D. All
11
285If ( vec{A} times vec{B}=vec{B} times vec{C}=vec{C} times vec{A} ) then ( vec{A}+ )
( vec{B}+vec{C} ) is equal to:
A. zero
B. sum of magnitudes
c. twice of the sum of magnitudes.
D. unity.
11
286Five forces are separately applied to the flat object lying on a horizontal table of negligible friction as shown in the
figure above. The line of action of each force is shown by a dashed line. Identify
which of the five forces will cause the
object to rotate about point ( O ? )
( A )
B.
( c )
( D )
E
11
287A 2 -dimensional bent rod is made out of
a material with uniform density.
Its center of mass is located at which
position coordinate? Refer to the
diagram of the bent rod and ignore the
( mathbf{A} cdot(0,0) )
B ( cdotleft(frac{w}{4}, frac{l}{4}right) )
c. ( left(frac{w}{3}, frac{l}{3}right) )
D ( cdotleft(frac{w}{2}, frac{l}{2}right) )
E ( cdotleft(frac{w^{2}}{2(l+w)}, frac{l^{2}}{2(l+w)}right) )
11
288A hoop rolls down an inclined plane. The
fraction of its total kinetic energy that is associated with rotational motion is
A .1: 2
B. 1: 3
c. 1: 4
D. 2: 3
11
289If ( overline{boldsymbol{F}}=mathbf{2} overline{boldsymbol{i}}-mathbf{3} overline{boldsymbol{j}} boldsymbol{N} ) and ( overline{boldsymbol{r}}=mathbf{3} overline{boldsymbol{i}}+mathbf{2} overline{boldsymbol{j}} boldsymbol{m} )
The torque ( boldsymbol{tau} ) is:
( mathbf{A} cdot 12 hat{k} )
в. ( 13 hat{k} )
c. ( -12 hat{k} )
D. ( -13 hat{k} )
11
290Assertion
STATEMENT1: Work done by a force on a body whose centre of mass does not move may be non-zero.
Reason
STATEMENT2: Work done by a force depends on the displacement of the
centre of mass
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True
11
291A uniform disc of radius ( boldsymbol{R}=mathbf{0 . 2 m} ) kept
over a rough horizontal surface is given
velocity ( omega_{0} . ) After some time its kinetic
energy becomes zero. If ( v_{0}=10 m / s )
find ( omega_{0} )
11
292A mass of ( 10 mathrm{kg} ) is suspended vertically by a rope from the roof. when a horizontal force is applied on the rope at same points, the rope deviated at an
angle of ( 45^{0} ) at the roof point. if the
suspended mass is at equilibrium, the
magnitude of the force applied is ( (g= )
( left.10 m s^{-2}right) )
A . 200 N
B. 100 N
c. 70
D. 140 N
11
293Find the acceleration of the bar.
A. ( w_{0}=frac{2 g m r^{2}}{I} )
B. ( w_{0}=frac{g m r^{2}}{I} )
c. ( _{w_{0}}=frac{g m r^{2}}{2 I} )
D. ( w_{0}=2 frac{g m r^{2}}{I} )
11
294Two equal masses attached to a rod is made to experience equal force.Force on both rod is perpendicular to it but in one rod it acts on attached mass and in
other rod it is acted on the mid point of rod. now choose the correct statement
A. Both rod has same motion
B. they have different linear acceleration
c. one of the rod shows no angular motion
D. none of the above
11
295Establish the relation between moment
of inertia and angular momentum. Define moment of inertia on the basis of
this relation.
11
296An electric motor rotates a wheel at a
constant angular velocity ( omega ) while
opposing torque is ( tau ). The power of that
electric motor is :
A ( cdot frac{pi}{2} )
B. ( pi )
( c cdot 2 tau omega )
D. ( frac{tau}{omega} )
11
297The mass of body is ( 10 mathrm{kg} ) at a place
where ( g=9.8 m / s^{2} . ) Find its weight.
11
298Three solid spheres each of mass ( P ) and
radius ( Q ) are arranged as shown in
figure. The moment inertia of the
arrangement about ( Y Y^{prime} ) axis will be
( ^{A} cdot frac{7}{2} P Q^{2} )
B. ( frac{2}{7} P Q^{2} )
c. ( frac{2}{5} P Q^{2} )
D. ( frac{5}{2} P Q )
11
299In the figure shown ( X ) and ( Y ) components of acceleration of center of mass are [All
surfaces are smooth]
A ( cdotleft(a_{C M}right)_{X}=frac{m_{1} m_{2} g}{m_{1}+m_{2}} )
В. ( left(a_{C M}right)_{X}=frac{m_{1} m_{2} g}{left(m_{1}+m_{2}right)^{2}} )
( ^{mathrm{c}}left(a_{C M}right)_{Y}=left(frac{m_{2}}{m_{1}+m_{2}}right)^{2} g )
D. Both (B) and (C) are correct
11
300A uniform solid cylindrical roller of mass ‘m’ is being pulled on a horizontal surface ( F ) parallel to the surface and applied at its centre. If the acceleration
of the cylinder is ‘a’ and it is rolling
without slipping then the value of ‘F’ is
A . ma
B . ( frac{5}{3} m a )
( c cdot 2 m a )
( D cdot frac{3}{2} m a )
11
301An electric motor exerts a constant
torque ( 10 mathrm{N}-mathrm{m} ) on a grind stone mounted on a shaft. MOI of the grind stone about
the shaft is ( 2 mathrm{kg} m^{-2} . ) If the system
starts from rest, find the work done in
( 8 s )
A . ( 1600 J )
B. ( 1200 J )
( c .800 J )
D. ( 600 J )
11
302Moment of inertia of a thin rod of mass
( M ) and length ( L ) about an axis passing through its center is ( frac{M L^{2}}{12} . ) Its moment of inertia about a parallel axis at a distance of ( frac{L}{4} ) from this axis is given by
A. ( frac{M L^{2}}{48} )
в. ( frac{M L^{3}}{48} )
c. ( frac{M L^{2}}{12} )
D. ( frac{7 M L^{2}}{48} )
11
303A uniform cylinder of radius ( R ) is
spinned about its axis to the angular
velocity ( omega_{0} ) and then placed into a corner. The coefficient of friction
between the corner walls and the
cylinder is ( mu_{2} . ) How many turns will the cylinder accomplish before it stops?
11
304Given ( overrightarrow{boldsymbol{F}}=(4 hat{boldsymbol{i}}-10 hat{boldsymbol{j}}) ) and ( overrightarrow{boldsymbol{r}}=(-5 hat{boldsymbol{i}}- )
( 3 hat{j}), ) then compute torque.
( mathbf{A} cdot-62 hat{j} ) unit
B. ( 62 hat{k} ) unit
c. ( 48 hat{i} ) unit
D. ( -48 hat{k} ) unit
11
305The diameter of a solid disc is ( 0.5 mathrm{m} ) and
its mass is ( 16 mathrm{Kg} ). Its angular velocity
increases from zero to 120
rotation/minute in 8 seconds, at what
rate is work done by the torque at the end of 8th second?
A . ( pi ) Watt ( t )
B . ( pi^{2} ) Watt
c. ( pi^{3} ) Watt
D. ( pi^{4} ) Watt
11
306of same length but made up of different
materials and kept as shown, an be, if
the meeting point is the origin of ( c 0 )
ordinates
( ^{mathrm{A}} cdotleft(frac{L}{2}, frac{L}{2}right) )
B ( cdotleft(frac{2 L}{3}, frac{L}{2}right) )
c. ( left(frac{L}{3}, frac{L}{3}right) )
D ( cdotleft(frac{L}{3}, frac{L}{6}right) )
11
307A uniform thin circular ring of mass ‘M’ and radius ‘R’ is rotating about its fixed axis, passing through its centre and perpendicular to its plane of rotation, with a constant angular velocity ( omega . ) Two objects each of mass ( mathrm{m}, ) are attached
gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity of :
A ( cdot frac{omega M}{(M+m)} )
в. ( frac{omega M}{(M+2 m)} )
c. ( frac{omega M}{M-2 m} )
D. ( frac{omega(M+3 m)}{M} )
11
308With what angular velocity and in what direction does the turntable rotate?
A. The table rotates anticlockwise (in direction of the mam motion) with angular velocity ( 0.05 r a d / s )
B. The table rotates clockwise (opposite to the man) with angular velocity ( 0.1 mathrm{rad} / mathrm{s} )
c. The table rotates clockwise (opposite to the man) with angular velocity ( 0.05 r a d / s )
D. The table rotates anticlockwise (in the direction of the man motion) with angular velocity ( 0.1 mathrm{rad} / mathrm{s} )
11
309with each other with the help of a
massless spring of spring-constant ( k )
Mass ( M_{1} ) is in contact with a wall and
the system is at rest on the frictionless
floor. ( M_{2} ) is displaced by distance ( x )
to compress the spring and released.
The velocity of COM (centre of mass) of
the system when ( M_{1} ) is detached from
wall is :
( mathbf{A} cdot frac{x sqrt{k M_{1}}}{M_{1}+M_{2}} )
B. ( frac{x sqrt{k M_{2}}}{M_{1}+M_{2}} )
c. ( frac{k x sqrt{M_{2}}}{M_{1}+M_{2}} )
D. ( frac{x}{sqrt{k M_{1}}left(M_{1}-M_{2}right)} )
11
310An automobile engine develops ( 100 mathrm{kW} ) when rotating at a speed of 1800 rev/min. What torque does it deliver?
A. 350 Nm
B. 440 Nm
( c .531 mathrm{Nm} )
D. ( 628 mathrm{Nm} )
11
311A body is freely rolling down on an
inclined plane whose angle of inclination is ( theta . ) If ( a ) is acceleration of
it’s centre of mass then which of the
relation holds true? ( Given acceleration
due to gravity ( =g) )
A ( . a=g sin theta )
B. ( ag sin theta )
( mathbf{D} cdot a=0 )
11
312Find the maximum power in the form of ( (10+x) ) which can be transmitted
by means of a steel shaft rotating about
its axis with an angular velocity ( omega= )
( 120 r a d / s, ) if its length ( l=200 c m )
radius ( r=1.50 mathrm{cm}, ) and the
permissible torsion angle ( varphi=2.5^{circ} )
Round off to the nearest integer of ( x )
11
313Assertion
Angular speed of a planet around the sun increases, when it is closer to the
sun.
Reason
Total angular momentum of the system
remains constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
314The tension in the upper portion of the
chain is equal to:
( mathbf{A} cdot 100 N )
B. 120
c. 160
D. 240
11
315In the HCl molecule, the separation between the nuclei of the two atoms is
about ( 1.27 dot{A}left(1 dot{A}=10^{-10} mright) . ) Find the
approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a
hydrogen atom and nearly all the mass
of an atom is concentrated in its
nucleus.
11
316Four identical thin rods each of mass ( mathrm{M} )
and length I, form a square frame. Moment of inertia of this frame about
an axis through the centre of the square and perpendicular to its plane is?
A ( cdot frac{1}{3} M l^{2} )
в. ( frac{8}{3} M l^{2} )
c. ( frac{2}{3} M l^{2} )
D. ( frac{13}{3} M l^{2} )
11
317The torque of a force ( overrightarrow{boldsymbol{F}}=mathbf{2} hat{boldsymbol{i}}+hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}} )
acting at a point ( vec{r}=mathbf{7} hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}+hat{boldsymbol{k}} ) is
( mathbf{A} cdot 14 hat{i}+38 hat{j}+16 hat{k} )
B . ( 4 hat{i}+4 hat{j}+6 hat{k} )
c. ( -14 hat{i}+38 hat{j}-16 hat{k} )
D. ( 11 hat{i}-26 hat{j}+hat{k} )
11
318Two bodies of mass ( 10 k g ) and ( 2 k g ) are
moving with velocities ( 2 i-7 j+3 k ) and
( -10 i+35 j-3 k m / s ) respectively. The
velocity of their ( mathrm{CM} ) is
A ( .2 i mathrm{m} / mathrm{s} )
B. ( 2 k ) m/s
( c cdot(2 i+2 k) m / s )
D. ( (2 i+2 j+2 k) mathrm{m} / mathrm{s} )
11
319Five uniform circular plates, each of
diameter D and mass m are laid out in
a pattern shown. Using the origin
shown, find the y coordinate of the
centre of mass of the fiveplate system.
( A cdot 2 D / 5 )
B. ( 40 / 5 )
( c cdot D / 3 )
D. D/5
11
320If principle of moments for any object holds, then object is in state of
A . inertia
B. equilibrium
c. suspension
D. motion
11
321Ratio of ( S I ) unit of torque to its CGS unit is
( mathbf{A} cdot 10^{5}: 1 )
B . ( 10^{7}: 1 )
( mathbf{c} cdot 10^{6}: 1 )
D. ( 10^{17}: 1 )
11
322A wheel of radius ( r ) rolling on a straight
line, the velocity of its centre being ( boldsymbol{v} ). At
a certain instant the point of contact of
the wheel with the grounds is ( M ) and ( N )
is the highest point on the wheel
(diametrically opposite to ( M ) ). The
incorrect statement is:
A. The velocity of any point ( P ) of the wheel is proportional to MP.
B. Points of the wheel moving with velocity greater than v form a larger area of the wheel than points moving with velocity less than v.
C. The point of contact M is instantaneously at rest.
D. The velocities of any two parts of the wheel which are equidistant from centre are equal
11
323The top in figure has a moment of
inertia of ( 4.00 times 10^{-4} k g-m^{2} ) and is
initially at rest. It is free to rotate about
the stationary axis ( boldsymbol{A} boldsymbol{A}^{prime} ) A string
wrapped around a peg along the axis of the top, is pulled in such a manner as to
maintain a constant tension of ( 2.5 M . ) If
the string does not slip while it is unwound from the peg, what is the
angular speed of the top after ( 80.0 mathrm{cm} )
string has been pulled off the peg?
A ( .75 mathrm{rad} / mathrm{s} )
B. 50 rad ( / s )
c. ( 125 r a d / s )
D. 100 rad ( / s )
11
324A wheel rolls purely on the ground. If the
velocity of a point ( ^{prime} boldsymbol{P}^{prime} ) as shown on the
periphery of a body has a velocity equal
to the velocity of the centre of mass of
the body. Find ( theta=? )
11
325A hole of radius ( R / 2 ) is cut from a solid
sphere of radius ( R ). If the mass of the
remaining part of sphere is ( M, ) then
find moment of inertia of the body about
an axis through ( boldsymbol{O} )
11
326A thin uniform rod of mass ( m ) and
length ( ell ) is free to rotate about its upper end. When it is at rest it recelves an
impulse ( J ) at its lowest point, normal to
its length. Immediately after impact, This question has multiple correct options
A. The angular momentum of the rod is ( J ell )
B. The angular velocity of the rod is ( 3 J / m ell )
C. The kinetic energy of the rod is ( 3 J^{2} / 2 m )
D. The linear velocity of the midpoint of the rod is ( 3 J / 2 M )
11
327The centre of mass of a system of
particles is at the origin. From this we
conclude that:
A. The numberof particles on positive x-axis is equal to the number of particles on negative x-axis
B. The total mass of the particles on positive x-axis is same as the total mass on negative x-axis
C. The number of particles on X-axis may be equal to the number of particles on Y-axis
D. If there is a particle on the positive ( X ) -axis, there must be at least one particle in the negative ( X ) -axis.:
11
328Final speed of the platform in situation
(ii), i.e.just after ( B ) have jumped will be
nearly
A. ( 7.5 m / s )
B. ( 5.5 m / s )
c. ( 4.5 m / s )
D. ( 2.5 m / s )
11
329Immediately after the right string is
cut, what is the linear acceleration
of the free end of the rod?
11
330The moment of inertia of a rod about its
perpendicular bisector is I. When the temperature of the rod is increased by ( triangle T, ) the increase in the moment of
inertia of the rod about the same axis is
(Here, ( alpha ) is the coefficient of linear
expansion of the rod)
( mathbf{A} cdot alpha I Delta T )
в. ( 2 alpha I Delta T )
c. ( frac{alpha I Delta T}{2} )
D. ( frac{2 I triangle T}{alpha} )
11
331A ladder of mass ( M ) and length ( L ) is
supported in equilibrium against a smooth vertical wall and a rough horizontal surface, as shown in figure. If ( theta ) be the angle of inclination of the rod
with the horizontal, then calculate
(a) normal reaction of the wall on the
(b) normal reaction of the ground on the
(c) net force applied by the ground on
11
332A machine part is shown in cross
section in figure consists of two homogeneous solid, coaxial cylinders ( A B ) as the common axis. Where is its
centre of mass from A? (in ( mathrm{m} ) )
( A )
( overline{7} )
B. 2 ( overline{7} )
c. ( frac{52}{7} )
D. 5
11
333Assertion
A solid sphere and a hollow sphere when allowed to roll down on an inclined
plane, the solid sphere reaches the bottom first.
Reason
Moment of inertia of solid sphere is greater than that of hollow sphere.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
334The moment of inertia of a non-
uniform semicircular wire having mass ( mathrm{m} ) and radius ( mathrm{r} ) about a line
perpendicular to the plane of the wire through the center is
( mathbf{A} cdot m r^{2} )
в. ( frac{1}{2} m r^{2} )
c. ( frac{1}{4} m r^{2} )
D. ( frac{2^{2}}{5} )
11
335The quantities ( A ) and ( B ) are related by
the relation ( boldsymbol{A} / boldsymbol{B}=boldsymbol{m}, ) where ( boldsymbol{m} ) is the
linear mass density and ( A ) is the force, the dimensions of ( B ) will be :
A. Same as that of pressure
B. Same as that of work
c. Same as that of momentum
D. Same as that of latent heat
11
336From a uniform disc of radius ( R, ) a
circular disc of radius ( boldsymbol{R} / 2 ) is cut out. The centre of the hole is at ( R / 2 ) from the centre of the original disc. Locate the centre of gravity of the resultant flat body.
A ( cdot frac{R}{6} ) from the centre
в. ( frac{R}{15} ) from the centre
c. ( -frac{R}{5} ) from the centre
D. ( frac{R}{20} ) from the centre
11
337Propeller blades in aeroplane are ( 2 m )
long
(a) When propeller is rotating at 1800rev/min, compute the tangential
velocity of tip of the blade.
(b) What is the tangential velocity at a point on blade midway between tip and
axis?
11
338A thin circular ring of mass ( M ) and
radius ( r ) is rotating about its axis with constant angular velocity ( omega . ) Two objects each of mass ( m ) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by:
A ( cdot frac{(M+2 m) omega}{2 m} )
в. ( frac{2 M omega}{M+2 m} )
c. ( frac{(M+2 m) omega}{M} )
D. ( frac{M omega}{M+2 m} )
11
339In case of torque of a couple, if the axis is changed by displacing it parallel to itself, torque will
A. Increase
B. Decrease
c. Remain constant
D. None of these
11
340A body of mass ( M ) is attached to one
end of a rod of mass ( M ) and length ( L )
The entire system is rotated about an axis passing through the other end of
the rod. The ( M . I . ) of the system about die given axis of rotation is:
( ^{mathrm{A}} cdot frac{M L^{2}}{3} )
B. ( frac{4}{3} M L^{2} )
( mathbf{c} cdot 2 M L^{2} )
D. ( 3 M L^{2} )
11
341Two bodies of mass ( 1 mathrm{kg} ) and ( 4 mathrm{kg} ) are massing with equal kinetic energies. The ratio of their linear momantum is-
A . 1: 2
B. 2:
( c cdot 4: )
D. 1:
11
342Two wheels ( A ) and ( B ) are mounted on the
same axle. moment of inertia of ( A ) is 6
( mathrm{kg} boldsymbol{m}^{2} ) ans it is rotating at ( 600 mathrm{rpm} )
when ( mathrm{B} ) is at rest. What is moment of inertia of ( mathrm{B} ), if their combined speed ids
400 rpm?
( A cdot 9 mathrm{kg} m^{2} )
B. 4 kg ( m^{2} )
( mathrm{c} cdot 3 mathrm{kg} mathrm{m}^{2} )
( D cdot 5 mathrm{kg} m^{2} )
11
343Inner and outer radii of a spool are ( r ) and
( R ) respectively. A thread is wound over
its inner surface and placed over a
pulled by a force ( F ) as shown in fig. then
in case of pure rolling:
A. Thread unwinds, spool rotates anticlockwise and friction act leftwards.
B. Thread winds, spool rotates clockwise and friction acts leftwards
C. Thread winds, spool moves to the right and friction act rightwards.
D. Thread winds, spool moves to the right and friction does not come into existence
11
344Centre of gravity of a rectangle will be at its:
A. Centre
B. At its periphery
c. Intersection of its diagonal
D. None
11
345toppr
dilu wattı, , Itsptulvely. Inte un anu water are immiscible. If the above ball
is in equilibrium in a mixture of this oil
and water, which of the following
pictures represents its equilibrium position?
( A )
B.
( c )
D.
11
346A rod of mass ( mathrm{m} ) and length lis bent into
shape of L. Its moment of inertia about
the axis shown in figure:
A ( cdot frac{m^{2}}{6} )
B. ( frac{m^{2}}{3} )
( c cdot frac{m l^{2}}{12} )
D. None
11
347Find a vector ( vec{x} ) which is perpendicular to both ( vec{A} ) and ( vec{B} ) but has magnitude equal to that of ( vec{B} ). Vector ( vec{A}=3 hat{i}- ) ( mathbf{2} hat{boldsymbol{j}}+hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=mathbf{4} hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}-mathbf{2} hat{boldsymbol{k}} )
A ( cdot frac{1}{sqrt{10}}(hat{i}+10 hat{j}+17 hat{k}) )
B ( cdot frac{1}{sqrt{10}}(hat{i}-10 hat{j}+17 hat{k}) )
c. ( sqrt{frac{29}{390}}(hat{i}-10 hat{j}+17 hat{k}) )
D. ( sqrt{frac{29}{390}}(hat{i}+10 hat{j}+17 hat{k}) )
11
348A solid sphere, a thin hoop, and a solid cylinder all roll down an incline plane
from rest. All three have a mass, ( m ) and
a radius, ( r ) and all start at the same
position on the ramp. Which of the following correctly describes the order in which they would reach the bottom of the ramp?
A. First the hoop, then cylinder, then sphere
B. First the cylinder, then hoop, then sphere
c. First the sphere, then hoop, then cylinder
D. First the sphere, then cylinder, then hoop
E. First the cylinder, then the sphere, then the hoop
11
349A rope thrown over a pulley has a ladder
with a man A no one of its ends and a
counterbalancing mass ( mathrm{M} ) on its other end. The man whose mass is ( mathrm{m} ), climbs upwards by ( vec{Delta} r ) relative to the ladder
and then stops. Ignoring the masses of the pulley and the rope, as well as the friction in the pulley axis, find the displacement of the centre of mass of
this system
11
350The passengers in a boat are not allowed to stand because:
A. This will raise the centre of gravity and the boat will be rocked
B. This will lower centre of gravity and the boat will rocked
c. The effective weight of system increases
D. of surface tension effects
11
351A wheel starts rotating from rest at time ( t=0 ) with a angular acceleration
of 50 radians/s( ^{2} . ) The angular
acceleration ( (alpha) ) decreases to zero
value after 5 seconds. During this
interval, ( alpha ) varies according to the
question ( boldsymbol{alpha}=boldsymbol{alpha}_{0}left(1-frac{boldsymbol{t}}{mathbf{5}}right) )
The angular velocity at ( boldsymbol{T}=mathbf{5} boldsymbol{s} ) will be
( mathbf{A} cdot 10 mathrm{rad} / mathrm{s} )
B. ( 250 mathrm{rad} / mathrm{s} )
C ( .125 mathrm{rad} / mathrm{s} )
D. ( 100 mathrm{rad} / mathrm{s} )
11
352A solid cylinder at rest at the top of an
inclined plane of height ( 2.7 m ) rolls down without slipping. If the same cylinder has to slide down a frictionless inclined
plane and acquire the same velocity as that acquired by the center of mass of
the rolling cylinder at the bottom of the
inclined plane, the height of the inclined plane in meters should be: ( (boldsymbol{g}= )
( left(0 m / s^{2}right) )
A ( .2 .2 m )
в. ( 1.2 m )
c. ( 1.6 m )
D. ( 1.8 m )
11
353A circular disc of radius R and
thickness R/6 has moment of inertia I
about an axis passing through its center and perpendicular to its plane. It is melt and recast into a solid sphere.
The moment of inertia of the sphere
about its diameter as axis of rotation is:
A ( cdot frac{1}{5} )
в. ( frac{2 I}{5} )
c. ( frac{4 I}{5} )
D. ( frac{I}{10} )
11
354A small object of mass ( m ) is attached to a light string which passes through a hollow tube. The tube is hold by one hand and the string by the other. The object is set into rotation in a circle of
radius ( R ) and velocity ( v ). The string is
then pulled down, shortening the radius of path to ( r . ) What is conserved?
A. Angular momentum
B. Linear momentum
c. Kinetic energy
D. None of these
11
355A square frame ABCD is formed by four identical rods each of mass ‘m’ and
length ‘T’. This frame is in ( X ) – Y plane such that side ( A B ) coincides with ( X- )
axis and side ( A D ) along ( Y ) – axis. The moment of inertia of the frame about ( X )
axis is
A ( cdot frac{5 m l^{2}}{3} )
B. ( frac{2 m l^{2}}{3} )
c. ( frac{4 m l^{2}}{3} )
D. ( frac{m l^{2}}{12} )
11
356A solid uniform disk of mass m rolls
without slipping down a fixed inclined plane with an acceleration a. The
frictional force on the disk due to
surface of the plane is?
A . 2 ma
B. ( 3 / 2 ) ma
c. ( m a / 2 )
D. ( 1 / 2 ) ma
11
357What can you say about the motion of
an object whose distance time graph is a straight line parallel to the time axis?
11
358A uniform rod ( A B ) of length ( l ) and mass
( m ) hangs from point ( A ) in a car moving
with velocity ( v_{0} ) on an inclined plane as
shown in the figure. The rod can rotate
in vertical plane about the axis at point
A. If the car suddenly stops, the angular
speed with which the rod starts rotating
is :
A ( cdot frac{3}{2} frac{v_{0}}{l} cos theta )
B. ( frac{v_{0}}{2} frac{cos theta}{l} )
c. ( frac{3}{2} frac{v_{0}}{l} sin theta )
( D )
11
359A uniform circular disc of radius is taken. A circular portion of radius b has
been removed from its as shown in the
figure. If the centre of hole is at a
distance c from the centre of the disc,
the distance ( x_{2} ) of the centre of mass of
the remaining part from the initial
centre of mass 0 is given by :
A ( cdot frac{pi b^{2}}{a^{2}-c^{2}} )
B. ( frac{b^{2} c}{left(a^{2}-b^{2}right)} )
c. ( frac{pi e^{2}}{a^{2}-b^{2}} )
D. ( frac{c a^{2}}{c^{2}-b^{2}} )
11
360A tightrope walker in a circus holds a
long flexible pole to help stay balanced
on the rope. Holding the pole
horizontally and perpendicular to the
rope helps the performer.
This question has multiple correct options
A. by lowering the overall centre-of-gravity.
B. by increasing the rotation inertia.
C. in the ability to adjust the centre-of-gravity to be over the rope
D. in achieving the centre of gravity to be under the rope
11
361Three masses are placed on the x-axis:
( 300 mathrm{g} ) at origin, ( 500 mathrm{g} ) at ( mathrm{x}=40 mathrm{cm} ) and ( 400 mathrm{g} ) at ( x=70 mathrm{cm} . ) The distance of the center of mass from the origin is:
A. ( 45 mathrm{cm} )
B. 50cm
c. зост
D. ( 40 mathrm{cm} )
11
362According to principle of moments:
A. product of anticlockwise force = product of clockwise force
B. Sum of anticlockwise moments = sum of clockwise moments
c. both
D. none
11
363Assertion
The mass of a body cannot be
considered to be concentrated at the
centre of mass of the body for the
purpose of computing its moment of inertia.
Reason
Then the moment of inertia of every
body about an axis passing through its centre of mass would be zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
364A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total
kinetic energy is
A ( cdot frac{2}{3} )
в. ( frac{1}{3} )
( c cdot frac{2}{5} )
D.
11
365Two identical bricks of length ( L ) are
piled one on top of the other on a table
as shown in the figure. The maximum
distance ( S ) the top brick can overhang
the table with the system still balanced
is :
A ( cdot frac{1}{2} L )
в. ( frac{2}{3} L )
c. ( frac{3}{4} L )
D. ( frac{7}{8} L )
11
366Two blocks of masses ( 10 mathrm{kg} ) and ( 4 mathrm{kg} )
are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/ ( s ) to the heavier block
in the direction of the lighter block, The velocity of the centre of mass is:
A. ( 30 mathrm{m} / mathrm{s} )
в. 20 ( m / s )
c. ( 10 mathrm{m} / mathrm{s} )
D. ( 5 mathrm{m} / mathrm{s} )
11
367A thin bar of mass ( M ) and length ( L ) is
free to rotate about a fixed horizontal
axis through a point at its end. The bar
is brought to a horizontal position and then released. The axis is perpendicular
to the rod. The angular velocity when it
reaches the lowest point is This question has multiple correct options
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
C. dependent only upon the acceleration due to gravity and the length of the bar
D. directly proportional to its length and inversely proportional to the acceleration due to gravity
11
368In the shown figure half of the part is
disc and other half is a ring both of
mass ( m ) and radius r. Then moment of
inertia of this system about the shown
axis is:
A ( cdot frac{3}{4} m r^{2} )
в. ( frac{3}{8} m R^{2} )
( mathrm{c} cdot m r^{2} )
( D cdot frac{m r^{2}}{1} )
11
369Find the area of the quadrilateral whose vertices are ( boldsymbol{A}(mathbf{1}, mathbf{1}) boldsymbol{B}(mathbf{7},-mathbf{3}), boldsymbol{C}(mathbf{1} mathbf{2}, mathbf{2}) )
and ( D(7,21) )
11
370A solid sphere of radius ( boldsymbol{R} ) has total charge ( 2 Q ) and volume charge density
( rho=k r ) where ( r ) is distance from centre.
Now charges ( Q ) and ( -Q ) are placed diametrically opposite at distance ( 2 a ) where ( a ) is distance form centre of
sphere such that net force on charge ( Q ) is zero then relation between ( a ) and ( R ) is
A ( cdot a=R / 2 )
В . ( a=R )
c. ( a=2 R )
D. ( a=3 R / 4 )
11
371A translation is applied to an object by
A. Repositioning it along with straight line path
B. Repositioning it along with circular path
C. All of the mentioned
D. none of the mentioned
11
372AU the particles of a system are situated at a distance ( r ) from the origin. The distance of the centre of mass of
the system from the origin is :
( A cdot=r )
B. ( leq r )
( c cdot>r )
( D . leq 0 )
11
373Two uniform thin rods each of Length ( L )
and mass ( m ) are joined as shown in the figure. Find the distance of center of mass the system from point 0
11
374Given solid sphere is in pure rolling on a rough surface. Pick correct statement
(s) (take ( pi=22 / 7) )
This question has multiple correct options
A. There are two points in sphere having velocity in vertical direction
B. There is no point in sphere having velocity in vertical direction
C . Ratio of distance travelled by A and O is ( frac{14}{11} ) in one
complete round
D. Ratio of distance travelled by A and O is 1 in one complete round
11
375A rectangular solid box of length ( 0.3 m ) is held horizontally, with one of its sides on the edge of a platform of height ( 5 mathrm{m} ) When released, it slips off the table in a very short time ( tau=0.01 s, ) remaining
essentially horizontal. The angle by which it would rotate when it hits the
ground will be (in radians) close to :-
A. 0.02
2
в. 0.28
( c .0 .5 )
D. ( 0 . )
11
376If all of a sudden the radius of the earth
decreases, then which one of the
following statements will be true?
A. The angular momentum of the earth will become greater than that of the sun
B. The periodic time of the earth will increase
C. The energy and angular momentum will remain constant
D. The angular velocity of the earth will increase
11
377A weightless ladder 20 ft long assets
against a frictionless wall at an angle
( 60^{circ} ) from the horizontal. A 150 pound
man is 4 ft from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude from the following.
A . ( 175 ~ l b )
B. ( 100 l b )
c. ( 120 l b )
D. 17.3 lb
11
378Two bodies of masres ( 1 k g ) and ( 3 k g ) have position vectors ( hat{boldsymbol{i}}+boldsymbol{2} hat{boldsymbol{j}}+hat{boldsymbol{k}} ) and ( -boldsymbol{3} boldsymbol{i}- )
( 2 hat{j}+hat{k} ) respectively. The centre of mass
of this system has a position vector
B . ( -2 hat{i}-1 hat{j}+hat{k} )
c. ( 2 hat{i}-hat{j}-2 hat{k} )
D. ( -hat{i}+hat{j}+hat{k} )
11
379A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their velocities
will be:
A. ( sqrt{4}: sqrt{3} )
B. ( sqrt{3}: sqrt{4} )
c. ( sqrt{3}: sqrt{2} )
D. ( sqrt{2}: sqrt{3} )
11
380A thin circular ring first slip down a
smooth incline then rolls down a rough
incline of identical geometry from the same height. The ratio of time taken in the two motion is :
A ( cdot frac{1}{2} )
B.
c. ( frac{1}{sqrt{2}} )
D.
11
381(o)
(d)
11
chord is attached to the object through
this hole The object is set into motion
with initial velocity of magnitude ( v_{0} ) at
right angle to the chord and at tehsame
time the chord is pulled through the
hole at uniform speed c m/s. Initially
object is at point ( mathbf{A}left(0, r_{0}right) ) and at any
time I it is at point ( P(r cos theta, r sin theta) )
Neglect the dimension of object Choose
CORRECT options(s)
This question has multiple correct options
A ( cdot ) tension in the chord at any time t is ( frac{m r_{0}^{2} v_{0}^{2}}{left(r_{0}-c tright)^{3}} )
B. Tension in the chord at any time t is ( frac{2 m_{0}^{2} v_{0}^{2}}{left(r_{0}-c tright)^{2}} )
Condar speed of the object at any time is ( frac{2 r_{0} v_{0}}{left(r_{0}-c tright)^{2}} )
D. Angular speed of the object at any time t is ( frac{r_{0} v_{0}}{left(r_{0}-c tright)^{2}} )
11
383Net torque on the rear wheel of the
bicycle is equal to:
A. Zero
( mathbf{B} cdot 16 N-m )
c. ( 6.4 N-m )
( mathbf{D} cdot 4.8 N-m )
11
384What is meant by the term ‘moment of force’?11
385A solid sphere of mass ( m ) and radius ( R ) is placed on a plank of equal mass,
which lies on a smooth horizontal
surface. The sphere is given a sharp impulse in the horizontal direction so
that it starts sliding with a speed of ( v_{0} )
Find the time taken by the sphere to
start pure rolling on the plank. The coefficient of friction between plank
and sphere is ( mu )
11
386If ( F ) is force and ( r ) is radius, then torque
is :
( mathbf{A} cdot vec{r} times vec{F} )
В. ( vec{r} vec{F} )
c. ( |r||F| )
D. r/F
11
387When a body remains in the same state of motion (translational or rotational)
under the influence of the applied forces, the body is said to be
A. Static equilibrium
B. Dynamic equilibrium
( c . ) Both
D. None
11
388A chain ( A B ) of mass ( m ) and length ( L ) is
hanging on a smooth horizontal table as shown in the figure. If it is released from
the position shown then the displacement of centre of mass of chain
in magnitude, when end ( A ) moves a
distance ( frac{L}{2} i s X sqrt{2} m )
Find ( boldsymbol{X} .(boldsymbol{L}=mathbf{3} 2 boldsymbol{m}) )
A ( cdot frac{m g l}{4} )
в. ( frac{m g}{8} )
c. ( frac{m g}{24} )
D. ( frac{m g}{32} )
11
389A man stands on a rotating platform, with his arms stretched horizontally holding a ( 5 mathrm{kg} ) weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then
brings his arms close to his body with the distance of each weight from the axis changing from ( 90 mathrm{cm} ) to ( 20 mathrm{cm} . ) The moment of inertia of the man together
with the platform may be taken to be
constant and equal to ( 7.6 mathrm{kg} mathrm{m}^{2} ).
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
11
390A uniform disc of mass ( m ) and radius ( R )
is pivoted at the point ( P ) and is free to
rotate in a vertical plane. The center ( C ) of the disc is initially in a horizontal position with ( P ) as shown in the figure.
It is released from this position, then its
angular acceleration when the line ( boldsymbol{P C} )
is inclined to the horizontal at an angle
( theta ) is:
A ( cdot frac{2 g cos theta}{3 R} )
B. ( frac{g sin theta}{2 R} )
c. ( frac{2 g sin theta}{R} )
D. ( frac{2 g sin theta}{3 R} )
11
391The moment of inertia of a straight thin
rod of mass ( M, ) length ( L ) about an axis
perpendicular to its length and passing through its one end is :
11
392A rail road car of mass ( mathrm{M} ) is at rest on
friction less rails when a man of mass
of mass ( mathrm{m} ) starts moving on the car towards the engine. If the car recoils with a speed v backward on the rails, with what velocity is the man
approaching the engine?
11
393A planar object made up of a uniform square plate and four semicircular
discs of the same thickness and
material is being acted upon by four forces of equal magnitude as shown. The coordinates of point of application of forces is given by
A . ( (0, a) )
в. ( (0,-a) )
( c .(a, 0) )
D. ( (-a, 0) )
11
394A streamlined and almost symmetrical
car of mass ( M ) has centre of gravity at a
distance ( p ) from the rear wheel, ( q ) from
the front wheel and ( h ) from the road. If
the car has required power and friction,
the maximum acceleration developed without tipping over towards back is:
A ( cdot frac{p g}{h} )
в. hg( q )
c. ( frac{h M g}{q} )
D. ( frac{p h}{g} )
11
395Three badies ( A, B ) and ( C ) having masses ( 10 k g, 5 k g ) and ( 15 k g ) representively are projected from top of a tower with ( A ) vertically upwards with
( mathbf{1 0} boldsymbol{m} / boldsymbol{s}, boldsymbol{B} ) with ( mathbf{2 0} boldsymbol{m} / boldsymbol{s} mathbf{5 3}^{boldsymbol{o}} ) above east
horizontal and ( C ) horizontally southward
with ( 15 ~ m / s . ) Find
(a) Velocity of centre of mass of the
systrem.
11
396A man is standing on a boat in still water. If he walks towards the shore the
boat will
A. move away from the shore
B. remain stationary
c. move towards the shore
D. sink
11
397Find the moment of inertia of a uniform
sphere of mass ( m ) and radius ( R ) about a tangent if the sphere is hollow.
11
398if force ( overrightarrow{boldsymbol{F}}=(hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}) boldsymbol{N} ) acts on a body
at a point whose distance from the axis of rotation is given by ( vec{r}=(3 hat{i}+hat{j}) N ) then torque acting on the body is:
( mathbf{A} cdot 9 N m )
B. ( 8 N m )
( mathbf{c} .6 N m )
D. ( 1 N m )
11
399Assertion
Internal forces cannot change linear
momentum.
Reason
Internal forces can change the kinetic
energy of a system.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
400A man stands at one end of the open
truck which can run on frictionless
horizontal rails. Initially, the man and the truck are at rest. Man now walks to
the other end and stops. Then which of the following is true?
A. The truck moves opposite to direction of motion of the man even after the man ceases to walk
B. The centre of mass of the man and the truck remains at the same point throughout the man’s walk
C. The kinetic energy of the man and the truck are exactly equal throughout the man’s walk.
D. The truck does not move at all during the man’s walk
11
401is the Moment of inertia of ( triangle A B C )
(equilateral) about and an axis passing through 0 (D,E,F are midpoints). And
point 0 is the center of ( triangle A B C . I_{o} ) is a
moment of inertia of a remaining
triangle when ( triangle ) DEF is cut from ( triangle A B C ).
A ( cdot frac{15}{16} I )
в. ( frac{3}{1} I )
c. ( frac{I_{o}}{4} )
D. ( frac{16}{15} I )
11
402A square plate of edge d and a circular disc of diameter dare placed touching
each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination,
assuming same mass per unit area for
the two plates.
11
403Locate the centre of mass of three
particles of mass ( boldsymbol{m}_{1}=mathbf{1} boldsymbol{k} boldsymbol{g}, boldsymbol{m}_{2}= )
( 2 k g ) and ( m_{3}=3 k g ) at the corners of an
equilateral triangle of each side of ( 1 boldsymbol{m} )
11
404A light weight boy holds two heavy dumbbells of equal masses with outstretched arms while standing on a
turn-table which is rotating at an
angular frequency ( omega_{1} ) when the
dumbbells are at distance ( r_{1} ) from the
axis of rotation. The boy suddenly pulls
the dumbbells towards his chest until
they are at distance ( r_{2} ) from the axis of rotation. The new angular frequency of
rotation ( omega_{2} ) of the turn-table will be
equal to
A ( cdot omega_{1} frac{r_{2}}{r_{1}} )
В. ( _{omega_{1}} frac{r_{1}^{2}}{r_{2}^{2}} )
c. ( _{omega_{1}} frac{r_{1}}{r_{2}} )
D. ( _{omega_{1}} frac{r_{2}^{2}}{r_{1}^{2}} )
11
405particle moves uniform in a circle of
radius ( 10 mathrm{cm}, ) converting a linear distance of ( mathrm{cm} ) in a time 2.5 sec. Find
the time taken for 10 revolutions,
A ( .0 .2 s e c )
B. 18.34 sec
c. 79.12 sec
D. 50 sec
11
406A particle of mass ( mathrm{m} ) is revolving in a horizontal circle of radius r with
constant angular speed ( omega . ) The areal
velocity of the particle is:
A ( cdot r^{2} omega )
B . ( r^{2} theta )
( ^{c cdot frac{r^{2} omega}{2}} )
D. ( frac{r omega^{2}}{2} )
11
( mathbf{A} cdot 4 N m ) (clockwise)
B. ( 4 N m ) (anti clockwise)
c. ( 2 N m ) (clockwise)
D. ( 2 N m ) (anti clockwise)
11
408Angular velocity of minute hand of a clock is
A ( cdot frac{pi}{30} r a d / s )
в. ( 8 pi r a d / s )
c. ( frac{2 pi}{1800} ) rad/s
D. ( frac{pi}{1800} ) rad ( / s )
11
409A thin circular ring of a mass ( mathrm{m} ) and radius R is rotating about its axis with a constant angular velocity ( (mathbf{5} pm mathbf{1 . 5}) mathbf{Omega} )
Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The angular velocity of ring is.
A ( cdot frac{omega m}{M+m} )
в. ( frac{omega m}{M+2 m} )
c. ( frac{omega(M+2 m)}{m} )
D. ( frac{omega(m-2 m)}{m+2 M} )
11
410Under the effect of mutual internal
attractions-
A. The linear momentum of a system increases
B. The linear momentum of a system decreases
c. The linear momentum of a system is conserved
D. The angular momentum increases
11
411Three ants on the floor of a moving bus along a straight line with a uniform speed of ( 2 mathrm{cm} / mathrm{s} ) also moves with the
same velocity with respect to the ground along the straight line. Then
A. The collection of three ants can be considered as a rigid body with respect to the bus frame of reference
B. The collection of three ants can be considered as a rigid body with respect to the ground frame of reference
c. The collection of three ants is not a rigid body, since they are moving
D. The first ant can be considered as a rigid body, while the others are moving relative to first ant
11
412Rotary motion is of two types.
A. True
B. False
11
413A force ( overrightarrow{boldsymbol{F}}=boldsymbol{alpha} hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}+boldsymbol{6} hat{boldsymbol{k}} ) is acting at a
point ( vec{r}=2 hat{i}-6 j-12 hat{k} . ) The value of ( alpha )
for which angular momentum about origin is conserved is
( mathbf{A} cdot mathbf{0} )
B.
c. -1
D.
11
414toppr
Velocities are shown with the red arrows
ant the corresponding values.
A. blue and yellow tie, green and purple and orange tie
B. purple and orange tie, blue, yellow, green
c. blue, purple and orange tie, green yellow
D. green and purple tie, or orange, blue and yellow tie
E. green and purple and orange tie, blue and yellow tif
11
415A particle of mass ( 2 mathrm{kg} ) is on a smooth
horizontal table and moves in a circular
path of radius 0.6m. The height of the table from the ground is ( 0.8 mathrm{m} ) If the angular speed of the particle is
12rads ( ^{-1} ), the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
A. ( 8.64 mathrm{kg} mathrm{m}^{2} s^{-1} )
B. ( 11.52 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-1} )
c. ( 14.4 mathrm{kg} mathrm{m}^{2} s^{-1} )
D. ( 20.16 mathrm{kg} mathrm{m}^{2} mathrm{s}^{-1} )
11
416Only rotating bodies can have angular
momentum
A . True
B. False
11
417Where does the center of gravity of the
atmosphere of the earth lie?
11
418A lawn roller in the form of a thin-walled
hollow cylinder of mass ( M ) is pulled horizontally with a constant horizontal
force ( boldsymbol{F} ) applied by a handle attached to
the axle. Ifit rolls without slipping, find the acceleration and the friction force.
11
419A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that line of action passes
through the center of the shell. As a result, shell starts moving with a linear
speed ( nu ) without any initial angular
velocity. Find the linear velocity of the shell when it starts pure rolling.
A ( cdot frac{3}{5} nu )
B. ( 2_{-nu} )
( c cdot 4 )
D. None
11
420The angular velocity ( omega(text { in } mathrm{rad} / mathrm{s}) ) is:
A .25
B. 100
( c .50 )
D. 75
11
421A stationary light, smooth pulley can rotate without friction about a fixed
horizontal axis. A light rope passes over
the pulley. One end of the rope supports
a ladder with man and the other end
supports a counterweight of mass ( mathrm{M} )
Mass of the man is m. Initially, the
centre of mass of the counterweight is
at a height h from that of man as shown
in figure.

If the man starts to climb up the ladder
slowly, calculate work done by him to
reach his centre of mass in level with
that of the counterweight

11
422Torque is the cause of:
A. Translatory motion
B. Rotatory motion
c. oscillatory motion
D. Combine translatory and rotatory motion
11
423Density of a sphere of mass ( M, ) radius ( R ) varies with distance ( r ) from its centre ( operatorname{as} boldsymbol{P}=boldsymbol{P} cdotleft(1+frac{boldsymbol{r}}{boldsymbol{R}}right) boldsymbol{P}_{0} ) is ( mathbf{a}+boldsymbol{v} boldsymbol{e} )
constant find its MOI about its
diameter.
11
424A solid sphere roll down an inclined
plane inclined at an angle ( theta ) with horizontal. Find its linear acceleration ( vec{a} )
11
425A ballet dancer spins with angular velocity of 2.8 rev/s with her arms stretched out and moment of inertia
about the vertical axis. She then
retracts her arms and moment of
inertial becomes 0.71 about the same
axis. Find the new angular velocity
A. 3.2 rev / s
B. 4 rev/s
c. 4.8 rev/s
D. 5.6 rev / s
11
426The coordinates of centre of mass of
particles of mass ( 10,20,30 g m ) are ( (1,1,1) c m . ) The position of coordinates
of mass ( 40 g m ) which when added to the
system, the position of combined centre
of mass be at (0,0,0) are
A ( cdot(3 / 2,3 / 2,3 / 2) )
B . ( (-3 / 2,-3 / 2,-3 / 2) )
c. ( (3 / 4,3 / 4,3 / 4) )
D. ( (-3 / 4,-3 / 4,-3 / 4) )
11
427A sphere rolls down on an inclined plane of inclination ( theta . ) What is the
acceleration as the sphere reaches bottom?
A ( cdot frac{5}{7} g sin theta )
в. ( frac{3}{5} g sin theta )
c. ( frac{2}{7} g sin theta )
D. ( frac{2}{5} g sin theta )
11
428A solid cylinder of mass ( M ) and radius
( R ) rolls down an inclined plane without
slipping. The speed of its centre of mass when it reaches the bottom is
A ( cdot sqrt{(2 g h)} )
в. ( sqrt{frac{4}{3} g h} )
c. ( sqrt{frac{3}{4} g h} )
D. ( sqrt{(4 g / h)} )
11
429A small ball of mass ( m ) collides with a
rough wall having coefficient of friction
( mu ) at an angle ( theta ) with the normal to the
wall. If after collision the ball moves
angle ( alpha ) with the normal to the wall and
the coefficient of restitution is ( e ), then
find the reflected velocity ( nu ) of the ball
just after collision.
11
430If momentum of a body remains
constant, then mass-speed graph of body is:
A . a circle
B. a straight line
c. a rectangular hyperbola
D. a parabola
11
431The diameter of a solid disc is ( 0.5 mathrm{m} )
and its mass is ( 16 mathrm{Kg} ). What torque will increase its angular velocity from zero to 120 rotation/minute in 8
seconds?
A ( cdot frac{pi}{4} N / m )
в. ( frac{pi}{2} N / m )
c. ( frac{pi}{3} N / m )
D. ( pi N / m )
11
432From the following, find the pair of physical quantities which are analogous to one another in translatory motion and rotatory motion:
A. Mass, Moment of inertia
B. Force, Torque
c. Linear momentum, Angular momentum
D. All of these
11
433Two particles ( A ) and ( B ), initially at rest, moves towards each other under a
mutual force of attraction. At the
instant when the speed of ( A ) is ( v ) and the
speed ( B ) is ( 2 v, ) the speed of centre of
mass is :
A . zero
в.
c. ( 1.5 v )
D. ( 3 v )
11
434A force ( overrightarrow{boldsymbol{F}}=(2 hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}-boldsymbol{5} hat{boldsymbol{k}}) boldsymbol{N} ) acts at a
point ( vec{r}_{1}=(2 hat{i}+4 hat{j}+7 hat{k}) m . ) The
torque of the force about the point ( vec{r}_{2}= ) ( (hat{mathbf{i}}+mathbf{2} hat{mathbf{j}}+mathbf{3} hat{boldsymbol{k}}) boldsymbol{m} ) is :
A ( .17 hat{j}+5 hat{k}-3 hat{i}) N m )
B . ( 2 hat{i}+4 hat{j}-6 hat{k}) N m )
c. ( 12 hat{i}-5 hat{k}+7 hat{k}) N m )
D. ( 13 hat{j}-22 hat{i}-hat{k}) N m )
11
435In the figure, the velocities are in ground frame and the cylinder is
performing pure rolling on the plank,
velocity of point ( ^{prime} A^{prime} ) would be :
( A cdot 2 V_{C} )
В ( cdot 2 V_{C}+V_{P} )
( mathbf{c} cdot 2 V_{C}-V_{P} )
D ( cdot 2left(V_{C}-V_{P}right) )
11
436One oscillation completed by a vibrating body in one second is known
as:
A . 1 tesla
B. 1 Hertz
c. 1 horse power
D. none
11
437Four cubes of side ‘a’ each of mass 40 g. 20 ( g, ) 10 ( g ) and 20 g are arranged in ( x Y ) plane as shown in the figure. The coordinates of COM of the combination
with respect to point 0 is:
A ( frac{19 a}{18}, frac{17 a}{18} )
в. ( frac{17 a}{18}, frac{11 a}{18} )
с. ( frac{17 a}{18}, frac{13 a}{18} )
“. ( frac{13 a}{18}, frac{17 a}{18} )
11
438While opening a tap with two fingers, the forces applied by the fingers are:
A . equal in magnitude
B. parallel to each other
c. opposite in direction
D. all the above
11
439A circular disc of mass ( 10 mathrm{kg} ) and radius
( 0.2 mathrm{m} ) is set into rotation about an axis
passing through its centre and perpendicular to its plane by applying torque ( 10 mathrm{Nm} ). Calculate angular velocity of the disc that it will attain at the end
of 6 s from the rest.
11
440The diameter of a solid disc is ( 0.5 m ) and
its mass is ( 16 k g )
At what rate is the work done by the torque at the end of eighth second?
( mathbf{A} cdot pi W )
в. ( pi^{2} W )
( mathbf{c} cdot pi^{3} W )
D. ( pi^{4} W )
11
441Seven homogeneous bricks, each of length L, are arranged as shown in figure. Each brick is displaced with respect to the one in contact by ( boldsymbol{L} / mathbf{1 0} )
Find the ( x ) coordinate of the center of
mass relative to the origin 0
11
442The moment of inertia of a ring of mass
( 10 g ) and radius ( 1 c m ) about a tangent to
the ring and normal to its plane is :
A ( cdot 2 times 10^{-6} k g m^{2} )
в. ( 5 times 10^{-7} mathrm{kgm}^{2} )
c. ( 5 times 10^{-8} k g m^{2} )
D. ( 4 times 10^{-6} k g m^{2} )
11
443A 250 -Turn rectangular coil of length ( 2.1 mathrm{cm} ) and width ( 1.25 mathrm{cmcarries} ) a
current of ( 85 mu A ) and subjected to a
magnetic field of strength 0.85T. Work
done for rotating the coil by ( 180^{circ} )
against the torque is:
B. ( 9.1 mu J )
c. ( 4.55 mu ) J
D. ( 23 mu J )
11
444Which of the following cannot be considered an example of precession?
A. A spinning top
B. A spinning wheel
c. Rolling ball
D. Spinning of the earth
11
445Moment of inertia of a thin circular
A. axis perpendicular to plane of plate passing through its centre.
B. axis passing through any diameter of plate.
C. axis passing through any tangent of plate in its plane.
D. axis passing through any tangent perpendicular to its plane.
11
446From the base of hemisphere, a right ( boldsymbol{R} )
cone of height ( frac{1}{2} ) and same base has
been scooped out. Find the C.M of the
remaining part
11
447Two stones, having masses in the ratio of ( 3: 2, ) are dropped from the heights in the ratio of ( 4: 9 . ) The ratio of magnitudes of their linear momenta just before reaching the ground is (neglect air resistance)
A . 4:
B. 2:3
( c cdot 3: 2 )
D. 1:
11
448A disc of mass ( mathrm{M} ) and radius ( mathrm{R} ) is rolling
with angular speed ( omega ) on a horizontal
plane as shown. The magnitude of
angular momentum of the disc about
the origin 0 is
A ( cdot frac{1}{2} M R^{2} omega )
B. ( M R^{2} omega^{omega} )
c. ( frac{3}{2} M R^{2} omega )
D. ( 2 M R^{2} omega )
11
449The momentum of a system is
conserved
A. always
B. never
( mathrm{C} ). in the absence of external forces in the system
D. in presence of external forces in the system
11
450The centre of gravity of regular shaped objects is at their11
451If the direction of position vector ( vec{r} ) is towards south and the direction of force vector ( vec{F} ) is towards east, then the
direction of torque vector ( overrightarrow{boldsymbol{T}} ) is
A. towards North
B. towards west
c. vertically upward
D. vertically downward
11
452A solid sphere is rotating in free space. If the radius of the sphere is increased keeping the mass same without applying any external force, which one of the following will not be affected?
A. Moment of inertia
B. Angular momentum
c. Angular velocity
D. Rotational kinetic energy
11
453Two identical particles each of mass
( mathrm{m} ) are projected from points ( mathrm{A} ) and ( mathrm{B} ) on
the ground with same initial speed ( u )
making an angle ( theta ) as shown in the
figure, such that their trajectories are
in the same vertical plane. The initial velocity of the centre of mass is
A . ucos ( theta )
B. 2u cos ( theta )
( c cdot u sin theta )
D. 2u sin ( theta )
11
454Figure shows a composite system of
two uniform rods of lengths as
indicated. If both the rods are of same
density. Then the coordinates of the
centre of mass of the system of rods
are:
A ( cdotleft(frac{L}{2}, frac{2 L}{3}right) )
B ( cdotleft(frac{L}{4}, frac{2 L}{3}right) )
c. ( left(frac{L}{6}, frac{2 L}{3}right) )
D. ( left(frac{L}{6}, frac{L}{3}right) )
11
455A bomb of mass ( mathrm{m} ) at rest at the
coordinate
origin explodes into three equal pieces. At a certain instant one piece is on the
( mathbf{x} ) -axis at ( boldsymbol{x}=mathbf{4 0} boldsymbol{c m} ) and another is at
( boldsymbol{x}=mathbf{2 0} boldsymbol{c m}, boldsymbol{y}=-mathbf{6 0} boldsymbol{c m} . ) The position
of the third piece is:
A. ( x=60 mathrm{cm}, y=60 mathrm{cm} )
в. ( x=-60 mathrm{cm}, y=-60 mathrm{cm} )
c. ( x=60 mathrm{cm}, y=-60 mathrm{cm} )
D. ( x=-60 c m, y=60 c m )
11
456At a time ( t=t_{0}, ) the string is suddenly
broken and the balls are released to
move. Mark the incorrect statement.
Consider the momentum and angular momentum after and before string
breaks.
A. Total angular momentum of system is conserved in table reference frame as well as center of mass reference frame
B. In the centre of mass frame, angular momentum of each of the mass is separately conserved
c. Total linear momentum of system is conserved in table reference frame
D. In the table frame momentum of individual balls is ss conserved
11
457The sum of products of masses and velocities of two moving bodies before and after their collision remains the
same .The law involved here is:
A. Law of conservation of mass
B. Law of conservation of velocity
c. Law of conservation of energy
D. Law of conservation of momentum
11
458If ( overrightarrow{mathrm{A}}, overrightarrow{mathrm{B}} ) and ( overrightarrow{mathrm{C}} ) are non-zero vectors, and if ( overrightarrow{mathbf{A}} times overrightarrow{mathbf{B}}=mathbf{0} ) and ( overrightarrow{mathbf{B}} times overrightarrow{mathbf{C}}=mathbf{0}, ) then the
value of ( overrightarrow{mathbf{A}} times overrightarrow{mathbf{C}} ) is:
A .
B.
c. ( mathrm{B}^{2} )
D. ( A C cos theta )
11
459A force ( mathbf{F}(-hat{mathbf{k}}) ) acts on the origin of the
co-ordinate system. The torque about the point (1,-1) is
A. ( mathrm{F}(hat{mathrm{i}}-hat{mathrm{j}}) )
B . ( -mathrm{F}(hat{mathrm{i}}+hat{mathrm{j}}) )
( mathbf{c} cdot mathbf{F}(hat{mathbf{i}}+hat{mathbf{j}}) )
D. ( -mathrm{F}(hat{mathrm{i}}-mathrm{j}) )
11
460A wheel of radius R rolls without
slipping on the ground with a uniform
velocity v. The relative acceleration of
the top most point ofthe wheel with
respect to the bottom most point is
( mathbf{A} cdot frac{v^{2}}{R} )
B. ( frac{2 v^{2}}{R} )
c. ( frac{v^{2}}{2 R} )
D. ( frac{4 v^{2}}{R} )
11
461The ends ( A ) and ( B ) of a rod of length ( l ) have velocities of magnitudes ( left|overrightarrow{boldsymbol{v}}_{boldsymbol{A}}right|= )
( boldsymbol{v} quad ) and ( left|overrightarrow{boldsymbol{v}}_{boldsymbol{B}}right|=2 boldsymbol{v}, ) respectively. If the
inclination of ( vec{v}_{A} ) relative to the rid is ( alpha )
find the:
(a) inclination ( beta ) of ( vec{v}_{B} ) relative to the
rod.
(b) angular velocity of the rod
11
462A body of mass ( m ) and radius ( r ) is
released from rest along a smooth inclined plane of angle of inclination ( boldsymbol{theta} ) The angular momentum of the body about the instantaneous point of
contact after a time ( t ) from the instant
of release is equal to
A. mgrt cos ( theta )
B. ( m g r t sin theta )
c. ( (3 / 2) ) mgrt sin ( theta )
D. None of the above
11
463Four particles of masses ( mathrm{m}, 2 mathrm{m}, 3 mathrm{m} ) and ( 4 mathrm{m} ) are arranged at the corners of the parallelogram with each side equal to a
and one of the angle between two
adjacent sides is ( 60^{circ} ).The parallelogram
lies in the ( x ) -y plane with mass ( m ) at the origin and ( 4 mathrm{m} ) on the ( mathrm{X} ) -axis.The center
of mass of the arrangement will be
located at
A ( cdotleft(frac{sqrt{3}}{2} a, 0.95 aright) )
в. ( quadleft(0.95 a, frac{sqrt{3}}{4} aright) )
c. ( M R^{2}=2 I )
D. ( left(frac{a}{2}, frac{3 a}{4}right) )
11
464A uniform metal disc of radius R is
taken and out of it a disc of diametere ( mathrm{R} )
is out off from the end. The centre of
mass of the remaining part will be
( ^{A} cdot frac{R}{4} ) from the centre
B. ( frac{R}{3} ) from the centre
( ^{mathrm{C}} cdot frac{R}{5} ) from the centre
D. ( frac{R}{6} ) from the centre
11
465Two forces, each of magnitude ( F, ) act at
points ( V ) and ( W ) on an object.

The two forces form a couple. The shape
of the object is a right-angled triangle with sides of
lengths ( x ) and ( y, ) as shown.
Which expression gives the torque
exerted by the couple?
( mathbf{A} cdot F x )
B. ( F y )
( mathbf{c} cdot 2 F x )
D. ( 2 F y )

11
466A uniform cylinder of radius ( boldsymbol{R} )
is spinned about its axis to the angular
velocity ( omega_{0} ) and then placed into a
corner. The coefficient of friction
between the corner walls and the
cylinder is ( mu_{k} . ) How many turns will the
cylinder accomplish before it stops?
11
467A particle starts with angular
acceleration 2 rad/sec( ^{2} ). It moves
100 rad in a random interval of 5 sec.
Find out the time at which random
interval starts.
A. 7.5 sec
B. 4.5 sec
( mathrm{c} .5 mathrm{sec} )
D. 6 sec
11
468The moment of inertia of a solid cylinder
about its own axis is the same as its
moment of inertia about an axis
passing through its centre of gravity and perpendicular to its length.The relation between its length ( L )
and radius ( boldsymbol{R} ) is:
A. ( L=sqrt{2} R )
В. ( L=sqrt{3} R )
c. ( L=3 R )
D. ( L=R )
11
469What quantities are conserved in this
collision?
A. Linear and angular momentum, but not kinetic energy
B. Linear momentum only
C. Angular momentum only
D. Linear momentum, angular momentum and kinetic energy
11
470If the extension of the spring is ( x_{0} ) at
time ( t, ) then the displacement of the
first block at this instant is :
( ^{mathbf{A}} cdot frac{1}{2}left(frac{F t^{2}}{2 m}+x_{0}right) )
B ( cdot-frac{1}{2}left(frac{F t^{2}}{2 m}+x_{0}right) )
c. ( frac{1}{2}left(frac{F t^{2}}{2 m}-x_{0}right) )
D. ( frac{F t^{2}}{2 m}+x_{0} )
11
471When disc ( B ) is brought in contact with
disc ( A, ) they acquire a common angular velocity in time ( t . ) The average frictional torque on one disc by the other during this period is
A ( cdot frac{2 I omega}{3 t} )
в. ( frac{9 text { Гс }}{2 t} )
c. ( frac{9 text { ा }}{4 t} )
D. ( frac{3 I omega}{2 t} )
11
472Moments are measured in:
A ( cdot frac{k g}{s} )
B. Nm
c. ( N times s )
D. ( frac{N}{s} )
11
473If a street light of mass ( mathrm{M} ) is suspended from the end of a uniform rod of length
in different possible patterns as shown in figure, then
( (a) )
( (b) )
A. Pattern A is more sturdy
B. Pattern B is more sturdy
c. Pattern C is more sturdy
D. All will have same sturdiness
11
474Two homogenous spheres ( A ) and ( B ) of
masses ( m ) and ( 2 m ) having radii ( 2 a ) and
( a ) respectively are placed in touch. The distance of centre of mass from first
sphere is:
( A )
B . ( 2 a )
( c .3 a )
D. ( 3 a / 2 )
11
475A ball kept in a closed container moves in it making collision with the walls. The container is kept on a smooth surface.
The velocity of the centre of mass of :
A. the ball remains fixed
B. the ball relative to container remains fixed
c. the container remains fixed
D. both container and ball remain fixed
11
476Consider the following statements  ( mathrm{CM} ) of a uniform semicircular disc of
radius ( R=2 R / pi ) from the centre
 CM of a uniform semicircular ring of radius ( R=4 R / 3 pi ) from the centre
 CM of a solid hemisphere of radius ( boldsymbol{R}=boldsymbol{4} boldsymbol{R} / mathbf{3} boldsymbol{pi} ) from the centre
 CM of a hemisphere shell of radius ( boldsymbol{R}=boldsymbol{R} / 2 ) from the centre
Which statement are correct:
A ( cdot 1,2,4 )
в. 1,3,4
( c cdot 4 ) only
D. 1,2 only
11
477A uniform rod mass ( mathrm{m} ) and length lis attached to smooth hinge at end ( A ) and to a string at end B as shown in figure. It
is at rest. The angular acceleration of
the rod just after the string is cut is:
11
478A particles performing uniform circular motion. Its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
A ( cdot frac{L}{4} )
B. ( 2 L )
c. ( 4 L )
D. ( frac{L}{2} )
11
479The diagonals of a parallelogram are ( 2 hat{i} ) and ( 2 hat{j} ). What is the area of the parallelogram?
A. 0.5 unit
B. 1 unit
c. 2 unit
D. 4 unit
11
480The mass of uniform square plate is
( 120 g ) and its side length is ( 20 c m ). About an axis perpendicular to the plane of plate and passing through its centre, the moment of inertia is :
A ( cdot 8 times 10^{-3} k g m^{2} )
B . ( 8 times 10^{-4} k g m^{2} )
c. ( 4 times 10^{-3} k g m^{2} )
D. ( 4 times 10^{-4} k g m^{2} )
11
481If the resultant of two forces ( P ) and ( Q ) be
equal in magnitude to one of the
components ( boldsymbol{P} ) and perpendicular to it
in direction, then the value of ( Q ) is
A. ( P )
в. ( frac{1}{sqrt{2}} P )
( c cdot sqrt{2} P )
D. ( sqrt{3} P )
11
482Assertion
In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun.
Reason
In firing, momentum is conserved.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
483A charged particle ( X ) moves directly towards another charged particle Y. For the ‘X plus Y’ system, the total
momentum is p and the total energy is
( E )
This question has multiple correct options
A. p and ( E ) are conserved if both ( x ) and ( Y ) are free to move
B. (A) is true only if ( x ) and ( Y ) has similar charges.
c. If ( Y ) is fixed, ( E ) is conserved but not ( p )
D. If ( Y ) is fixed, neither E nor ( p ) is conserved
11
484The figure shows a square plate of
uniform mass distribution. ( A A^{prime} ) and
( B B^{prime} ) are the two axes lying in the plane
of the plate and passing through its
centre of mass. It ( I_{0} ) is the moment of
inertia of the plate about ( A A^{prime} ) then its
moment of inertia. about the ( B B^{prime} ) axis
is
( A cdot I_{b} )
B ( cdot I_{6} cos theta )
( mathbf{c} cdot I_{theta} cos ^{2} theta )
D. None of thes
11
485A uniform disc of mass ( m ) and radius ( R )
is rotating with angular velocity ( omega ) on a smooth horizontal surface. Another
identical disc is moving translationally
with velocity ( v ) as shown. When they
touch each other, they stick together.
The angular velocity of centre of mass of
the system after contact will be
A. Zero
B.
c. ( frac{v}{R} )
D. ( frac{omega}{2^{2}} )
11
486A disc is rotated about its axis with a
certain angular velocity and lowered
gently on a rough inclined plane as
shown in figure, then
A. It will rotate at the position where it is placed and then will move downwards
B. It will go downwards just after it is lowered
c. It will go downwards first and then climb up
D. It will climb upwards and then move downwards
11
487State whether true or false.
Only a couple can produce pure rotation in a body.
A. True
B. False
11
488Two men ‘ ( A ) ‘ and ‘ ( B ) ‘ are standing on a
plank.’ ( B^{prime} ) is at the middle of the plank
and ‘ ( A ) ‘ is at the left end of the plank. Surface of the plank is smooth. System
is initially at rest and masses are as
shown in figure. ‘ ( boldsymbol{A}^{prime} ) and ( ^{prime} boldsymbol{B}^{prime} ) start moving
such that the position of ‘ ( B ) ‘ remains
fixed with respect to ground and ‘ ( boldsymbol{A}^{prime} )
meets ‘ ( B ) ‘. Then the point where ( A )
meets ( B ) is located at
A. the middleof the plank
B. 30cm from the left end of the. plank
c. the right end of the plank
D. None of these
11
489Two bodies of mass ( 10 mathrm{kg} ) and ( 2 mathrm{kg} ) are moving with velocities ( 2 hat{i}-7 hat{j}+ ) ( 3 hat{k} m s^{-1} ) and ( -10 hat{i}+35 hat{j}-3 hat{k} m s^{-1} )
respectively. The velocity of their centre of mass is:
A . 2 ims ( ^{-1} )
B. ( 2 hat{k} m s^{-1} )
( mathbf{c} cdot(2 hat{j}+2 hat{k}) m s^{-1} )
D. ( (2 hat{j}+2 hat{k}+hat{k}) m s^{-1} )
11
490Find the moment of inertia of a uniform
square plate of mass ( m ) and edge ( a ) about one of its diagonals.
11
491Two identical rods are joined to form the shape of ( X ). the smaller angle between rods is ( theta ). The moment of inertia of the
system about an axis passing through the point of intersection of the rod and perpendicular to their plane is
( mathbf{A} cdot I propto theta )
B. ( I propto sin ^{2} theta )
( mathbf{c} cdot I propto cos ^{2} theta )
D. Independent of ( theta )
11
492The disc of the radius ( R ) is confined to
roll without slipping at ( A ) and ( B ). If the
plates having the velocities as shown
determine the angular velocity of disc.
11
493Two points of a rod move with velocities ( 3 v ) and ( v ) perpendicular to the rod and in the same direction,
separated by a distance ‘r’. at Then the angular velocity of rod is :
A ( cdot frac{4 v}{r} )
в. ( frac{3 v}{r} )
c. ( frac{2 v}{r} )
D. ( frac{v}{r} )
11
494There are some passengers inside a stationary railway compartment. The
centre of mass of the compartment
itself (without the passengers) is ( C_{1} )
while the centre of mass of the
compartment plus passengers’ system
is ( C_{2} ). If the passengers move about
inside the compartment then
A ( . ) both ( C_{1} ) and ( C_{2} ) will move with respect to the ground
B. neither ( C_{1} ) nor ( C_{2} ) will be stationary with respect to the ground
C. ( C_{1} ) will move but ( C_{2} ) will be stationary with respect to the ground
D. ( C_{2} ) will move but ( C_{1} ) will be stationary with respect to the ground
11
495The door of an almirah is ( 6 f t ) high, ( 1.5 f t ) wide and weighs 8 kg. The door is supported by two hinges situated at a
distance of ( 1 mathrm{ft} ) from the ends. If the
magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude
11
496A pan containing a layer of uniform thickness of ice is placed on a circular turn- table with its centre coinciding with the centre of the turn-table.
The turn-table is now rotated at a
constant angular velocity about a vertical axis passing through its centre and the driving torque is withdrawn. There is no friction between the table
and the pivot. The pan rotates with the
table. As the ice melts,
This question has multiple correct options
A. the angular velocity of the system decreases
B. the angular velocity of the system increases
c. the angular velocity of the system remains unchanged
D. the moment of inertia of the system increases
11
497Which of the following is practical
applications of the law of conservation
of linear momentum?
This question has multiple correct options
A. When a manjumps out of a boat on the shore, the boat is pushed slightly away from the shore
B. A person left on a frictionless surface can get away from it by blowing air out of his mouth or by throwing some object in a direction opposite to the direction in which he wants to move.
C. Recoiling of a gun
D. None of these
11
498A ring and a disc are initially at rest, side by side, at the top of an inclined
plane which makes an angle ( 60^{circ} ) with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is ( frac{(2-sqrt{3})}{sqrt{10} s}, ) then the height of the top of the inclined plane, in meters.
is ( _{-1} ). Take ( g=10 m s^{-2} )
11
499A disc is rolling without slipping with
angular velocity ( omega . P ) and ( Q ) are two
points equidistant from the centre ( C )
The order of magnitude of velocity is:
( mathbf{A} cdot V_{Q}>V_{C}>V_{P} )
в. ( V_{P}>V_{C}>V_{Q} )
( mathbf{c} cdot V_{Q}=V_{P}, V_{C}=V_{P} / 2 )
( mathbf{D} cdot V_{P}V_{Q} )
11
500The angular velocity of a wheel is 70 rad/s. If the radius of the wheel is
( mathbf{0 . 5} boldsymbol{m}, ) then linear velocity of the whee
is
A. ( 70 mathrm{m} / mathrm{s} )
B. ( 35 mathrm{m} / mathrm{s} )
c. ( 30 m / s 30 m / s )
D. 20m/s2om/s
11
501( I_{1} ) is moment of inertia of a thin circular
ring about its own axis. The ring is cut at a point then it is unfolded into a
straight rod. If ( I_{2} ) is moment of inertia of
the rod about an axis perpendicular to the length of rod and passing through
its centre, then the ratio of ( I_{1} ) to ( I_{2} ) is:
A . ( 3: pi )
B. ( 3: pi^{2} )
c. ( 4: pi )
D. ( 4: pi^{2} )
11
502State whether true or false.
A couple can never be replaced by a single force.
A. True
B. False
11
503To maintain a rotor at a uniform angular
speed of 200 rad ( s^{-1}, ) an engine needs to transmit a torque of ( 180 mathrm{N} ) m. What is the power required by the engine
? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is ( 100 % ) efficient.
11
504Two blocks of masses ( 10 mathrm{kg} ) and ( 4 mathrm{kg} ) and are connected by a spring of negligible mass and placed on a
frictionless horizontal surface. An
impulse gives a velocity of ( 14 mathrm{m} / mathrm{s} ) to the heavier block in the direction of the
lighter block. The velocity of the centre of mass is
11
505A sector cut from a uniform disk of
radius ( 12 mathrm{cm} ) and a uniform rod of the
same mass bent into shape of an arc
arranged facing each other as shown in
the figure. If center of mass of the
combination is at the origin, what is the
( mathbf{A} cdot 8 mathrm{cm} )
( mathbf{B} cdot 9 mathrm{cm} )
( c .12 mathrm{cm} )
D. ( 18 mathrm{cm} )
11
506A hemisphere and a solid cone have a
common base. The center of mass of the
common structure coincides with the
centre of the common base. If ( boldsymbol{R} ) is the
radius of hemisphere and ( h ) is height of
the cone then:
A ( cdot frac{h}{R}=sqrt{3} )
в. ( frac{h}{R}=frac{1}{sqrt{3}} )
c. ( frac{h}{R}=3 )
D. ( frac{h}{R}=frac{2}{sqrt{3}} )
11
507Two solid spheres ( A ) and ( B ) each of
densities ( rho_{A} ) and ( rho_{B} ) respectively. Their moments of inertia about a diameter
( operatorname{are} I_{A} ) and ( I_{B} ) respectively. The value of ( frac{boldsymbol{I}_{A}}{boldsymbol{I}_{B}} ) is:
A. ( sqrt{frac{rho_{A}}{rho_{B}}} )
в. ( sqrt{frac{rho_{B}}{rho_{A}}} )
c. ( frac{rho_{A}}{rho_{B}} )
D. ( frac{rho_{B}}{rho_{A}} )
11
508The stability of a flexible body depends
on:
A. height of the center of gravity from the ground.
B. base area of the body.
c. shape of the body.
D. all the above
11
509PR, side of the triangle PQR.11
510Calculate the moment of inertia of a
ring having mass ( M, ) radius ( R ) and
having uniform mass distribution
about an axis passing through the centre of the ring and perpendicular to
the plane of the ring
(mass elements
11
511The linear density of a thin rod of length 1.0m varies as ( boldsymbol{lambda}=2 mathrm{kg} / mathrm{m}+left(frac{2 mathrm{kg}}{boldsymbol{m}^{2}}right) boldsymbol{x} )
where ( x ) is the distance from its one end
The distance of its centre of mass from
its end is?
A ( cdot frac{2}{3} mathrm{m} )
в. ( frac{5}{9} mathrm{m} )
c. ( frac{4}{3} mathrm{m} )
D. ( frac{1}{2} ) n
11
512From a square of uniform density, a
portion removed as shown in fig. Find
the center of mass of the remaining
portion if the side of the square is a.
11
513A solid cylinder of mass ‘ ( m ) ‘ is kept in
balance position on a fixed incline of
angle ( alpha=37^{circ} ) with the help of a thread
fastened to its jacket. The cylinder does not slip. What force ( boldsymbol{F} ) is required to
keep the cylinder in balance when the
( mathbf{A} cdot m g / 2 )
в. ( 3 m g / 4 )
( mathrm{c} .3 mathrm{mg} / 8 )
D. ( 5 m g / 8 )
11
514A body starts rolling down an inclined plane of length ( L ) and height ( h ) This body reaches the bottom of the plane in time ( t . ) The relation between ( L )
and ( t ) is
( mathbf{A} cdot t propto L )
в. ( t propto frac{1}{L} )
c. ( L propto t^{2} )
D ( cdot t propto frac{1}{L^{2}} )
11
515Three particles ( A, B ) and ( C ) of equal
mass move with equal speed ( V ) along the medians of an equilateral triangles as shown in the figure. They collide at
the centroid ( G ) of the triangle. After the
collision, ( A ) comes to rest, ( B ) retraces
its path with the speed ( V ). What is the velocity of ( C ? )
11
516( I ) is the moment of inertia of a thin
square plate about an axis passing through opposite corners of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through its centre is :
A ( cdot frac{I}{2} )
в. ( frac{I}{sqrt{2}} )
( c cdot sqrt{2} I )
D. ( 2 I )
11
517A ring disc and solid sphere are having
same speed of their COM at the bottom
of incline as shown in the figure. If
surface of incline is sufficiently rough.
The ratio of height by ring, disc and
sphere is
A . 15: 14: 20
B . 20: 15: 14
c. 14: 20: 15
D. 7: 5: 15
11
518Two like parallel forces ( 20 N ) and ( 30 N )
act at the ends ( A ) and ( B ) of a rod ( 1.5 m )
long. The resultant of the forces will act
at the point:
A. ( 90 mathrm{cm} ) from A
B. ( 75 mathrm{cm} ) from ( mathrm{B} )
( mathrm{c} .20 mathrm{cm} ) from ( mathrm{B} )
D. ( 85 mathrm{cm} ) from ( mathrm{A} )
11
519Find how long the cylinder will move with sliding.
A ( cdot t=frac{omega_{0} R}{3 k g} )
В. ( t=frac{omega_{0} R}{6 k g} )
c. ( _{t=2} frac{omega_{0} R}{3 k g} )
D. ( t=2 frac{omega_{0} R}{6 k g} )
11
520A circular disc of radius ( 10 mathrm{cm} ) is free to
rotate about an axis passing through its centre without friction and its moment of inertia is ( frac{1}{2} pi k g m^{2} . A ) tangential force of ( 20 N ) is acting on the
disc along its rim. Starting from rest, the number of rotations made by the disc in ( 10 s ) is:
A . 50
в. 100
( c .150 )
D. 200
11
521The rate of recombination or generation
are governed by the law(s) of
A. Mass conservation
B. Electrical neutrality
c. Thermodynamics
D. chromodynamics
11
522Two particles of equal mass have initial velocities ( 2 hat{i} m s^{-1} ) and ( 2 hat{j} m s^{-1} . ) First
particle has a constant acceleration ( (hat{boldsymbol{i}}+hat{boldsymbol{j}}) boldsymbol{m} boldsymbol{s}^{-1} ) while the acceleration of
the second particle is always zero. The centre of mass of the two particles moves in:
A . Circle
B. Parabola
c. Ellipse
D. Straight line
11
523A sphere of mass ( m ) and radius ( r ) is
pushed onto the fixed horizontal surface such that it rolls without
slipping from the beginning. The
minimum speed v of its mass centre at
the bottom so that it rolls completely around the loop of radius ( (boldsymbol{R}+boldsymbol{r}) )
without leaving the track in between is ( operatorname{given} operatorname{as} v=sqrt{frac{x}{7} g R} ) Find ( x )
11
524Two thin uniform circular rings each of
radius ( 10 mathrm{cm} ) and mass ( 0.1 mathrm{Kg} ) are
arranged such that they have common centre and their planes are perpendicular to each other. The moment of inertia of this system about an axis passing through their common centre and perpendicular to the plane of one of the rings in ( k g m^{2} ) is:
A ( cdot 15 times 10^{-3} )
В . ( 5 times 10^{-3} )
c. ( 15 times 10^{-4} )
D. ( 18 times 10^{-4} )
11
525A uniform solid cylinder is given a linear
velocity and angular velocity, so that it rolls without sliding up the incline. Out
of the four points ( A, B, C ) and centre of mass, about which point its angular
momentum will be conserved?
(A and ( C ) are taken at appropriate distance)
( A cdot ) Point ( A )
B. Point B
C. Point ( C )
D. Centre of mass
11
526In the given figure of square plate, possible axis of rotation is shown,if in
each case we give same angular
impulse parallel to the axis shown then
A. angular momentum about axis 1 and 2 will be same
B. angular momentum about axis 1 and 3 will be same
C . angular momentum about axis 1 and 4 will be same
D. none of the above
11
527ILLUSTRATION 9.24 A cylindrical drum, pushed along by a
board rolls forward on the ground. There is no slipping at any
contact. Find the distance moved by
the man who is pushing the board, —
when axis of the cylinder covers a
distance L.
nder covers a
0
.
11
528When a force 6 N is exerted at ( 30^{circ} ) to a
wrench at a distance of ( 8 mathrm{cm} ) from a nut
as shown in Fig, it is just able to loosen
it. What force ( F ) is required to loosen the
nut if applied ( 16 mathrm{cm} ) away to the wrench
and normal to the wrench ?
( A cdot 3 N )
B. ( sqrt{3} N )
c. 1.5
D. None
11
529Distance of the center of mass of a solid
uniform cone from its vertex is ( z_{0} . ) If the
radius of its base is ( R ) and its height is
( h ) then ( z_{0} ) is equal to:
A ( cdot frac{h^{2}}{4 R} )
в. ( frac{3 h}{4} )
( c cdot frac{5 h}{8} )
D. ( frac{3 h^{2}}{8 R} )
11
530The Moon orbits the Earth once in 27.3
days in an almost circular orbit Calculate the centripetal acceleration experienced by the Earth? (Radius of the Earth is ( 6.4 times 10^{6} mathrm{m} ) )
11
531COM of a semicular here11
532Locate the COM of following system of
particle
A . 45.5 a
B. 49.5a
( c cdot 50 a )
D. None of these
11
533A body rotating with uniform angular acceleration covers ( 100 pi(text {radian}) ) in
the first ( 5 s ) after the start. Its angular
speed at the end of ( 5 s( ) in radian/s) is
then
A . ( 40 pi )
B. ( 30 pi )
( c cdot 20 pi )
D. ( 10 pi )
11
534Three masses are placed on the x-axis:
( 300 g ) at origin, ( 500 g ) at ( x=40 c m ) and
( 400 g ) at ( x=70 c m . ) The distance of the
centre of mass from the origin is-
( mathbf{A} cdot 45 mathrm{cm} )
в. ( 50 mathrm{cm} )
( mathbf{c} .30 mathrm{cm} )
D. ( 40 mathrm{cm} )
11
535A gun fires a bullet of mass 50 g with a velocity of ( 30 mathrm{m} mathrm{s}^{-1} ). Because of this
gun is pushed back with a velocity of 1
( mathrm{m} mathrm{s}^{-1} . ) Mass of the gun is :
( A cdot 3.5 mathrm{kg} )
c. ( 1.5 mathrm{kg} )
D. 2 kg
11
53674. Letr be the distance of a particle from a fixed point to
which it is attracted by an inverse square law force given by
F = k/r (k = constant). Let m be the mass of the particle
and L be its angular momentum with respect to the fixed
point. Which of the following formulae is correct about
the total energy of the system?
1 k L .
= Constant
r 2mr²
1
(dr
bo žment * – Constant
= Constant
12
+
+-
= Constant
1 (dr
2 a
d. None

r
2mr
11
537Two wheels ( A ) and ( B ) are released from
rest from points ( X ) and ( Y ) respectively
on an inclined plane as shown in figure. Which of the following statement(s) is/are incorrect?
This question has multiple correct options
A. Wheel ( B ) takes twice as much time to roll from ( Y ) to ( Z ) than that of wheel ( A ) from ( X ) to ( Z )
B. At point ( Z ) velocity of wheel ( A ) is four times that of wheel ( B )
c. Acceleration of the wheel ( A ) is four times that of wheel
( B )
D. Both wheel take same time to arrive at point ( Z ).
11
538A uniform disc of mass ( M ) and radius ( R )
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and
a steady downward pull ( T ) is exerted on
the cord. If we hang a body of mass ( m ) with the cord, the tangential acceleration of the disc will be
A. ( frac{m g}{M+m} )
в. ( frac{m g}{M+2 m} )
c. ( frac{2 m g}{M+2 m} )
D. ( frac{M+2 m}{2 m g} )
11
539At ( t=0, ) the position and velocities of
two particle are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of
center of mass at ( t=2 s )
A. ( X=5 ) m
в. ( X=7 m )
c. ( x=3 ) т
D. ( X=2 m )
11
540What is the torque of a force ( boldsymbol{F}=(2 hat{boldsymbol{i}}- ) ( 3 widehat{j}+4 k) N ) acting at a point ( r=(3 hat{i}+ ) ( 2 widehat{j}+3 widehat{k}) mathrm{m} ) about the origin in ( mathrm{N}-mathrm{m} )
? (Given ( boldsymbol{tau}=boldsymbol{r} times boldsymbol{F}) )
A ( .6 hat{i}-6 hat{j}+12 widehat{k} )
B . ( 17 hat{i}-6 widehat{j}-13 widehat{k} )
( mathbf{c} .-6 hat{i}+6 widehat{j}-2 widehat{k} )
D. ( -17 hat{i}+6 hat{j}+13 widehat{k} )
11
541single Correct Answer Type A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completed half of the circular
path?
( mathbf{A} cdot 360 )
B. 180
( c cdot 45 )
D. 0
11
542Three particles, each of mass ( m ) are
situated at the vertices of an
equilateral triangle ( A B C ) of side ( C mathrm{cm} )
(as shown in the figure). The moment of
inertia of the system about a line ( A x )
perpendicular to ( A B ) and in the plane of
( A B C, ) in ( g r a m c m^{2} ) units will be :-
( mathbf{A} cdot 2 mathrm{m} ell^{2} )
( mathbf{B} cdot frac{5}{4} m ell^{2} )
( mathbf{c} cdot frac{3}{2} m t^{2} )
D ( cdot frac{3}{4} m^{2} )
11
543Which of the following statements
is/are true?
This question has multiple correct options
A. Work done by kinetic friction on an object may be positive
B. A rigid body rolls up an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
C. A rigid body rolls down an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
D. A rigid body is left from rest and having no angular velocity from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be up the incline.
11
544A sphere is released on a smooth
inclined plane from the top. When it
moves down its angular momentum is:
B. conserved about the point of contact only
c. conserved about the centre of the sphere only
D. conserved about any point on a fixed line parallel to the inclined plane and passing through the centre of the ball
11
545The velocity of the CM of the rod
A ( frac{5}{7} v_{0} ) at ( tan ^{-1} frac{4}{3} ) below horizonta
B. ( 5_{0} ) at ( tan ^{-1} frac{3}{4} ) below horizonta
( 7^{0} ) a
C ( cdot frac{5}{8} v_{0} ) at ( tan ^{-1} frac{3}{4} ) below horizontal
( stackrel{-5}{-} frac{5}{6} 0 ) at ( tan ^{-1} frac{4}{3} ) below horizonta
11
546andiscilicia du
consists of two identical uniform solid
cylinders, each of mass ( m, ) on which two
The friction in the axle of the upper
cylinder is assumed to be absent. If the
tension of each thread in the process of motion is ( boldsymbol{T}=frac{boldsymbol{m} boldsymbol{g}}{boldsymbol{x}}, ) then the value of ( boldsymbol{x} )
is :
A . 10
B. 20
c. 15
( D )
11
547A large rimmed hoop with a bowling bal inside it rolls down an incline plane.
Identify the statements which best
describes the relationship between the
hoop and the bowling ball?
A. Their angular accelerations are the same
B. Their angular displacements are the same
c. Their angular velocities are the same
D. Their tangential displacements are the same
E. Their centripetal accelerations are the same
11
548A thin horizontal uniform rod ( A B ) of
mass ( m ) and length ( l ) can rotate freely about a vertical axis passing through its end ( A . ) At a certain moment, the end
( B ) starts experiencing a constant force
( F ) which is always perpendicular to the original position of the stationary rod
and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle ( theta ) measured relative to the initial position
11
549A steel plate of thickness ( h ) has the
shape of a square whose side equals ( l )
with ( h ll l . ) The plate is rigidly fixed to a
vertical axle ( O O ) which is rotated with a
constant angular acceleration ( boldsymbol{beta} ) (figure
shown above). Find the deflection ( lambda )
assuming the sagging to be small.
A ( cdot lambda=frac{9 rho beta l^{5}}{5 E h^{2}} )
B. ( lambda=frac{7 rho beta l^{5}}{3 E h^{2}} )
c. ( lambda=frac{7 rho beta l^{5}}{5 E h^{2}} )
D. None of these
11
550Two bodies have their moments of
inertia I and 21 respectively about their axis of rotation.lf their kinetic energies
of rotation are equal, their angular
momenta will be in the ratio-
A ( cdot sqrt{frac{3}{1}} )
в. ( sqrt{frac{6}{1}} )
c. ( sqrt{frac{2}{1}} )
D. ( sqrt{frac{5}{1}} )
11
551A length ( L=15 m ) if flexible tape is
tightly wound. It is then allowed to unwinding as it rolls down a fixed
incline that makes and angle ( boldsymbol{theta}=mathbf{3 0}^{circ} )
with the horizontal, the upper end of the
tape being fixed. Find the time taken (in
second) by the tapes to unwind completely. Neglect radius at any time
w.r.t. the length of the rope.
11
552A metre stick is balanced on a knife
edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the ( 12.0 mathrm{cm} ) mark, the stick is
found to be balanced at ( 45.0 mathrm{cm} . ) What
is the mass of the metre stick?
11
553Find the angular displacement (in rad) of a particle moving on a circle with angular velocity ( (2 pi) ) rad/s in ( 15 s )
( mathbf{A} cdot 2 pi )
B. ( 30 pi )
( c . pi )
D. ( 9 pi )
11
554A ladder is more apt to slip when you
are high up on its rung than when you are just begin to climb. Why?
A. When you are high up, the moment of force tending to rotate the ladder about its base increases, while in the latter case, the moment of the force is insufficient to cause slipping
B. When you are high up, the ladder is in unstable, equilibrium
C. As you climb up, your potential energy increases
D. When you are high up, the centre of gravity of the system shifts upwards so the ladder is unstable, while in the latter case the system is more stable
11
555n Fig. (i), a metre stick, half of which is
wood and the other half steel is pivoted at the wooden end at ( a ) ‘ and a Force ( mathrm{F} ) is
applied to the steel end a. In Fig(ii) the stick is pivoted at the steel end at a and
the same force ( F ) is applied at the wooden end at ( a^{prime} . ) The angular acceleration
A ( . ) In (i) is greater than in (ii)
B. In (ii) is greater than in (i)
c. Is equal both in (i) and (ii)
D. None of the above
11
556Two bodies ( m_{1} ) and ( m_{2} ) are attached to
the two ends of a string figure. The
string passes over a pulley of mass ( M )
and radius ( R ) If ( m_{1}>m_{2} ), then the
acceleration of the system is
A ( cdot frac{left.m_{1}-m_{2}+mright) g}{m_{1}+m_{2}+m} )
B. ( frac{left(m_{1}-m_{2}right) g}{m_{1}+m_{2}} )
c. ( frac{left(m_{1}+m_{2}right) g}{m_{1}-m_{2}} )
D. ( frac{left(m_{1}-m_{2}right) g}{m_{1}-m_{2}+m / 2} )
11
557Out of the following equations which is
WRONG?
A ( cdot vec{tau}=vec{r} times vec{F} )
B . ( vec{a} r=vec{omega} times vec{v} )
c. ( vec{a} t=vec{alpha} times vec{r} )
( mathbf{D} cdot vec{v}=vec{r} times vec{omega} )
11
558Three particles, each of mass ( m ), are
placed at the corner of right angle triangle as shown in the figure. if ( mathrm{OA}=mathrm{a} )
and ( mathrm{OB}=mathrm{b}, ) the position vector of the
centre of mass is :
(here ( hat{i} ) and ( hat{j} ) are unit vector along ( times ) and ( y ) axes, respectively
A ( cdot frac{1}{3}(a hat{i}+b hat{j}) )
B ( cdot frac{1}{3}(a hat{i}-b hat{j}) )
c ( cdot frac{2}{3}(a hat{i}+b hat{j}) )
( D )
11
559For the pivoted slender rod of length ( l ) as
shown in figure., find the angular
velocity as the bar reaches the vertical
position after being released in the
horizontal position
11
560A force ( -F widehat{k} ) acts on ( 0, ) the origin of the
coordinate system.The torque about the point (1,-1) is
A ( . F(hat{i}-hat{j}) )
B . ( -F(hat{i}+widehat{j}) )
C ( . F(hat{i}+widehat{j}) )
D . ( -F(hat{i}-widehat{j}) )
11
561What is the angular speed of the second hand of a clock? If the second hand is
10cm long, then find the linear speed of
its tip. (in ( r a d / s text { and } m / s) )
В. 1047,0.01047
c. 0.1047,1047
D. 0.0047,0.01047
11
562Two rings of radius ( R ) and ( n R ) made up of same material have the ratio of
moment of inertia about an axis
passing through centre ( 1: 8 . ) The value
of ( n ) is
A .2
B. ( 2 sqrt{2} )
( c cdot 4 )
D. ( frac{1}{2} )
11
563Find the static friction force acting on
the cone ( A, ) if ( omega=1.0 ) rad/s.
( mathbf{A} cdot F_{f r}=12 N )
( mathbf{B} cdot F_{f r}=6 N )
( mathbf{C} cdot F_{f r}=18 N )
( mathbf{D} cdot F_{f r}=3 N )
11
564Different minerals are being mined from within the earth and multi-
storeyed are being constructed. Due to this activity theoretically
A. Angular speed of earth would increase
B. Angular momentum would increase
c. Time period of earth would decrease
D. Length of day would increase
11
565A hemisphere and a solid cone have a common base. The centre of mass of the
common structure coincides with the
centre of the common base. If ( mathrm{R} ) is the
radius of hemisphere and h is the height of the cone, then :
A ( cdot frac{h}{R}=sqrt{3} )
в. ( frac{h}{R}=frac{1}{sqrt{3}} )
c. ( frac{h}{R}=3 )
D. ( frac{h}{R}=frac{1}{3} )
11
566If the velocity of the body is quadrupled then the momentum of the body
doubles.
A. True
B. False
11
567Two horizontal discs of different radii
are free to rotate about their central
vertical axes. One is given some angular
velocity, the other is stationary. Their rims are now brought in contact. There
is friction between the rims. Then which
of the following statement(s) is/are true
( ? )
This question has multiple correct options
A. The force of friction between the rims will disappear when the discs rotate with equal angular speeds.
B. The force of friction between the rims will disappear when they have equal linear velocities
C. The angular momentum of the system will be conserved.
D. The rotational kinetic energy of the system will not be conserved
11
568Find the centre of mass of three
particles at the vertices of an
equilateral triangle. The masses of the
particles are ( 100 g, 150 g, ) and ( 200 g )
respectively. Each side of the
equilateral triangle is 0.5 m long.
11
569The potential energy function for the
force between two atoms in a diatomic
molecule can be expressed approximately as ( U(r)=frac{a}{r^{12}}-frac{b}{r^{6}} )
where ( a ) and ( b ) are constants and ( r ) is the
separation between the atoms.
(a) Determine the force function ( boldsymbol{F}(boldsymbol{r}) )
(b) Find the value of for which the
molecule will be in the stable
equilibrium.
11
570Moment of inertia of a uniform rod of mass ( m ) and length ( l=sqrt{2} ) is ( frac{7}{12} m l^{2} ) about a line perpendicular to the rod. Find the distance of this line from the
middle point of the rod.
11
571The moment of inertia of a non-uniform
semicircular wire having mass ( m ) and
the plane of the wire through the centre is
( mathbf{A} cdot m r^{2} )
B. ( frac{1}{2} m r^{2} )
c. ( frac{1}{4} m r^{2} )
D. ( frac{2}{5}^{m r^{2}} )
11
572The angular momentum of a rotating
body changes from ( A_{0} ) to ( 4 A_{0} ) in 4 seconds. The torque acting on the body is :
A ( cdot frac{3}{4} A_{0} )
B . ( 4 A_{0} )
c. ( 3 A_{0} )
D. ( frac{3}{2} A_{0} )
11
573You are marooned on a frictionless
horizontal plane and cannot exert any
horizontal force by pushing against the
surface. How can you get off
( mathbf{A} cdot ) By jumping
B. By rolling your body on the surface
C. By splitting or sneezing or throwing any object
D. By throwing an object in opposite direction
11
574A hoop and a solid cylinder have the
same mass and radius. They both roll,
without slipping, on a horizontal
surface. If their kinetic energies are
equal, then:
A. the hoop has a greater translational speed than the cylinder
B. the cylinder has a greater translational speed than the hoop.
C. the hoop and the cylinder have the same translational speed.
D. the hoop has a greater rotational speed than the cylinder
11
575Ideally a rigid body is-
A. which is solid at room temperature.
B. on applying force the distance between two point does not change.
c. both of them
D. none of them
11
576A solid sphere, a hollow sphere and a disc, all having the same mass and
radeius, are placed at the top of an incline and released. The friction
coefficients between the objects and
the incline are same and not sufficient
to allow pure rolling. The least time will be taken in reaching the bottom by
A. the solid sphere
B. the hollow sphere
c. the disc
D. all will take the same time
11
577If they start together at ( t=0 ) at what
time does each reach the bottom?
11
578A circular disc of M.I. ( 10 mathrm{kg}-mathrm{m}^{2} ) rotates
about its own axis at a constant speed of 60 r.p.m. under the action of an
electric motor of power 31.4 W. If the motor is switched off, how many
rotations will it cover before coming to rest?
A . 3.14
в. 31.4
c. 314
D. 6.28
11
579Two block of equal mass are tied with a
light which passes over a masseless pulley as shown in figure. The magnitude of acceleration of centre of
mass of both the block is (neglect
friction everywhere)
A ( cdot frac{sqrt{3}-1}{2} g )
B ( cdot(sqrt{3}-1) g )
c. ( frac{g}{2} )
D. None of these
11
580A circular disc ( D_{1} ) of mass ( mathrm{M} ) and radius
R has two identical discs ( D_{2} ) and ( D_{3} ) of
the same mass ( mathrm{M} ) and radius ( mathrm{R} )
attached rigidly at its opposite ends(see figure). The moment of inertia of the system about the axis 00 ‘,
passing through the centre of ( D_{1}, ) as
shown in the figure, will be?
( mathbf{A} cdot 3 M R^{2} )
B. ( frac{2}{3} M R^{2} )
c. ( M R^{2} )
D. ( frac{4}{5} M R^{2} )
11
581At a given instant, four particle having
masses and acceleration as shown in
the figure lie at vertices of a square.
Acceleration of the center of mass of the
system is:
A ( cdot frac{1}{5}(hat{i}+hat{j}) )
B ( cdot frac{1}{5}(hat{j}-hat{i}) )
c. ( frac{1}{5}(hat{i}-hat{j}) )
D. ( -frac{1}{5}(hat{i}+hat{j}) )
11
582Two cars of masses ( m_{1} ) and ( m_{2} ) are
moving along the circular paths of
radius ( r_{1} ) and ( r_{2} ) respectively. The speeds are such that they complete one round at the same time. The ratio of
angular speeds of two cars is
В. ( r_{1}: r_{2} )
c. 1:
D. ( m_{1} r_{1}: m_{2} r_{2} )
11
583A hollow sphere partly filled with water has moment of inertia ( I ) when it is
rotating about its own axis at an angular velocity ( omega . ) If its angular velocity
is doubled then its moment of
inertia becomes:
A . Less than ( I )
B. More than I
c. ( I )
D. zero
11
584A solid sphere and a hollow sphere of
the same mass have the same M.I.
A .1: 2
B. ( sqrt{3}: sqrt{5} )
c. ( sqrt{5}: sqrt{2} )
D. 5: 4
11
585A hollow cylinder has mass ( M ) outside
moments of inertia about an axis
parallel to its symmetry axis and tangent to the outer surface in equal to:
( ^{mathrm{A}} cdot frac{M}{2}left(R_{2}^{2}+R_{1}^{2}right) )
B. ( frac{M}{2}left(R_{2}^{2}-R_{1}^{2}right) )
c. ( frac{M}{4}left(R_{2}+R_{1}right)^{2} )
D. ( frac{M}{2}left(3 R_{2}^{2}+R_{1}^{2}right) )
11
586Two man ‘A’ and ‘B’ are standing on opposite edge of a ( 6 mathrm{m} ) long platform which is further kept on a smooth floor.
They starts moving towards each other and finally meet at the midpoint of platform. Find the displacement of platform. Find the displacement of platform if mass of ( A, B ) and platform ( operatorname{are} 40 mathrm{kg}, 60 mathrm{kg} ) and ( 50 mathrm{kg} ) respectively.
11
587A slender uniform rod of mass ( mathrm{M} ) and
length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The
angular acceleration of the rod when it
makes an angle ( theta ) with vertical is
A ( cdot frac{3 g}{2 l} cos theta )
в. ( frac{2 g}{3 l} cos theta )
( c )
D.
11
588a body is rotating nonuniformly about a vetical axis fixed is an intertial frame.
The resultant force on a particle of the
body not on the axis is
A. Vetical
B. horizontal and skew with the axis
c. horizontal and intersection the axis
D. None of these
11
589In an experiment with a beam balance,
an unknown mass ( m ) is balanced by two
known masses of ( 16 mathrm{kg} ) and ( 4 mathrm{kg} ) as
shown in fig. Find ( boldsymbol{m} )
A . ( 10 mathrm{kg} )
B. ( 6 k g )
( c .8 k g )
D. ( 12 mathrm{kg} )
11
590The M.I. of a disc about an axis passing through its centre and perpendicular to plane is ( frac{1}{2} M R^{2}, ) then its M.I. about a tangent parallel to its diameter is
( ^{mathbf{A}} cdot frac{1}{2} M R^{2} )
в. ( frac{4}{5} M R^{2} )
c. ( frac{5}{4} M R^{2} )
D. ( frac{3}{4} M R^{2} )
11
591Which is the only vector quantity out of the following?
A. Charge of a gold leaf electroscope
B. Electrostatic potential
c. current flowing in a metal
D. Angular momentum of a spinning body
11
592A car (open at the top) of mass ( 9.75 mathrm{kg} ) is coasting along a level track at 1.36 ( mathrm{m} / mathrm{s}, ) when it begins to rain hard. The raindrops fall vertically with respect to the ground. When it has collected 0.5 kg of rain, the speed of the car is
A. ( 0.68 mathrm{m} / mathrm{s} )
B. 1.29 ( mathrm{m} / mathrm{s} )
c. ( 2.48 mathrm{m} / mathrm{s} )
D. ( 9.8 mathrm{m} / mathrm{s} )
11
593A sphere is rotating between two tough
inclined walls as shown in figure.

Coefficient of friction between each wall
and the sphere is ( 1 / 3 . ) If ( f_{1} ) and ( f_{2} ) be the
friction forces at ( P ) and ( Q . ) Then ( frac{f_{1}}{f_{2}} ) is:
A ( cdot frac{4}{sqrt{3}}+1 )
B. ( frac{1}{sqrt{3}}+2 )
c. ( frac{4}{2}+sqrt{3} )
D. ( 1+2 sqrt{3} )

11
594Assertion
If no external force acts on a system of
particles, then the centre of mass will
not move in any direction.
Reason
If net external force is zero, then the
linear momentum of the system
changes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
595A wheel having moment of inertia
( 4 k g m^{2} ) about its symmetrical axis, rotates at rate of 240 rpm about it. The torque which can stop the rotation of the wheel in one minute is:
( ^{mathbf{A}} cdot frac{5 pi}{7} N m )
в. ( frac{8 pi}{15} mathrm{Nm} )
c. ( frac{2 pi}{9} N m )
D. ( frac{3 pi}{7} N m )
11
596A light non-stretchable thread is wound
on a massive fixed pulley of radius ( boldsymbol{R} ). A
small body of mass ( m ) is tied to the free
endof the thread. At a moment ( t=0 ) the
system is released and starts moving. Find its angular momentum relative to
the pulley axle as a function of time ( t )
11
597A thin rod of length ( 3 mathrm{L} ) is bent at right
angles at a distance ( L ) from one end.
Locate the centre of mass of the
arrangement w.r.t the corner (see figure). (Given, ( L=1 mathrm{m} ) )
( mathbf{A} cdot r_{C O M}=(0.2 hat{i}+0.8 hat{j}) mathrm{m} )
B ( cdot r_{C O M}=(0.4 hat{i}+0.6 hat{j}) mathrm{m} )
( mathbf{c} cdot r_{C O M}=(0.5 hat{i}+hat{j}) m )
( mathbf{D} cdot r_{C O M}=(0.2 hat{i}+0.6 hat{j}) m )
11
598Let ( l_{1} ) and ( l_{2} ) be the moment of inertia of
a uniform square plate about axes APC
and OPO’ respectively as shown in the figure. ( P ) is centre of square. The ratio ( frac{I_{1}}{I_{2}} ) of moment of inertia is :
A ( cdot frac{1}{sqrt{2}} )
B. 2
( c cdot frac{1}{2} )
D.
11
599Two particles ( A ) and ( B ) initially at rest, move towards each other under a
mutual force of attraction. At the
instant when the speed of A is v and speed of ( mathrm{B} ) is ( 2 mathrm{v} ), the speed of centre of
mass of the system is :
A. zero
в.
( c cdot 1.5 v )
D. 3
11
600A solid cylinder of mass ( 50 mathrm{kg} ) and radius ( 0.5 mathrm{m} ) is free to rotate about horizontal axis. A massless string
is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2
revolutions ( s^{-2} ) is :
A. 25
B. 50 N
c. 78.5 N
D. 157 N
11
601A truck is moving with the speed of
( 20 m / s ) and having a momentum of ( 12,000 k g m / s . ) Find out the mass of
the truck?
A. ( 240,000 k g )
в. 6,000 kg
c. ( 1,200 k g )
D. ( 600 k g )
E . ( 120 k g )
11
602A solid cylinder has mass ‘ ( M ) ‘, radius ‘ ( boldsymbol{R} ) and length ‘l’. Its moment of inertia about an axis passing through its center and perpendicular to its own axis is
( ^{mathrm{A}} cdot frac{2 M R^{2}}{3}+frac{M l^{2}}{12} )
B. ( frac{M R^{2}}{3}+frac{M l^{2}}{12} )
( ^{mathbf{C}} cdot frac{3 M R^{2}}{4}+frac{M l^{2}}{12} )
D. ( frac{M R^{2}}{4}+frac{M l^{2}}{12} )
11
603A spherical rigid ball is released from rest and starts rolling down an inclined
plane from height ( h=7 m ), as shown in
the figure, It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of the both the
ball and the block is ( m ) and the ball is
rolling without sliding, then the speed of the after collision is close to :
( A cdot 6 m / s )
в. ( 8 m / s )
c. ( 10 m / s )
D. ( 12 m / s )
11
604( vec{A} ) and ( vec{B} ) are two vectors in a plane at an
angle of ( 60^{0} ) with each other. ( vec{C} ) is
another vector perpendicular to the plane containing vectors ( overrightarrow{boldsymbol{A}} ) and ( overrightarrow{boldsymbol{B}} ) Which of the following relations is possible?
A ( cdot vec{A}+vec{B}=vec{C} )
в. ( vec{A}+vec{C}=vec{B} )
c. ( vec{A} times vec{B}=vec{C} )
D. ( vec{A} times vec{C}=vec{B} )
11
605Find the moment of inertia of a hollow
sphere about a chord that is at a distance of ( 3 mathrm{m} ) from the centre of the
sphere. The radius of the sphere is ( 5 mathrm{m} ) and mass ( =10 mathrm{kg} )
A. ( 257 k g-m^{2} )
B . ( 57 k g-m^{2} )
c. ( 27 k g-m^{2} )
D. ( 157 k g-m^{2} )
11
606Explain why friction is necessary to make the disc in Fig. roll in the direction indicated.
(a) Give the direction of frictional force
at ( mathrm{B} ), and the sense of frictional torque,
before perfect rolling begins.
(b) What is the force of friction after
perfect rolling begins?
11
607State S.I. unit of angular momentum
Obtain its dimensions.
11
608Two stars each of one solar mass ( (= )
( left.2 times 10^{30} k gright) ) are approaching each other
for a head on collision. When they are a
distance ( 10^{9} k m, ) their speeds are
negligible. What is the speed with which they collide? The radius of each star is ( 10^{4} k m . ) Assume the stars to remain
undistorted until they collide. (Use the
known value of ( G ) )
11
609The ration of the linear velocities of
point at distance ( r ) and ( frac{r}{4} ) from the axis
rotation of a rigid body is
A . 0.25
B. 2
( c cdot 4 )
D. 0.5
11
610Four particles, each of mass ( 1 mathrm{kg} ) are placed at the corners of a square OABC of side ( 1 mathrm{m} .0 ) is at the origin of the coordinate system. OA and OC are aligned along positive X-axis and positive Y-axis respectively. the position the vector of the center of mass is (in
( mathrm{m}) )
11
611Two particles ( A ) and ( B ) are moving as
shown in the figure. At this moment
of time the angular speed of ( A ) with
respect to ( B ) is
A ( cdot frac{1}{rleft(v_{a}+v_{b}right)} )
B. ( frac{v_{a} sin theta_{a}+v_{b} sin theta_{b}}{r} ) in the anticlockwise direction
c. ( frac{v_{a} sin theta_{a}-v_{b} sin theta_{b}}{r} ) in the clockwise direction
D ( frac{1}{rleft(v_{a}-v_{b}right)} )
11
612A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the
ship is stationary with respect to water,
the tension in the string is ( T_{0} . ) Find the difference between tension when the
ship is sailing with a velocity ( v )
A . mv
B. 2 mv ( omega )
c. ( frac{m v omega}{2} )
D. ( sqrt{2} m v omega )
11
613Three rods of the same mass are placed as shown in the figure. What will be the coordinate of centre of mass of the
system?
A ( cdotleft(frac{2 a}{3}, frac{2 a}{3}right) )
B・ ( left(frac{4 a}{3}, frac{4 a}{3}right) )
( mathbf{c} cdotleft(frac{a}{3}, frac{a}{3}right) )
D. ( left(frac{5 a}{6}, frac{4 a}{9}right) )
11
614From a complete ring of mass ( M ) and
radius ( R, ) a ( 30^{circ} ) sector is removed. The
moment of inertia of the incomplete
ring about an axis passing through the
centre of the ring and perpendicular to the plane of the ring is
( ^{A} cdot frac{9}{12} M R^{2} )
( ^{text {В }} frac{11}{12}^{M R^{2}} )
( ^{mathrm{c}} cdot frac{11.3}{12} M R^{2} )
D. ( M R^{2} )
11
615The displacement of centre of mass of
( A+B ) system till the string becomes
vertical is :
A. zer
в. ( frac{L}{2}(1-cos theta) )
c ( cdot frac{L}{2}(1-sin theta) )
D. none of these
11
616It is easier to roll a stone up a sloping
road than to lift it vertical upwards
because
A. work done in rolling is more than in lifting
B. work done in lifting the stone is equal to rolling it
C. work done in both is same but the rate of doing work is less in rolling
D. work done in rolling a stone is less than in lifting it
11
617A block of mass ( 12 mathrm{Kg} ) is attached to a
string wrapped around a wheel of
radius ( 10 mathrm{cm} . ) The acceleration of the
block moving down an inclined plane is
measured as ( 2 m / s^{2} . ) The tension in the string is :
A . ( 24.5 N )
B. ( 68.7 N )
c. ( 23.4 N )
D. ( 46.8 N )
11
618In the figure shown, the plank is being
pulled to the right with a constant
speed ( v . ) If the cylinder does not slip
then
A. The speed of the centre of mass of the cylinder is 22
B. The speed of the centre of mass of the cylinder is zero
C. The angular velocity of the cylinder is ( v / R )
D. The angular velocity of the cylinder is zero
11
619Moment of inertia of a thin semi
circular disc ( (operatorname{mass}=M & text { radius }=R) )
about an axis through point 0 and perpendicular to plane of disc, is given
by :
( ^{mathrm{A}} cdot frac{1}{4} M R^{2} )
B. ( frac{1}{2} M R^{2} )
c. ( frac{1}{8} M R^{2} )
D. ( M R^{2} )
11
6202. A system is shown in Fig. 6.351. Assume that the cylinder
remains in contact with the two wedges. Then the velocity
of cylinder is
Cylinder
2u ms-
ums-
30°
30°
Fig. 6.351
a. V19-473 ms-1
c. ſums
b. V13 u ms-1
d. ſimst
11
621If a rigid body rolls on a surface without
slipping, then:
A. linear speed is maximum at the highest point but minimum at the point of contact
B. linear speed is minimum at highest point but maximum at the point of contact
C. linear speed is same at all points of the rigid body
D. angular speed is different at different points of a rigid body
11
622( underbrace{=}_{i=0} )11
623A machine part consist of two
homogeneous solid cylinders coaxially.
Then find the distance of center of mass
from 0
( mathbf{A} cdot frac{17}{2} m m )
( mathbf{B} cdot frac{52}{7} m m )
( mathbf{c} cdot frac{15}{17} m m )
( mathbf{D} cdot frac{12}{7} m m )
11
624The line of action of a force ( overrightarrow{boldsymbol{F}}= )
( (-3 hat{i}+hat{j}+5 hat{k}) N ) passes through ( a )
point ( (7,3,1) . ) The moment of force ( (vec{tau}=vec{r} times vec{F}) ) about the origin is given by
( mathbf{A} cdot 14 hat{i}+38 hat{j}+16 hat{k} )
B . ( 14 hat{i}+38 hat{j}-16 hat{k} )
c. ( 14 hat{i}-38 hat{j}+16 hat{k} )
D. ( 14 hat{i}-38 hat{j}-16 hat{k} )
11
625fall the masses in the figure have a
mass of ( 2 k g ) and ( m_{2} ) has speed ( 2 m / s )
and ( m_{3} ) has a speed of ( 4 m / s, ) what is
the ( x ) -component of the momentum of
the centre of mass of system?
A. 2 kg ( m / s )
B. 4 kg ( m / s )
c. ( 6 mathrm{kg} mathrm{m} / mathrm{s} )
D. ( 10 mathrm{kg} mathrm{m} / mathrm{s} )
11
626The figure below shows a pattern of two
fishes. Write the mapping rule for the
rotation of Image A to Image B.
A. Image B has to be rotated by 90 degrees anticlockwise to map with image ( A )
B. Image B should first have a mirror reflection and then be rotated to map with image ( A )
C. The width of image B should be reduced by 1 unit ( square in the graph shown) and then rotated by 90 degrees to map with image ( A )
D. The width of image B should be increased by 1 unit square in the graph shown) and then rotated by 90 degrees to map with image ( A )
11
627A loop and a disc roll without slipping
with same linear velocity ( v ). The mass of
the loop and the disc is same. If the total kinetic energy of the loop is ( 8 J )
find the kinetic energy of the disc (in ( J) )
11
628A circular platform is mounted on a
vertical frictionless axle. Its radius is
( r=2 m ) and its moment inertia is ( I= )
( 200 k g m^{2} . ) It is initially at rest. A ( 70 k g )
man stands on the edge of the platform
and begins to walk along the edge at
speed ( v_{0}=10 m s^{-1} ) relative to the
ground. The angular velocity of the
platform is
A ( .1 .2 mathrm{rad} mathrm{s}^{-1} )
B. 0.4 rad ( s^{-1} )
c. 2.0 rad ( s^{-1} )
D. 7.0 rad ( s^{-1} )
11
629Four particles are in ( x-y ) plane at :
(1) ( 1 k g ) at (0,0)( quad(2) 2 k g ) at
(1,0)( quad(3) 3 k g ) at (1,2)
(4) ( 4 k g ) at (2,0)
The centre of mass is located at:
A. (0.3,1.2)
В. (1.3,0.6)
c. (0.5,1.4)
D. (1.2,0.3)
11
630The moments of inertia of a non-
uniform circular disc (of mass ( mathrm{M} ) and
radius ( R ) ) about four mutually perpendicular tangents ( A B, B C C D, D A )
( operatorname{are} I_{1}, I_{2}, I_{3} ) and ( I_{4} ) respectively (the
square ABCD circumscribes the circle.)
The distance of the center of mass of
the disc from its geometrical center is
given by
A ( cdot frac{1}{4 M R} sqrt{left(I_{3}-I_{3}right)^{2}+left(I_{2}-I_{4}right)^{2}} )
B ( cdot frac{1}{12 M R} sqrt{left(I_{3}-I_{3}right)^{2}+left(I_{2}-I_{4}right)^{2}} )
C ( cdot frac{1}{3 M R} sqrt{left(I_{1}-I_{2}right)^{2}+left(I_{3}-I_{4}right)^{2}} )
D. ( frac{1}{2 M R} sqrt{left(I_{1}-I_{2}right)^{2}+left(I_{3}-I_{4}right)^{2}} )
11
631A solid hemisphere of radius R is
mounted on a solid cylinder of same
radius and density as shown. The height of the cylinder is such that resulting center of mass is ( 0 . ) If the radius of the
sphere is ( 2 sqrt{2} m ) and the height of the
cylinder is ( n ) meter. Find ( n )
11
632A cannon ball of mass ( 5 mathrm{kg} ) is discharged horizontally with a velocity of ( 500 m / s . ) If the cannon be free to move on the horizontal ground, what is the velocity with which it recoils? Mass of
the cannon is ( 100 mathrm{kg} )
A . ( 15 mathrm{m} / mathrm{s} )
B. 25m/s
( c cdot 35 m / s )
D. ( 45 mathrm{m} / mathrm{s} )
11
633Three particle ( A, B, C ) mass ( m, 2 m & m )
are connected with the cup of massless
rod of length I. Rod can rotate freely
about c. Sys. released from rest when
rod almost vertical. ( A & B ) start moving
in opposite direction. Find
displacement of ( C ) when it list the ground.
11
634For the given square lamina, the
moment of inertia through EF and ( A C ) is
11
635Three particles, each of mass m are
placed at the vertices of a right angled triangle as shown in figure. The position
vector of the center of mass of the
system is:
(O is the origin and ( hat{i}, hat{j}, hat{k} ) are unit vectors)
A ( cdot frac{2}{3}(a hat{i}+b hat{j}) )
B ( cdot frac{2}{3}(a hat{i}-b hat{j}) )
c. ( frac{1}{3}(a hat{i}+b hat{j}) )
D ( cdot frac{1}{3}(a hat{i}-b hat{j}) )
11
636Derive an expression for kinetic energy,
when a rigid body is rolling on a horizontal surface without slipping.
Hence find kinetic energy for a solid sphere
11
637The ratio of the radii of gyration of the disc about its axis and about a tangent perpendicular to its plane will be:
A ( cdot frac{1}{sqrt{3}} )
в. ( sqrt{frac{3}{2}} )
c. ( frac{1}{sqrt{2}} )
D. ( sqrt{frac{5}{3}} )
11
638A solid disk is rolling without slipping on a level surface at a constant speed of
( 2.00 m / s . ) How far can it roll up a ( 30^{circ} )
ramp before it stops? (Take ( boldsymbol{g}= )
( left.9.8 m / s^{2}right) )
11
639which is free to rotate about the smooth
vertical hinge passing through the center and perpendicular to the plate, is lying on a smooth horizontal surface. A
particle of mass ( m ) moving with speed
( u^{prime} ) collides with the plate and sticks to
it as shown in figure. The angular velocity of the plate after collision will
be:
( A cdot frac{12}{5} )
B. ( frac{12}{19} )
c. ( frac{3}{-} underline{u} )
( 2 a )
D. ( frac{3}{5} )
11
640A circular disc of radius ( mathrm{R} ) is removed
from a bigger circular disc of radius ( 2 mathrm{R} ) such that the circumference of the
discs coincide. The centre of mass of
the new disc is ( alpha R ) from the centre of
the bigger disc. The value of ( alpha ) is
A. ( 1 / 3 )
B. ( 1 / 2 )
c. ( 1 / 6 )
D. ( 1 / 4 )
11
641A cylinder of mass ( M_{c} ) and sphere of
( operatorname{mass} M_{s} ) are placed at points ( A ) and ( B )
of two inclines, respectively. (See

Figure). If they roll on the incline without
slipping such that their accelerations are the same, then the ratio ( frac{sin theta_{c}}{sin theta_{s}} ) is :
( A cdot sqrt{frac{8}{7}} )
B. ( sqrt{frac{15}{14}} )
( c )
7
D. 15
14

11
642Jet plane works on the principal of conservation of
A. mass
B. energy
c. linear momentum
D. angular momentum
11
643A uniform cylinder of mass ( M ) and
radius ( R ) has a string wrapped around
it. The string is held fixed and the
cylinder falls vertically, as in figure. Show that the acceleration of the
cylinder is downward with magnitude ( boldsymbol{a}=frac{mathbf{2} boldsymbol{g}}{mathbf{3}} )
11
644The uniform disc shown in the figure
has a moment of inertia of ( 0.6 k g m^{2} )
around the axis that passes through 0
and is perpendicular to the plane of the
page. If a segment is cut out from
the disc as shown, the moment of inertia of the remaining disc is ( frac{1}{x} k g m^{2} )
Find ( x )
11
645If ( overrightarrow{boldsymbol{A}}=(1,1,1), vec{C}=(0,1,-1) ) are given
vectors, then a vector ( vec{B} ) satisfying the equation ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{C}} ) and
( vec{A} cdot vec{B}=3 ) is :
( A cdot(5,2,2) )
B. ( left(frac{5}{3}, frac{2}{3}, frac{2}{3}right) )
c. ( left(frac{2}{3}, frac{5}{3}, frac{2}{3}right) )
D. ( left(frac{2}{3}, frac{2}{3}, frac{5}{3}right) )
11
646The moments of inertia of a thin square
plate ( A B C D ) of uniform thickness
about an axis passing through the
centre ( boldsymbol{O} ) and perpendicular to the plate
are
This question has multiple correct options
( mathbf{A} cdot I_{1}+I_{2} )
B. ( I_{3}+I_{4} )
c. ( I_{1}+I_{3} )
D. ( I_{2}+I_{3} )
11
647The C. M. of a uniform card board cut in
T shape as shown in figure is:
4. ( 4 mathrm{cm} ) from A towards
B. ( 4 mathrm{cm} ) from B towards
( mathrm{c} .3 mathrm{cm} ) from ( mathrm{B} ) towards ( mathrm{A} )
D. 3 cm from A towards
11
648A force ( overrightarrow{boldsymbol{F}}=boldsymbol{alpha} hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}+boldsymbol{6} hat{boldsymbol{k}} ) is acting at ( mathbf{a} )
point ( vec{r}=2 hat{i}-6 hat{j}-12 hat{k} . ) The value of ( alpha ) for which angular momentum about origine is conserved is
( mathbf{A} cdot mathbf{1} )
B. –
( c cdot 2 )
D. zero
11
649A particle of mass ( m ) is moving with
constant velocity ( v ) parallel to the ( x- )
axis as shown in the figure. Its angular
momentum about origin ( O ) is
A . ( m v b )
B. mva
c. ( m v sqrt{a^{2}+b^{2}} )
D. ( m v(a+b) )
11
650I wo lathtical roas one and two each on
mass M and length L are performing
general plane motion on the horizontal
plane as shown in the figure if ( V ) is
velocity of center of mass of both the
rods and ( omega ) is the angular speed about
the certical axis then angular momentum of rod 1 in the frame of
reference of center of mass of rod 2 at
the given instant will be
( ^{mathbf{A}} cdotleft(M v frac{3 L}{2}+frac{M L^{2}}{12} omegaright)(-k) )
B ( cdotleft(M v frac{3 L}{2}right)(-k) )
( ^{mathbf{C}} cdotleft(frac{M L^{2}}{12} omegaright)(-K) )
D ( cdotleft(M v frac{3 L}{4}right)(-k) )
11
651The diagram below shows a lever of uniform mass, supported at the middle point. Four coins of equal masses are placed at mark 4 on the left hand side. Where should be 5 coins of same mass,
as that of previous coins be located to balance the lever?
11
652A disc of mass ( m ), radius ( r ) wrapped
over by a light and inextensible string is
pulled by force ( boldsymbol{F} ) at the free end of the string. If it moves on a smooth
horizontal surface, find linear and
angular acceleration of the disc.
11
653is rotated about an axis passing
through the point ( P ) as shown in figure.
The magnitude of angular momentum
of the rod, about the rotational axis ( y y^{prime} )
passing through the point ( boldsymbol{P} ) is
A ( cdot frac{M L^{2}}{18} )
B. ( frac{M(x+y)^{2}}{9} )
c. ( frac{Mleft(L^{2}+x^{2}right)}{9} )
D. ( frac{Mleft(L^{2}+2 y^{2}right)}{18} )
11
654A particle of charge ( Q ) and mass ( m )
travels through a potential difference ( V ) from rest. The final momentum of the
particle is:
A ( cdot p=sqrt{frac{Q m}{V}} )
в. ( P=sqrt{Q V} )
c. ( P=sqrt{2 m Q V} )
D. ( P=sqrt{frac{2 Q V}{m}} )
11
655A cord is wound around the
circumference of wheel of radius ‘r’. The
axis of the wheel is horizontal and
moment of inertia about it is ‘l’. The
weight ‘mg’ is attached to the end of the cord and falls from rest. After falling
through a distance ‘h’, the angular
velocity of the wheel will be
( mathbf{A} cdot[m g h]^{1 / 2} )
B. ( left[frac{m g h}{I+2 m r^{2}}right]^{1 / 2} )
c. ( left[frac{2 m g h}{I+m r^{2}}right]^{1 / 2} )
D. ( left[frac{m g h}{I+m r^{2}}right]^{1 / 2} )
11
656The diagonals of a parallelogram are represented by ( R_{1}=3 hat{i}+2 hat{j}-7 hat{k} ) and ( boldsymbol{R}_{2}=mathbf{5} hat{boldsymbol{i}}+boldsymbol{6} hat{boldsymbol{j}}-boldsymbol{3} hat{k} . ) Find the area of the
parallelogram.
11
657Which of the following statements can
be suitable?
A. Rotational motion is a type of circular motion.
B. Circular motion is similar to rotational motion.
C. Rotational and circular motion are fundamentally unrelated.
D. None of these
11
658While opening a tap with two fingers, the forces applied are
A . equal in magnitude
B. parallel to each other
c. opposite in direction
D. All of the above
11
659A wheel has moment of inertia ( 5 x )
( 10^{-3} k g m^{2} ) and is making 20 rev/sec.
The torque needed to stop it in 10 sec is
[
mathbf{x} mathbf{1 0}^{-mathbf{2}} mathbf{N}-boldsymbol{m}:
]
A . ( 2 pi )
в. ( 2.5 pi )
c. ( 4 pi )
D. ( 4.5 pi )
11
660A uniform meter scale of mass ( 1 k g ) is placed on table such that a part of the scale is beyond the edge. If a body of
mass ( 0.25 k g ) is hung at the end of the scale then the minimum length of
scale that should lie on the table so that
it does not tilt is :
( mathbf{A} cdot 90 mathrm{cm} )
B. ( 80 mathrm{cm} )
( mathbf{c} .70 mathrm{cm} )
D. ( 60 mathrm{cm} )
11
661Two bodies, ( A ) and ( B ) initially, at rest, move towards each other under mutual force of attraction. At the instant when
the speed of ( A ) is ( v ) and that of ( B ) is ( 2 v )
the speed of the center of mass of the
bodies is
A . ( 3 v )
B . ( 2 v )
c. ( 1.5 v )
D. zero
11
662Calculate Moment of force ( F_{2} ) about ( O )
A. ( 10 N m ) (clockwise)
B. ( 10 N ) m (anti clockwise)
c. ( 12 N m ) (clockwise).
D. ( 12 N m ) (anti clockwise)
11
663A spring wrapped on a wheel of MOI 0.2
( mathrm{kg} mathrm{m}^{2} ) and radius ( 10 mathrm{cm} ) over a light
pulley to support a block of mass ( 2 mathrm{kg} ) as shown in fig. Find the acceleration of the block.
A ( cdot 0.89 mathrm{ms}^{-2} )
B. ( 1.12 mathrm{ms}^{-2} )
( c cdot 0.69 mathrm{ms}^{-2} )
D. none
11
664A uniform meter rule balances
horizontally on a knife-edge placed at the ( 60 mathrm{cm} ) mark when a weight of ( 1 mathrm{g} ) is suspended from one end. What is the weight of the rule?
11
665ILLUSTRATION 9.24 A cylindrical drum, pushed along by a
board rolls forward on the ground. There is no slipping at any
contact. Find the distance moved by
the man who is pushing the board,
when axis of the cylinder covers a
distance L.
11
666A flywheel rotates at a constant speed
of 3000 rpm. The angle described by the
shaft in radian in one second is:
( mathbf{A} cdot 3000 pi )
в. ( 100 pi )
( c .50 pi )
D. ( 2 pi )
11
667below?
The shape is uniformly dense.
All answers are stated with respect to
the origin, which is at the center of the
large sphere.
( ^{mathbf{A}} cdotleft(0, frac{R}{2}right) )
B. ( left(0, frac{R}{4}right) )
c. ( left(0,-frac{R}{4}right) )
D. ( left(0,-frac{R}{6}right) )
( E cdotleft(0,-frac{R}{3}right) )
11
668A couple always tends to produce:
A. Linear motion
B. Rotatory motion
C. Both linear and rotatory motion
D. Vibratory motion
11
669A couple produces
A. Linear motion
B. Rotational motion
c. Both ( A ) and ( B )
D. Nether ( A ) nor ( B )
11
670A hollow cylinder with a very thin wall and a block are placed at rest at the top
of a plane with inclination ( boldsymbol{theta}=mathbf{4 5}^{circ} )
above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found
that both objects reach the bottom of the plane simultaneously. If the coefficient of kinetic friction between
the block and the plane is ( mu, ) the value of
( 18 mu ) is
11
671A man of mass ( m ) moves on a plank of
mass ( M ) with a constant velocity ( u ) with
respect to the plank. as shown in Fig.
a) If the plank rests on a smooth
horizontal surface, determine the
velocity of the plank.
b) If the man travels a distance ( L ) with
respect to the plank, find the distance
travelled by the plank with respect to the ground.
11
672The angular momentum of an electron revolving in a circular orbit is
What is its magnetic moment?
A ( cdot frac{m}{2 e} )
B. ( frac{e J}{2 m} )
( c cdot frac{2 m}{e J} )
( D cdot frac{e m J}{2} )
11
673A circular disc rotates in a vertical
plane about a fixed horizontal axis which passes through a point ( X ) on the circumference of disc. When the centre
of the disc moves with speed ( v ), the
speed of the opposite end of the
diameter through ( boldsymbol{X} ) is
A ( .2 v )
B. ( sqrt{2} v )
( c )
D. ( v / 2 )
11
674Solid body with no deformation is-
A. rigid body
B. liquid body
c. both of them
D. none of them
11
675Find coordinates of center of mass of a
quarter ring of radius ( r ) placed in the first quadrant of a Cartesian coordinate system, with centre at origin.
11
676Equal torques are applied about a central axis on two rings of same mass and same thickness but made up of different materials. If ratio of their
densities is 4: 1 then the ratio of their
angular acceleration will be :
A . 4: 1
B. 1: 16
( c cdot 8: 1 )
D. 1: 12
11
677A wheel of moment of inertia ( 5 times )
( 10^{-3} k g m^{2} ) is making 20 rev ( / s . ) The
torque required to stop it in ( 10 s ) is :
A ( cdot 2 pi times 10^{-2} N m )
В . ( 2 pi times 10^{2} N m )
( mathbf{c} cdot 4 pi times 10^{-2} N m )
D. ( 4 pi times 10^{2} N m )
11
678A thin uniform rod of mass m moves
translationally with acceleration a due to two antiparallel force of lever arm ( I )
One force is of magnitude ( F ) and acts at one extreme end. The length of the rod is:
A ( cdot frac{2(F+m a) I}{m a} )
B. ( _{Ileft(1+frac{F}{m a}right)} )
c. ( frac{(F+m a) I}{2 m a} )
D. ( frac{m a I}{m a+F} )
11
679Find the unit vectors perpendicular to
each of the following pairs of vectors:
( vec{i}+vec{j}+vec{k} ) and ( vec{i}+overrightarrow{2} j-vec{k} )
( mathbf{A} cdot a_{1} vec{i}+a_{2} vec{j}+a_{3} vec{k}, ) where ( a_{1}=mp 3 / sqrt{14}, a_{2}= )
( pm 2 / sqrt{14}, a_{3}=pm 1 / sqrt{14} )
B ( cdot a_{1} vec{i}+a_{2} vec{j}+a_{3} vec{k}, ) where ( a_{1}=mp 3 / sqrt{14}, a_{2}= )
( pm 2 / sqrt{14}, a_{3}=pm 2 / sqrt{14} )
C ( cdot a_{1} vec{i}+a_{2} vec{j}+a_{3} vec{k}, ) where ( a_{1}=mp 2 / sqrt{14}, a_{2}= )
( pm 2 / sqrt{14}, a_{3}=pm 1 / sqrt{14} )
( mathbf{D} cdot a_{1} vec{i}+a_{2} vec{j}+a_{3} vec{k}, ) where ( a_{1}=mp 3 / sqrt{14}, a_{2}= )
( pm 2 / sqrt{14}, a_{3}=pm 3 / sqrt{14} )
11
680Lower surface of a plank is rough and
lying at rest on a rough horizontal surface. Upper surface of the plank is smooth and has a smooth hemisphere placed over it through a light string as shown in the figure. After the string is burnt, trajectory of centre of mass of the sphere is:
A . a circle
B. an ellipse
c. a stright line
D. a parabola
11
681The potential energy function for diatomic molecule is ( U(x)=frac{a}{x^{12}}-frac{b}{x^{6}} )
In a stable equilibrium, the distance between the particles is:
( ^{A} cdotleft(frac{2 a}{b}right)^{1 / 6} )
B. ( left(frac{a}{b}right)^{1 / 6} )
( ^{mathrm{c}}left(frac{b}{2 a}right)^{1 / 6} )
( left(frac{b}{a}right)^{1 / 6} )
11
682The centre of mass of the disk
undergoes simple harmonic motion
with angular frequency ( omega ) equal to:
( A cdot sqrt{frac{k}{M}} )
3. ( sqrt{frac{2 k}{M}} )
c. ( sqrt{frac{2 mathrm{k}}{3 mathrm{M}}} )
D
11
683The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is:
A . 2: 1
B. ( sqrt{5}: sqrt{6} )
c. 2: 3
D. ( 1: sqrt{2} )
11
684A tennis racket can be idealized as a
uniform ring of mass ( mathrm{M} ) and radius ( mathrm{R} ) attached to a uniform rod also of mass
M and length L. The rod and the ring are coplanar, and the line of the rod passes through the centre of the ring. The moment of inertia of the object (racket) about an axis through the centre of the ring and perpendicular to its plane is
A ( cdot frac{1}{12} Mleft(6 R^{2}+L^{2}right) )
B cdotfrac{12 } { 1 2 } M ( 1 8 R ^ { 2 } + L ^ { 2 } )
C ( cdot frac{1}{3} Mleft(6 R^{2}+L^{2}+3 L Rright) )
D. None of these
11
685fixed plane inclined at angle ( boldsymbol{theta} ) with
horizontal. A light string is tied to the cylinder at the right most point, and a
mass ( m ) hangs from the string, as
shown in. Assume that the coefficient of
friction between the cylinder and the
inclined plane is sufficiently large to
prevent slipping. For the cylinder to
remain static, the value of m is
( A cdot frac{M sin theta}{1-sin theta} )
B. ( frac{M cos theta}{1+sin theta} )
( c cdot frac{M sin theta}{1+sin theta} )
D. ( frac{M cos theta}{1-sin theta} )
11
686Calculate the M.I. of a thin uniform ring about an axis tangent to the ring and in a plane of the ring, if its M.I. about an axis passing through the centre and
perpendicular to plane is ( 4 k g m^{2} )
A ( cdot 12 k g m^{2} )
B. ( 3 k g m^{2} )
c. ( 6 k g m^{2} )
D. ( 9 k g m^{2} )
11
687The resultant of all the forces acting on the body in static equilibrium should be
equal to
A. one
B. zero
c. Two
D. More than one
11
688Three particles of mass ( 1 k g, 2 k g ) and
( 3 k g ) are placed at the corners ( A, B ) and
( C ) respectively of an equilateral triangle
( A B C ) of edge 1 m. Find the distance of their centre of mass from ( boldsymbol{A} )
11
689Area of a parallelogram, whose diagonals are ( 3 hat{i}+hat{j}-2 hat{k} ) and ( hat{i}-3 hat{j}+ ) ( 4 hat{k} ) will be
A . ( 14 u n i t )
B. ( 5 sqrt{3} ) unit
c. ( 10 sqrt{3} ) unit
D. ( 20 sqrt{3} u ) unit.
11
690Three rings, each of mass ( m ) and radius
( r, ) are so placed that they touch each
other. Find the moment of inertia about
the axis as shown in the figure:
( A cdot 5 m r^{2} )
B. ( frac{5}{7} m r^{2} )
( c cdot 7 m r^{2} )
11
691Moment of any force is equal to the algebraic sum of the component of that force. This statement is known as:
A. Principle of moment
B. Varignon’s theorem
c. Both A and B
D. None
11
692An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest rotational momentum is (if rotated with same angular momentum)
A. solid sphere
B. spherical shell
c. solid disc
D. thin hollow cylinder
11
693Given, ( vec{omega}=2 hat{k} ) and ( vec{r}=2 hat{i}+2 hat{j} . ) Find the linear velocity.
A ( cdot 4 hat{i}+4 hat{j} )
B – ( 4 hat{i}-4 hat{k} )
( mathbf{c} cdot_{-4 hat{i}+4 hat{j}} )
D. ( -4 hat{i}-4 hat{j} )
11
694A bicycle tyre in motion has:
A. linear motion only
B. rotatory motion only
c. linear and rotatory motion
D. vibratory motion only
11
695A small bead of mass m moving with
velocity v gets threaded on a stationary semicircular ring of mass ( mathrm{m} ) and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of
the system?
A. \$\$displaystyle {vyl《R\$\$
B. \$\$|displaystyle(2v)|(R)\$\$
c. \$\$ ldisplaystyle {v)|(2R) \$\$
D. \$\$ldisplaystyle {3v)|(R)\$\$
11
696A body is said to be in static
Equilibrium?
A. When it is moving around a circular path
B. When it is a. rest
C. When it is moving with uniform velocity
D. When it is accelerated by the external force
11
697A uniform sphere of mass ( m ) and radius
( r ) rolls without sliding over a horizontal
plane, rotating about a horizontal axle
OA. In the process, the centre of the sphere moves with a velocity ( v ) along a
circle of radius ( R ) Find the kinetic
energy of the sphere.
11
698A body is under the action of two equal and oppositely directed forces and the body is rotating with constant non-zero angular acceleration. Which of the following cannot be the separation between the lines of action of the
forces?
A. ( 1 m )
в. ( 0.4 m )
c. ( 0.25 m )
D. zero
11
699Two particles ( A ) and ( B ) are moving with constant velocities ( v_{1}=hat{j} ) and ( v_{2}=2 hat{i} ) respectively ( A ) is at ( c o ) -ordinates (0,0) and B is at (-4,0) . the angular velocity of B with respect to ( A ) at ( t=2 s ) is (all
physical quantities are in Sl units)
A ( cdot frac{1}{2} r a d / s )
B. ( 2 r a d / s )
c. ( 4 r a d / s )
D. ( 1 r a d / s )
11
700Drum A undergoes
A. rotational motion
B. translational motion
c. rotational as well as translational motion
D. None of these
11
701A uniform circular disc placed on a
rough horizontal surface has initially
velocity ( v_{0} ) and an angular velocity ( omega_{0} ) as
shown in the figure. The disc comes to
rest after moving some distance in the direction of motion. Then ( frac{v_{0}}{r omega_{0}} ) is
A . ( 1 / 2 )
B.
( c cdot 3 / 2 )
D. 2
11
702Find the instantaneous axis of rotation
of a rod of length ( l ) when its end ( A ) moves with a velocity ( overrightarrow{boldsymbol{v}}_{boldsymbol{A}}=boldsymbol{v} hat{boldsymbol{i}} ) and the
rod rotates with an angular velocity
( omega=-frac{v}{2 l} hat{k} )
11
703A stick is thrown in the air and lands on
the ground at some distance from the
thrower. The centre of mass of the stick
will move along a parabolic path
A. in all cases
B. only if the stick is uniform
c. only if the stick has linear motion but no rotational motion
D. only if the stick has a shape such that its centre of
11
704Two skaters have weight in the ratio 4:
5 and are ( 9 mathrm{m} ) apart, on a smooth
frictionless surface,They pull on a rope stretched between them. The ratio of the
distance covered by them when they meet each other will be
A .5: 4
в. 4: 5
c. 25: 16
D. 16: 25
11
705A uniform triangle of side length ( l ),and
mass ( M ) is rotating about an axis (passing through its one of side) with angular velocity ( omega ) then its angular momentum is given as ( frac{M l^{2}}{k} omega ) then the value of k is
11
706A circular track has a circumference of
( 3140 mathrm{m} ) with ( mathrm{AB} ) as one of its diameter
shooter moves from A to B along the circular path with a uniform speed of 10
A. Distance covers by the scooter
B. Displacement of scooters
c. Time taken by the scooter in maching from A to B
D. None of these
11
707Two particles ( A ) and ( B ) are moving as
shown in the figure. At this moment
of time, the angular speed of A with
respect to B is:
A ( cdot frac{v_{a}+v_{b}}{r} )
в. ( frac{v_{a}-v_{b}}{r} )
( frac{v_{a} sin theta-v_{b} sin theta}{r} ) in anticlockwise direction
D. ( frac{v_{a} sin theta+v_{b} sin theta}{r} ) in anticlockwise direction
11
708How will you weight the sun that estimates its mass? The mean orbital
radius of the earth around the sun is
11
709Figure shows position and velocities of
two particles moving under mutual gravitational attraction in space at
time ( t=0 )
The position of centre of mass after one
second is
A ( . x=4 m )
в. ( x=6 m )
c. ( x=8 m )
D. ( x=10 m )
11
710Torque applied on a particle is zero,
then, its angular momentum will be
A . Equal in direction
B. Equal in magnitude
c. Both (a) and (b)
D. Data Insufficient
11
711If a rigid body is subjected to two forces ( vec{F}_{1}=2 hat{i}+3 hat{j}+4 hat{k} ) acting at (3,3,4)
and ( vec{F}_{2}=-2 hat{i}-3 hat{i}-4 hat{k} ) acting at (1
0, 0) then which of the following is (are)
true?
A. The body maybe in equilibrium
B. The body is under the influence of a torque only
c. The body is under the influence of a single force.
D. The body is under the influence of a force together with torque
11
712A parallelogram has diagonals expressed as ( vec{A}=5 hat{i}-4 hat{j}+3 hat{k} ) and ( vec{B}=3 hat{i}+2 hat{j}-hat{k} )
Area of parallelogram is:
A. ( sqrt{117} ) units
B. ( sqrt{171} ) units
c. ( sqrt{711} ) units
D. ( sqrt{107} ) units
11
713The rocket works on the principle of conservation of:
A. Energy
B. Angular momentum
c. Momentum
D. Mass
11
714A shell of mass ( 0.020 mathrm{kg} ) is fired by a
gun of mass ( 100 mathrm{kg} ). If the muzzle speed of the shell is ( 80 m / s, ) what is the recoil
speed of the gun?
11
715A solid sphere and a solid cylinder having the same mass and radius, rol
down the same incline. What will the
ratio of their acceleration be?
11
716A hoop rolls without slipping on a horizontal ground having centre of
mass speed ( v_{0} . ) The speed of a particle ( P ) on the circumference of the hoop at
angle ( boldsymbol{theta} ) is?
11
717When the following bodies of same radius starts rolling down on same inclined plane, identify the decreasing order of their time of descent:
I) Solid cylinder
II) Hollow cylinder
III) Hollow sphere
IV) Solid sphere
A. ( I V, I, I I I, I I )
в. ( I I, I I I, I, I V )
c. ( I, I V, I I I, I I )
D. II, III, IV,
11
718Find the angle of the vector of the
angular velocity of the cone it forms
with the vertical.
( mathbf{A} cdot 60^{circ} )
B ( .67^{circ} )
( c cdot 62^{circ} )
D. ( 50^{circ} )
11
719If two particles of masses ( m_{1} ) and ( m_{2} )
move with velocities ( v_{1} ) and ( v_{2} ) towards
each other on a smooth horizontal
plane, what is the velocity of their
centre of mass.?
A ( cdot V=frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}} )
B. ( V=frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}+m_{2}} )
( mathbf{c} cdot V=frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}-m_{2}} )
D. ( V=frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}-m_{2}} )
11
720Which of the following set ups represent a second class lever?
( A )
[
frac{L F E}{Delta}
]
в.
[
begin{array}{lll}
F & L & E \
hline Delta
end{array}
]
( c )
[
frac{L}{L} E frac{F}{Delta}
]
D.
[
frac{F}{Delta} E L
]
11
721All the particles of a body are situated at a distance ( R ) from the origin. The
distance of centre of mass of the body from the origin is
( A .=R )
в. ( leq R )
( c cdot>R )
( D . geq R )
11
722State Parallel axis theorem?11
100010
equilateral triangular body of side ( l ) This body is placed on a horizontal frictionless table (x-y plane) and is
hinged at point ( A ) so that it can move
without friction about the vertical axis
through ( A ). The body is set into
rotational motion on the table about
this axis with a constant angular
velocity ( omega(a) ) Find the magnitude of the
horizontal force exerted by the hinge on
the body (b) At time ( T ), when side ( B C ) is
parallel to x-axis, force ( boldsymbol{F} ) is applied on
( B ) along ( B C ) (as in the figure). Obtain
the ( x ) -component and the ( y ) -component of the force exerted by the hinge on the body, immediately after time ( T )
11
724A and B are two solid spheres of equal masses. A rolls down an inclined plane
without slipping from a height ( boldsymbol{H} . ) B falls vertically from the same height. Then on reaching the ground. This question has multiple correct options
A. both can do equal work
B. A can do more work than B
c. B can do more work than A
D. both A and B will have different linear speeds
11
725Two small spheres of masses ( 10 mathrm{kg} ) and ( 30 mathrm{kg} ) are joined by a rod of length ( 0.5 mathrm{m} ) and of negligible mass. The M.I. of the system about a normal axis through centre of mass of the system is
A ( cdot 1.875 mathrm{kgm}^{2} )
B. 2.45 ( k g m^{2} )
c. ( 0.75 mathrm{kgm}^{2} )
D. ( 1.75 mathrm{kgm}^{2} )
11
726A solid sphere is projected up along an inclined plane from its bottom with a
velocity ( 2.8 m s^{-1} ) so that it rolls upward.
If the inclined plane makes an angle of
( 30^{circ} ) with the horizontal, the sphere can
roll to a maximum height of : (Take ( boldsymbol{g}= )
( left.10 m / s^{2}right) )
( mathbf{A} cdot 0.35 m )
B. ( 0.55 m )
( c .0 .7 m )
D. ( 0.84 m )
11
727A solid sphere of mass ( 1 mathrm{kg} ) rolls on a table with linear speed ( 2 mathrm{m} / mathrm{s} ), find its total kinetic energy.11
728Define a rigid body11
729Two balls are thrown simultaneously in air. The acceleration of the centre of
mass of the two balls while in air.
A. depends on the direction of the motion of the balls
B. depends on the masses of the two balls
c. depends on the speeds of the two balls
D. is equal to
11
730The moment of inertia of a ring about its geometrical axis is ( I ), then its moment of inertia about its diameter
will be :
A . ( 2 I )
в. ( frac{1}{2} )
c. ( I )
D. ( frac{I}{4} )
11
731A uniform sphere of mass ( boldsymbol{m}=mathbf{5 . 0} boldsymbol{k g} )
and radius ( R=6.0 mathrm{cm} ) rotates with an
a horizontal axle passing through its centre and fixed on the mounting base
by means of bearings. The distance between the bearings equals ( l=15 mathrm{cm} )
The base is set in rotation about a
vertical axis with an angular velocity
( omega^{prime}=5.0 ) rad ( / s . ) Find the magnitude of
the gyroscopic forces in ( mathrm{N} )
11
732revolution is equivalent to :
B. ( 2 pi ) radians
c. ( 3 pi ) radians
D. ( 4 pi ) radians
11
733If the sum of two unit vectors is a unit
vector, then the magnitude of their difference is:
A ( cdot sqrt{2} )
B. ( sqrt{3} )
c. ( 1 / sqrt{2} )
D. ( sqrt{5} )
11
734The law of conservation of angular
momentum is obtained from Newton’s II
law in rotational motion when:
A. External torque is maximum
B. External torque is minimum
c. External torque is zero
D. External torque is constant
11
735If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :
A. Kinetic energy will decrease
B. Moment of inertia will decrease.
c. Angular momentum will increase.
D. Angular velocity will remain constant
11
736Calculate the angular ( & ) Linear speed of tip of 2 nd hand of a clock a length ( 7 mathrm{cm} )11
737When we jump forward out of a boat standing in water it moves backwards.
A. True
B. False
11
738The area of the triangle whose adjacent sides are represented by the vector ( (4 bar{i}+3 bar{j}+4 bar{k}) ) and ( 5 bar{i} ) in square units
is:
A . 25
в. 12.5
c. 50
D. 45
11
739Two identical carts constrained to move
on a straight line, on which sit two twins of same mass, are moving with equal
velocity. At some time snow begins to
drop uniformly. Ram, sitting on one of
the carts, picks the snow from cart and
throws off the falling snow sideways and in the second cart Shyam is asleep:
A. cart carrying Ram will have more speed finally than that carrying Shyam.
B. cart carrying Ram will have less speed finally than that carrying Shyam.
C. cart carrying Ram will have same speed finally than that carrying Shyam.
D. The velocity of cart depends on the amount of snow thrown
11
740A particle moves parallel to ( x ) -axis with
constant velocity ( v ) as shown in the figure. The angular velocity of the particle about the origin ( boldsymbol{O} )
A. remains constant
B. continuously increases
c. continuously decreases
D. oscillates
11
741If the position vector of the vertices of a triangle are ( hat{boldsymbol{i}}-hat{boldsymbol{j}}+boldsymbol{2} hat{boldsymbol{k}} ; boldsymbol{2} hat{boldsymbol{i}}+hat{boldsymbol{j}}+hat{boldsymbol{k}} boldsymbol{&} )
( mathbf{3} hat{mathbf{i}}-hat{boldsymbol{j}}+mathbf{2} hat{boldsymbol{k}}, ) then find the area of the
triangle.
A. ( sqrt{5} m^{2} )
B. ( 5 m^{2} )
( c cdot 25 m^{2} )
D. ( 2 m^{2} )
11
742A thin bar of mass ‘M’ and length ‘L’ is
free to rotate about a fixed horizontal
axis through a point at its end.The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is:
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
c. dependent only upon the acceleration due to gravity
D. directly proportional to its length and inversely proportional to the acceleration due to gravity.
11
743A top of mass ( m=1.0 mathrm{kg} ) and
moment of inertia relative to its own
axis ( I=4.0 g m^{2} ) spins with an angular
velocity ( omega=310 ) rad/s. Its point of rest
is located on a block which is shifted in
a horizontal direction with a constant
acceleration ( boldsymbol{w}=mathbf{1 . 0} boldsymbol{m} / boldsymbol{s}^{2} . ) The
distance between the point of rest and the centre of inertia of the top equals
( l=10 mathrm{cm} . ) If the angular velocity of
precession ( omega^{prime} ) is ( x ) find the value of ( 10 x )
11
744Two particles of masses m and ( 2 mathrm{m} )
on an object are connected by a spring,
then with respect to the object’s frame
of reference
A. the two particles are considered as rigid body, if the object moves with uniform velocity
B. the two particles are considered as rigid body, if the object moves with uniform acceleration
C. the two particles are considered as rigid body, if the object moves with uniform speed
D. the two particles are cannot be a rigid body, since deformation in the spring can bring about a change in the positions of the particles
11
745Three identical sphere each of mass ( M )
are placed at the centre of a right angled triangle with mutually perpendicular sides equal to ( 2 m ) Taking their point of intersection on the origin, the position vector of the centre
of mass is:
( left.^{mathrm{A}} cdot frac{2}{3}^{(hat{imath}}+hat{j}right) )
B ( cdot frac{2}{3}(hat{i}-hat{j}) )
c. Both A and B
D. None of the above
11
746From a uniform disc of radius ( mathrm{R} ), a disc of radius ( frac{boldsymbol{R}}{mathbf{2}} ) is scooped out such that they have the common tangent. Find the centre of mass of the length remaining
part
11
747II the ngurt, and
( operatorname{masses} m_{1} ) and ( m_{2}left(m_{1}>m_{2}right) . m_{1} ) has
a downward acceleration ( a ). The pulley ( P )
has a radius ( r, ) and some mass. The
string does not slip on the pulley. Then which of the following statement(s) is/are true?
This question has multiple correct options
A. The two sections of the string have unequal tensions.
B. The two blocks have accelerations of equal magnitude.
C . The angular acceleration of P is ( frac{a}{r} )
D. ( a<left(frac{m_{1}-m_{2}}{m_{1}+m_{2}}right) g )
11
748A sphere pure rolls on a rough inclined plane with initial velocity ( 2.8 mathrm{m} / mathrm{s} ). Find
the maximum distance on the inclined
plane.
velocity
A. 2.74 m
В. 5.48 m
c. 1.38 m
D. ( 3.2 mathrm{m} )
11
749A spherical ball of mass ( 1 k g ) moving
with a uniform speed of ( 1 mathrm{m} / mathrm{s} ) collides symmetrically with two identical spherical balls of mass ( 1 k g ) each at rest touching each other. If the two balls move with ( 0.5 m / s ) in two directions at
the same angle of ( 60^{circ} ) with the direction of the first ball, the loss of kinetic
energy on account of the collision is:
в. ( 0.5 mathrm{J} )
c. ( 1.0 mathrm{J} )
D. ( 0.75 J )
11
750Two particles each of mass m move in opposite direction along Y-axis. One particle moves in positive direction
with velocity v while the other particle moves in negative direction with speed
2v. The total angular momentum of the system with respect to origin is:
A. Is zero
B. Goes on increasing
c. Goes on decreasing
D. None of these
11
751Angular momentum of the disc will be
A. centre of mass
B. point of contact
C. a point at a distance ( 3 R / 2 ) vertically above the point of contact
D. a point at a distance ( 4 R / 3 ) vertically above the point of contact
11
752If the moment of force is assigned a
negative sign then will the turning
tendency of the force be clockwise or anticlockwise?
11
753A particle of mass ( m ) is released from
rest at point ( A ) in Figure, falling parallel to the (vertical) y-axis. Find the angular momentum of the particle at any time ( t ) with respect to the same origin ( O )
11
754the linear acceleration of the ball down
the plane is ( x g sin theta-mu g cos theta . ) Find ( x )
11
755A body is dropped from a height ( h ), if it acquires a momentum p, then the mass of the body is:
A ( cdot frac{p}{sqrt{2 g h}} )
в. ( frac{P^{2}}{2 g h} )
c. ( frac{2 g h}{p} )
D. ( sqrt{2 g h / p} )
11
756A body with moment of inertia ( 3 K g m^{2} ) is
at rest. A torque of ( 6 N m ) applied on it rotates the body for 20 seconds. The angular displacement of the body is
11
757A cylinder of radius ( R ) is to roll without
slipping between two planks as shown in the figure, Then
This question has multiple correct options
A. angular velocity of the cylinder is ( frac{v}{R} ) counter clockwise
B. angular velocity of the cylinder is ( frac{2 v}{R} ) clockwise
c. velocity of centre of mass of the cylinder is v towards left
D. velocity of centre of mass of the cylinder is ( 2 v ) towards right
11
758A body of mass ( mathbf{m}=mathbf{3 . 5 1 3} mathbf{k g} ) is moving along the x-axis with a speed of 5.00
( mathrm{ms}^{-1} . ) The magnitude of its momentum
is recorded as :
A ( cdot 17.56 mathrm{kg} mathrm{ms}^{-1} )
B . 17.57 kg ms ( ^{-1} )
c. ( 17.6 mathrm{kg} mathrm{ms}^{-1} )
D. 17.565 kg ms ( ^{-1} )
11
759Prove that the points ( boldsymbol{A}(boldsymbol{a}, boldsymbol{b}+ )
( c), B(b, c+a) ) and ( C(c, a+b) ) are
collinear (By determinant)
11
760If you place pivot at center of a meter rule, weight has no
A. property
B. Concern
c. Turning effect
D. Magnitude
11
761How can be rule be brought in
weight of ( 40 g f ? )
A. By placing the additional weight of ( 80 g f ) at the 30 cm mark
mark
c. By placing the additional weight of ( 40 g f ) at the 30 cm mark
D. By placing the additional weight of ( 40 g f ) at the 70 cm mark
11
762Point masses 1,2,3 and ( 4 k g ) are lying at the points (0,0,0),(2,0,0),(0,3,0) and (-2,-2,0) respectively. The moment of inertia of this system about x-axis will
be:
A ( cdot 43 k g-m^{2} )
B . ( 34 mathrm{kg}-mathrm{m}^{2} )
c. ( 27 mathrm{kg}-mathrm{m}^{2} )
D. ( 72 mathrm{kg}-mathrm{m}^{2} )
11
763A thin uniform sheet of metal of uniform
thickness is cut into the shape bounded
by the line ( x=a ) and ( y=pm k x^{2}, ) as
shown. Find the coordinates of the
centre of mass
11
764Two points ( A & B ) on a disc have
velocities ( v_{1} & v_{2} ) at some moment
Their directions make angles ( 60^{circ} ) and
( 30^{circ} ) respectively with the line of
separation as shown in the figure. The
angular velocity of the disc is:
A ( cdot frac{sqrt{3} v_{1}}{d} )
B. ( frac{v_{2}}{sqrt{3}} )
c. ( frac{v_{2}-v_{2}}{d} )
D. ( frac{v_{2}}{d} )
11
765Three identical solid spheres each of
mass ( M ) and radius ( R ) are fixed at three
corners of light equilateral triangular
frame of side length ( 3 R ) such that centre of spheres coincide with corners
of the frame. Find the moment of inertia
of these 3 spheres about an axis passing through any side of frame.
( ^{mathbf{A}} cdot frac{121 M R^{2}}{5} )
B. ( frac{159 M R^{2}}{5} )
c. ( frac{121 M R^{2}}{20} )
D. ( frac{159 M R^{2}}{20} )
11
766A half meter rod is pivoted at the centre
with two weights of ( 20 g f ) and ( 12 g f )
suspended at a perpendicular distance of ( 6 mathrm{cm} ) and ( 10 mathrm{cm} ) from the pivot respectively
as shown below.
¡) Which of the two force acting on the
rigid rod causes clockwise moment?
ii) is the rod in equilibrium?
11
767calculate the torque developed by an airplane engine whose output is 2000
( mathrm{HP} ) at an angular velocity of 2400 rev/min.
11
768The wheel of a motor, accelerated
uniformly from rest, rotates through 2.5 radian during first second, find the angle rotates during next second
11
769The torque of force ( overrightarrow{boldsymbol{F}}=(2 hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}}) )
N acting at the point ( vec{r}= ) ( (3 hat{i}+2 hat{j}+3 hat{k}) m ) about origin is (in ( mathrm{N}- )
( mathrm{m}) )
A . ( 6 hat{i}-6 hat{j}+12 hat{k} )
B . ( 17 hat{i}-6 hat{j}-13 hat{k} )
c. ( -6 hat{i}+6 hat{j}-12 hat{k} )
D. ( -17 hat{i}+6 hat{j}+13 hat{k} )
11
770A beam of length ( l ) lies on the ( +x ) axis
with its left end on the origin. A cable pulls the beam in negative y-direction with a force ( boldsymbol{F}=boldsymbol{F}_{0}left(1-frac{boldsymbol{x}}{boldsymbol{l}}right) . ) If the axis
is fixed at ( x=0 ) then find the torque.
( mathbf{A} cdot-F_{0} l )
B. ( frac{F_{0} l}{2} )
( c cdot-frac{F_{0} l}{2} )
D. none of these
11
771A block of mass ( m ) slides down an
inclined wedge of same ( m ) shown in
figure. Friction is absent everywhere Magnitude of acceleration of center of
mass of the block and wedge is
A. zer
B. ( frac{g sin ^{2} theta}{left(1+sin ^{2} thetaright)} )
c. ( frac{g cos ^{2} theta}{left(1+sin ^{2} thetaright)} )
D. ( frac{g sin theta}{(1+cos theta)} )
11
772A solid cylinder of mass ( 20 k g ) rotates about its axis with angular speed
( 0.25 m . ) What is the kinetic energy associated with the rotation of cylinder? What is the magnitude of angular momentum of cylinder about its axis?
A. ( 62.5 T-s )
B. ( 70.4 T-s )
c. ( 79.6 T-s )
D. ( 60.5 T-s )
11
773A body moving uniformly along a circular path has:
A. a constant speed
B. a constant velocity
c. zero tangential velocity
11
774Figure shows a vertical force ( boldsymbol{F} ) that is
applied tangentially to a uniform
cylinder of weight ( W ). The coefficient of
static friction between the cylinder and
all surfaces is ( 0.5 . ) Find the maximum
force in terms of ( W ) that can be applied
without causing the cylinder to rotate.
11
775Find the distance of centre of mass of
( H_{2} O ) molecule
11
776A body of mass 5 kg undergoes a change in speed from 20 to ( 0.20 mathrm{m} / mathrm{s} )
The momentum of the body would
A. increase by ( 99 mathrm{kg} mathrm{m} / mathrm{s} )
B. decrease by ( 99 mathrm{kg} mathrm{m} / mathrm{s} )
c. increase by ( 101 mathrm{kg} mathrm{m} / mathrm{s} )
D. decrease by ( 90 mathrm{kg} mathrm{m} / mathrm{s} )
11
777Two bodies of mass ( m_{1} ) and ( m_{2}left(<m_{1}right) )
are connected to the end of massless
cord and allowed to move as shown. The
pulley is mass less and friction less
determine the acceleration of the centre
of mass
11
778The kinetic energy of a body of mass
( 4 k g ) and momentum ( 6 N s ) will be
( mathbf{A} cdot 2.5 J )
B. ( 3.5 J )
c. ( 4.5 J )
D. ( 5.5 J )
11
779State and prove principle of conservation of angular momentum.11
780In a clockwise system, which of the following is true?
в. ( hat{i} hat{.}=0 )
( mathbf{c} cdot hat{j} times hat{j}=1 )
D. ( hat{k} . hat{.}=1 )
11
781The center of gravity of an object is
A. the sum of its moments divided by the weight of the specific object.
B. the sum of its moments divided by the overall weight of the object.
C. the sum of its moments of product of the overall weight of the object.
D. none of the above
11
782A double star is a system of two stars of
masses ( mathrm{m} ) and ( 2 mathrm{m}, ) rotating about their centre of mass only under their mutual
gravitational attraction. If ( r ) is the
separation between these two stars
then their time period of rotation about their centre of mass will be proportional
to.
This question has multiple correct options
A ( cdot frac{3}{2} )
B.
D. ( _{m^{-}} frac{1}{2} )
11
783A square plate is of mass ( M ) and length
of the edge is 2a. Its Moment of inertia
about its centre of mass axis,
perpendicular to its plane is equal to ( l_{0} )
Four identical disks are cut from the
plane. Find the Moment of inertia of
leftover square about the same axis.
11
784A uniform wire of length ( l ) is bent into
the shape ( V ) as shown in the figure. The
distance of its center of mass from the
vertex ( boldsymbol{A} ) is ( (text { in } boldsymbol{m}) )
A. ( l / 2 )
( B cdot frac{1 sqrt{3}}{1} )
( c cdot frac{1 sqrt{3}}{0} )
D. none of thes
11
785A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder
with a man and the other end to the
counterweight of mass ( M . ) The man of
mass ( m ) climbs up a distance ( h ) with
respect to the ladder and then stops. If the mass of the rope and the friction in
the pulley axle are negligible, find the displacement of the centre of mass of
this system.
11
786Find the centre of mass of the letter ( F )
which cut from a uniform metal sheet
from point ( mathbf{A} )
A . ( 15 / 7,33 / 7 )
B. 15/7, 23/7
c. 22/7, 33/7
D. 33/7, 22/7
11
787Moment of inertia of a hollow sphere of
mass ( mathrm{M} ) and diameter ( mathrm{D} ) about its
diameter
A ( . M D^{2} / 5 )
В. ( 2 M D^{2} / 5 )
c. ( M D^{2} / 6 )
D. ( 5 M D^{2} / 2 )
11
788Figure represents a metre scale balancing on a knife edge at ( 20 mathrm{cm} )
mark. When a weight of 60 N is suspended from 10 cm mark. Calculate
the weight of the ruler(in N).
A . 30
B. 60
( c cdot 15 )
D. 20
11
789A particle is moving in a circle of radius ( R ) in such a way that at any instant the normal and tangential components of its acceleration are
equal. If its speed at ( t=0 ) is ( v_{o} ) the time
taken to complete the first revolution is
A ( cdot R / v_{o} )
в. ( v_{o} / R )
C ( cdotleft(R / v_{o}right) timesleft(1-e^{-2 pi}right) )
D. ( left(R / v_{o}right) timesleft(e^{-2 pi}right) )
11
790A midpoint of a thin uniform rod ( A B ) of
mass ( m ) and length ( l ) is rigidly fixed to a
rotation axle ( O O^{prime} ) as shown in figure
above. The rod is set into rotation with a
constant angular velocity ( omega . ) If the
resultant moment of the centrifugal
forces of inertia relative to the point ( boldsymbol{C} )
in the reference frame fixed to the axle
OO’ and to the rod is given by ( N= ) ( frac{1}{x} m omega^{2} l^{2} sin 2 theta, ) then the value of ( x / 4 ) is :
11
791Sl unit of moment of couple is
A ( cdot N^{2} m )
в. ( N m )
( mathrm{c} cdot mathrm{Nm}^{2} )
D. ( N / m^{2} )
11
792When mass is rotating in a plane about a
fixed point, its angular momentum is directed along
A. the axis of rotation
B. line at an angle of ( 45^{circ} ) to the axis of rotation
D. the tangent to the orbitt
11
793A ring type flywheel of mass ( 100 k g ) and
diameter ( 2 m ) is rotating at the rate of ( frac{5}{11} r e v / s . ) Then
A. the moment of inertia of the wheel is 100 kgm ( ^{-2} ).
B. the kinetic energy of rotation of the flywheel is ( 5 x ) ( 10^{3} J )
C. the angular momentum associated with the flywheel is ( 10^{3} J s )
D. the flywheel, if subjected to a retarding torque of ( 250 N m, ) will come to rest in ( 4 s )
11
794The distance of the centre of mass of
the T-shaped plate from O is
( A cdot 7 m )
B. 2.7 ( m )
( c cdot 4 m )
D. ( 1.7 mathrm{m} )
11
795The radius of gyration of a rotating
circular ring is maximum about which
of the following axis of rotation:
A. neutral axis
B. axis passing through diameter of ring
c. axis passing through tangent of ring in its plane
D. axis passing through tangent of ring perpendicular to plane of ring.
11
796A cubical block of side a is moving with velocity v on a horizontal smooth plane
as shown in figure. It hits a ridge at point ( 0 . ) The angular speed of the block after it hits 0 is:
( mathbf{A} cdot frac{3 v}{4 a} )
B. ( frac{3 v}{2 a} )
c. ( sqrt{frac{3}{2} c} )
D. zero
11
797The angular velocity of a body changes
fro ( omega_{1} ) to ( omega_{2} ) without applying a torque
but by changing the moment of inertia. The ratio of corresponding radii of
gyration ( boldsymbol{K}_{mathbf{1}}: boldsymbol{K}_{mathbf{2}} ) is
( A cdot omega_{1}: omega_{2} )
B . ( sqrt{omega_{1}}: sqrt{omega_{2}} )
D. ( omega_{2}: omega_{1} )
11
798Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system
A ( cdot 4 m w^{2} r )
B. ( 10 m w^{2} )
c. ( 30 m w^{2} r )
D. ( 20 m w^{2} r )
11
799A wheel rolling on a horizontal surface
is an example of
A. Stable equilibrium
B. Unstable equilibrium
c. Neutral equilibriumm
D. All of the above
11
800Tangential acceleration of the centre of
mass is:
( mathbf{A} cdot frac{3 F}{4 m} )
в. ( frac{F}{m} )
c. ( frac{2 F}{3 m} )
D. ( frac{4 F}{3 m} )
11
801Two discs of moments of inertia ( I_{1} ) and
( I_{2} ) about their respective axes (normal to the disc and passing through the centre), and rotating with angular
( operatorname{speeds} omega_{1} ) and ( omega_{2} ) are brought into contact face to face with their axes of
rotation coincident.
(a) What is the
angular speed of the two-disc system?
(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the
two discs. How do you account for this
loss in energy? Take ( omega_{1} neq omega_{2} )
11
802State one way to obtain a greater
moment of a force about a given axis of
rotation.
11
803A circular disc ( A ) of a radius ( r ) is made
from an iron plate of a thickness ( t ) and
another circular disc ( B ) of radius ( 4 r ) is made from an iron plate of thickness ( frac{t}{4} ) The relation between the moments of
inertia ( I_{A} ) and ( I_{B} ) is
( A cdot I_{A}>I_{B} )
B ( . I_{A}=I_{B} )
( mathrm{c} cdot I_{A}<I_{B} )
D. depends on the actual value of ( t ) and ( r )
11
804A smooth sphere ( A ) is moving on a
frictionless horizontal plane with
angular speed ( omega_{a} ) and ( omega_{b} )
respectively.Then: ( omega_{a}=omega_{b} ) Type 1 for true
and 0 for flase
11
805A rigid body can be hinged about any point in the ( x ) -axis. When it is hinged
such that the hinge is at ( x, ) the moment
of inertia is given by ( boldsymbol{I}=mathbf{2} boldsymbol{x}^{2}-mathbf{1} mathbf{2} boldsymbol{x}+ )
( mathbf{2 7} ) the ( mathbf{x} ) -coordinate of centre of mass is:
A ( . x=2 )
B. ( x=0 )
c. ( x=1 )
D. ( x=3 )
11
806Three man ( A, B, C ) of mass ( 40 mathrm{kg}, 50 mathrm{kg} )
( & 60 mathrm{kg} ) are standing on a plank of mass ( 90 mathrm{kg}, ) which is kept on a smooth
horizontal plane. If ( A & C ) exchange their
positions then mass B will shift
( mathbf{A} cdot 1 / 3 mathrm{m} ) towards left
B. 1/3 m towards right
c. will not move w.r.t. ground
D. ( 5 / 3 ) m toward left
11
807A solid sphere, a solid cylinder, a hollow sphere and a hollow cylinder (all of the same mass ) simultaneously start rolling down from top of an inclined plane, then the time to reach bottom of inclined plane is :
A. minimum for solid cylinder, maximum for hollow sphere
B. minimum for hollow sphere, maximum for solid cylinder
c. minimum for solid sphere, maximum for hollow cylinder
D. minimum for hollow cylinder, maximum for solid sphere
11
808From a unifrom disc of radius ( R ) an
equilateral triangle of side ( sqrt{3} R ) is cut
as shown. The new position of centre of mass is
A ( cdot(0,0) )
в. ( (0 . R) )
c. ( (R, 0) )
( 0 . frac{sqrt{3}}{28} )
11
809A constant torque of ( 1000 N ) m turns a wheel of moment of inertia ( 200 k g m^{2} ) about an axis through its centre. The wheel is at rest initially. Its angular velocity after ( 3 s ) is :
A ( cdot 15 ) rads( ^{-1} )
11
810A hollow cylinder of mass ( M ) and radius
( boldsymbol{R} ) is pulled by a horizontal force ( boldsymbol{F} ) acting at its centre of mass on a horizontal surface where the coefficient
of friction is ( mu )
If hollow cylinder is performing pure rolling then frictional force ( f ) will be :
A. ( F )
в. ( frac{F}{2} )
c. ( frac{F}{3} )
D. ( 2 F )
11
811What type of motion do the vehicles on a straight road perform?11
812In the figure shown, a spherical part of
( boldsymbol{R} )
radius ( frac{-k}{2} ) is removed from a bigger solid
sphere of radius ( R ). Assuming uniform mass distribution, shift in the centre of
mass will be:
( A cdot frac{R}{7} )
в. ( frac{R}{14} )
( c cdot frac{R}{9} )
D. ( frac{R}{6} )
11
813The radius of gyration of a body is ( 18 mathrm{cm} ) when it is rotating about an axis passing through center of mass of body. If radius of gyration of same body is 30 ( mathrm{cm} ) about a parallel axis to first axis then, perpendicular distance between
two parallel axes is:
( A cdot 12 mathrm{cm} )
B. ( 16 mathrm{cm} )
c. ( 24 mathrm{cm} )
D. 36 cm
11
814A loaded spring gun of mass ( M ) fires a bullet of mass ( m ) with a velocity ( v ) at an
angle of elevation ( theta ). The gun is initially at rest on a horizontal smooth surface.
After firing, the centre of mass of the
gun and bullet system
A . Moves with velocity ( frac{v}{M} ) m
B. Moves with velocity ( frac{v m}{M cos theta} ) in the horizontal direction
c. Does not move in horizontal direction
D. Moves with velocity ( frac{v(M-m)}{M+m} ) in the horizonta direction
11
815A bicycle can go up a gentle incline with
constant speed where the frictional force of ground pushing the rear whee
is ( F_{2}=4 N . ) With what force ( F_{1} ) must
the chain pull on the socket wheel if
( R_{1}=5 mathrm{cm} ) and ( R_{2}=30 mathrm{cm} ? )
( A cdot 4 N )
В. 24 .
( c .140 N )
D. ( frac{35}{4} ) N
11
816If a force ( 10 hat{i}+15 hat{j}+25 hat{k} ) acts on a
system and gives an acceleration ( 2 hat{mathbf{i}}+ ) ( 3 hat{j}-5 hat{k} ) to the centre of mass of the
system, the mass of the system is
A . 5 units
B. ( sqrt{38} )units
c. ( 5 sqrt{38} ) units
D. Given data is not correct
11
817What is the moment of intertia for a
solid sphere w.r.t. a tangent touching to its surface?
( ^{mathbf{A}} cdot frac{2}{5} M R^{2} )
B. ( frac{7}{5} M R^{2} )
c. ( frac{2}{3} M R^{2} )
D. ( frac{5}{3} M R^{2} )
11
818A rigid body is made of three identical uniform thin rods each of length ( boldsymbol{L} )
fastened together in the form of letter
H. The body is free to rotate about a
fixed horizontal axis ( A B ) that passes
through one of the legs of the ( boldsymbol{H} ). The
body is allowed to fall from rest from a
position in which the plane of ( boldsymbol{H} ) is
horizontal. What is the angular speed of
the body, when the plane of ( boldsymbol{H} ) is
vertical.
11
819A uniform disc is rolling on a horizontal surface. At a certain instant ( B ) is the
point of contact and ( A ) is a stationary
point at height ( 2 R ) from ground, where
( R ) is radius of disc :
This question has multiple correct options
A. The magnitude of the angular momentum of the disc about ( B ) is thrice that about ( A ).
B. The angular momentum of the disc about ( A ) is anticlockwise
C. The angular momentum of the disc about ( B ) is clockwise.
D. The angular momentum of the disc about ( A ) is equal to that about ( B ).
11
820A vessel with a symmetrical hole in its
bottom is fastened on a cart. The mass
of the vessel and the cart is 1.5 kg. With
what force ( Fleft(text { in } times 10^{2} Nright) ) should the
cart be pilled so that the maximum amount of water remains in the vessel.
The dimensions of the vessel are as
shown in the figure. Given that ( b= )
( mathbf{5 0} c boldsymbol{m}, boldsymbol{c}=mathbf{1 0} boldsymbol{c m} ) area of base ( boldsymbol{A}= )
( 40 c m^{2}, L=20 c m, g=10 m / s^{2} )
11
821A solid sphere of mass ( M ) and radius ( 2 R ) rolls down an inclined plane of
height ( h ) without slipping. The speed of its center of mass when it reaches the
bottom is
A ( cdot sqrt{frac{6}{7} g h} )
B. ( sqrt{3 g h} )
c. ( sqrt{frac{10}{7} g h} )
D. ( sqrt{frac{4}{3} g h} )
11
822A rigid spherical body is spinning
around an axis without any external
torque. Due to change in temperature, the
volume increases by ( 1 % . ) Its angular speed
A. Will increase approximately by ( 1 % )
B. Will decrease approximately by 1 %
C. Will decrease approximately by 0.67 %
D. Will increase approximately by 0.33 %
11
823Moment of inertia of a uniform disc of
mass ( m ) about an axis ( x=a ) is ( m k^{2} )
where ( k ) is the radius of gyration. What
is its moment of inertia about an axis
( boldsymbol{x}=boldsymbol{a}+boldsymbol{b} )
A ( cdot m k^{2}-m a^{2}+m(a+b)^{2} )
B ( cdot m k^{2}+m frac{(a+b)^{2}}{2} )
c. ( m k^{2}+m frac{b^{2}}{2} )
D. ( m k^{2}+m b^{2} )
11
824Which of the following choices correctly
ranks these objects by increasing moments of Inertia?
( A cdot B, D, A, C, E )
B. D, B, E, A, C
( c cdot B, D, E, A, C )
D. B, D, A, E, C
E. D, B, A, E, C
11
825A hemisphere and a solid cone of same
density have a common base. The
centre of mass of the common structure
coincides with the centre of the
common base. If ( boldsymbol{R} ) is the radius of
hemisphere and ( h ) is height of the cone, then :
( mathbf{A} cdot frac{h}{R}=sqrt{3} )
B. ( frac{h}{R}=frac{1}{sqrt{3}} )
( ^{mathbf{C}} cdot frac{h}{R}=3 )
D ( cdot frac{h}{R}=frac{1}{3} )
11
826The momentum of a system with
respect to centre of mass-
A. Is zero only if the system is moving uniformly.
B. Is zero only if no external force acts on the system.
C. Is always zero.
D. Can be zero in certain conditions.
11
827When a sphere rolls down an inclined plane, then identify the correct statement related to the work done by
friction force
A. The friction force does positive translational work
B. The friction force does negative rotational work
c. The net work done by friction is zero
D. All of the above
11
828Which of the following statements is
not correct?
A. Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced in the circuit.
B. The induced emf lasts so long as the change in magnetic flux continues.
C. The direction of induced emf is given by Lenzs law
D. Lenzs law is a consequence of the law of conservation of momentum.
11
829The moment of inertia of a square plate
side in its plane is ( I_{s} ) then
A ( cdot I_{s}=I_{d} )
в. ( I_{s}I_{d} )
D. None of these
11
830Find acceleration of com of two masses
1kg and 2kg having acceleration ( overrightarrow{a_{1}}=2 hat{i}+3 hat{j} ) and ( overrightarrow{a_{2}}=hat{i}-widehat{j}+ )
( 2 widehat{k} ) respectively.
11
831A solid sphere of mass ( mathrm{M} ) and radius ( mathrm{R} )
is divided into two unequal parts. The first part has a mass of ( frac{mathbf{7} M}{mathbf{8}} ) and is converted into a uniform disc of radius
( 2 R . ) The second part is converted into a
uniform solid sphere. Let ( boldsymbol{I}_{mathbf{1}} ) be the moment of inertia of the disc about its
axis and ( I_{2} ) be the moment of inertia of
the new sphere about its axis. The ratio
( boldsymbol{I}_{1} / boldsymbol{I}_{2} ) is given by :
A . 185
B. 65
c. 285
D. 140
11
832A solid disc rolls clockwise without
slipping over a horizontal path with a
constant speed ( v, ) Then the magnitude
of the velocities of points ( A, B ) and ( C ) with
respect to a standing observer are
respectively
11
833( A, B ) and ( C ) are the three forces each of
magnitude ( 4 N ) acting in the plane of
paper as shown in Fig. The point ( O ) lies
in the same plane. Which force has the
greatest moment about ( O ) ?
A . ( A )
в. ( B )
( c . c )
D. all of the above
11
834A uniform rod ( A B ) of mass ( m ) and length
is in equilibrium with the help of two
identical inextensible strings as shown
in figure. Choose the correct option ( (s) )
This question has multiple correct options
A. After cutting the string (2) motion of centre of mass of the rod is circular
B. After cutting the string (2) motion of centre of mass of the rod is not circular
c. Just after cutting the string (2) the acceleration of point A along the string (1) is zero.
D. Just after cutting the string (2) the acceleration of point A perpendicular to the string (1) is not zero.
11
835Assertion
It is harder to open and shut the door if
we apply force near the hinge.
Reason
Torque is maximum at hinge of the
door
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
836A flywheel making 120 r.p.m is acted upon by a retarding torque producing
angular retardation of ( pi ) rad/ ( s^{2} ). Time taken by it to come to rest is:
A . 1 s
B. 2 s
c. 3 s
D. 4 s
11
837If we suspend lamina at different positions, its center of gravity will still lie along the :
A. plumb line
B. line of force
c. line of weight
D. gravity line
11
838A body has its centre of mass at the
origin. The ( x ) -coordinates of the
particles
A. may be all positive
B. must be positive for some particles and negative in other particles
C. Must be all non- negative
D. may be positive for some particles and negative in other particles
11
839In which of the following case(s), the
angular momentum is conserved?
This question has multiple correct options
A. The planet Neptune moves in elliptical orbit around the sun with sun at one focus
B. A solid sphere rolling on an inclined plane
C. An electron revolving around the nucleus in an elliptical orbit
D. An ( alpha ) particle approaching a heavy nucleus from sufficient distance.
11
840Can a couple force acting on a body produce translatory motion?11
841The instantaneous velocity of a point on the outer edge of a disk with a diameter of ( 4 mathrm{m} ) that is rotating at 120 revolutions per minute is most nearly:
( A cdot 4 m / s )
B. 6 ( mathrm{m} / mathrm{s} )
( c cdot 12 m / s )
D. 25 ( mathrm{m} / mathrm{s} )
E. ( 50 mathrm{m} / mathrm{s} )
11
842A thin plank of mass ( M ) and length ( l ) is
pivoted at one end. The plank is
released at ( 60^{circ} ) from the vertical.What
is the magnitude and direction of the force on the pivot when the plank is horizontal?
11
843Figure shows a disc of mass ( mathrm{M} ) and radius R hinged at the centre. A small ball of mass ( frac{M}{2} ) is attached to point ( P )
with a thread of length ( 2 R ) and held at
rest at position shown. Now, the ball is released to fall under gravity. With what
angular speed does the disc start
turning when the string becomes taut?
A ( cdot sqrt{frac{g}{R}} )
в. ( sqrt{frac{g}{2 R}} )
( c cdot sqrt{frac{R}{q}} )
D. ( sqrt{frac{2 g}{R}} )
11
844A circular table has a radius of ( 1 mathrm{m} ) and
mass 20 kg. It has 4 legs of 1 m each
fixed symmetrically on its circumference. The maximum weight which can be placed anywhere on this
table without toppling it is :
A ( .84 .3 mathrm{kg} )
в. ( 34.8 mathrm{kg} )
c. ( 48.3 mathrm{kg} )
D. ( 43.8 mathrm{kg} )
11
845The moment of inertia of a uniform
circular disc of radius ‘R’ and mass ‘M’
about an axis touching the disc at its diameter and normal to the disc is:
( A cdot M R^{2} )
B . ( frac{2}{5} mathrm{MR}^{2} )
( mathbf{c} cdot frac{3}{2} mathbf{M} mathbf{R}^{2} )
D. ( frac{1}{2} mathrm{MR}^{2} )
11
846Heres a collision event as shown in the
figure. In which system would the
momentum be conserved?
A. System of ball ( A )
B. System of ball ( B )
c. System of ball ( A+ ) ball ( B )
D. In all of the above systems
11
847A car weighing 2000 kg moving with a velocity ( 36 mathrm{km} / mathrm{h} ) retards uniformly to rest in 10 s. Find the change in momentum in 1s.
A. 2.629
B. 500 N
c. 2000
D. o(zero)
11
848A gyroscope, a uniform disc of radius ( R=5.0 mathrm{cm} ) at the end of a rod of length
( l=10 mathrm{cm} ) (figure shown above), is
mounted on the floor of an elevator car
going up with a constant acceleration
( boldsymbol{w}=mathbf{2 . 0} boldsymbol{m} / boldsymbol{s}^{2} . ) The other end of the rod
is hinged at the point ( O . ) The gyroscope
precesses with an angular velocity ( n= )
0.5 rps. Neglecting the friction and the
mass of the rod, the proper angular
velocity of the disc in ( r a d / s ) is ( 100 x )
Find the value of ( x )
11
849A square plate of edge ‘a’ and a circular
disc of same diameter are placed
touching each other at the midpoint of an edge of the plate as shown in figure. If mass per unit area for the two plates
are same then find the distance of
centre of mass of the system from the
centre of the disc.
11
850A small mass ( mathrm{m} ) is attached to the
inside of a rigid ring of the same mass ( mathrm{m} ) and radius R. The ring rolls without slipping over a horizontal plane. At the moment when the mass m gets into the lowest position, the centre of the ring
moves with velocity ( boldsymbol{v}_{0} . ) If ( left(boldsymbol{v}_{0}right)_{max }= )
( sqrt{mathrm{ngR}}, ) when the ring moves without bouncing, find ( n )
11
851Assertion
If linear momentum of a particle is constant, then its angular momentum about any axis will also remain
constant.
Reason
Linear momentum remain constant, if ( vec{F}_{n e t}=0 ) and angular momentum remains constant if ( overrightarrow{boldsymbol{T}}_{boldsymbol{n e t}}=mathbf{0} )
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion
B. Both Assertion and Reason are true, Reason is not the correct explanation of Assertion
C. Assertion is true, but the Reason is false
D. Assertion is false but the Reason is true
11
852If the force acting on a particle is zero then the quantities which are conserved
are :
A. momentum and angular momentum.
B. momentum and mechanical energy
c. momentum and charge
D. angular momentum and mechanical energy
11
853If a disc slides from top to bottom of an
inclined plane, it takes time ( t_{1} ). If it rolls, it takes time ( t_{2} . ) Now, ( frac{t_{2}^{2}}{t_{1}^{2}} ) is
A ( cdot frac{1}{2} )
B. ( frac{2}{3} )
( c cdot frac{3}{2} )
D. ( frac{2}{5} )
11
854The density of a rod gradually decreases from one end to the other. It is pivoted at
an end so that it can move about a
vertical axis through the pivot. A horizontal force ( boldsymbol{F} ) is applied on the free end in a direction perpendiclar to the
rod. The quantities, that do not depend on which end of the rod is pivoted, are :
A . angular acceleration
B. angular velocity when the rod completes one rotation
c. angular momentum when the rod completes one rotation
D. torque of the applied force.
11
855In a clockwise system:
( mathbf{A} cdot hat{k} times hat{j}=hat{i} )
( mathbf{B} cdot hat{i} cdot hat{i}=0 )
c. ( hat{j} times hat{j}=hat{i} )
D. ( hat{k} cdot hat{j}=1 )
11
856A thin uniform disc of mass ( M ) and
radius ( R ) is rotating in a horizontal
plane about an axis passing through its centre and perpendicular to it with angular velocity ( omega . ) Another disc of the same radius but of mass ( frac{M}{4} ) is placed gently on the first disc coaxially. The angular velocity of the system will now finally change to:
A ( cdot frac{2 omega}{sqrt{5}} )
в. ( frac{2 omega}{5} )
c. ( frac{3 omega}{5} )
D. ( frac{4 omega}{5} )
11
857A particle tied to a string of negligible
weight and length ( L ) is rotated in a horizontal circular path with constant angular velocity having time period ( T . ) If
the string length is shortened by ( L / 2 )
while the particle is in motion, the time
period is:
A . 47
в. 27
c. ( T / 2 )
D. ( T / 4 )
11
858The length of the arm of a nutcracker is 15cm. A force of 22.5kgwt is required to cut a nut without cracker. Where should
the nut be placed on the cracker in order to cut it by a force of ( 2.25 k g / w t ? )
A. ( 1 mathrm{cm} ) from fulcrum
B. 1.5cm from fulcrum
( mathrm{c} .0 .5 mathrm{cm} ) from fulcrum
D. ( 2.0 mathrm{cm} ) from fulcrum
11
859Calculate the position of the centre of mass of a system consisting of two
particles of masses ( m_{1} ) and ( m_{2} ) separated by a distance L apart.
11
860During summer sault, a swimmer bends his body to
A. Increase moment of Inertia
B. Decrease moment of Inertia
c. Decrease the angular momentum
D. Reduce the angular velocity
11
861A bomb travelling in a parabolic path under the effect of gravity, explodes in mid-air. The centre of mass of
fragments will:
A. Move vertically upwards and then downwards
B. Move vertically downwards
c. Move in irregular path
D. Move in the parabolic path the unexploded bomb would have travelledd
11
862A circular disc is rotated in clockwise
direction in horizontal plane. The
direction of torque is
A. Horizontally right side
B. horizontally left side
c. Vertically upwards
D. Vertically downwards
11
863The ratio of the radii of gyration of the disc about its axis and about a tangent perpendicular to its plane will be:
A ( cdot frac{1}{sqrt{3}} )
в. ( sqrt{frac{3}{2}} )
c. ( frac{1}{sqrt{2}} )
D. ( sqrt{frac{5}{3}} )
11
864A uniform heavy disc of moment of
inertia ( I_{1} ) is rotating with constant
angular velocity ( omega_{1} . ) Then, a second
nonrotating disc of moment of inertia ( I_{2} )
is dropped on it. The two discs rotate together. The final angular velocity of the
system becomes
( mathbf{A} cdot frac{I_{1} omega_{1}}{I_{2}} )
B. ( sqrt{frac{I_{1}}{I_{2}} omega_{1}} )
C. ( frac{I_{1} omega_{1}}{I_{1}+I_{2}} )
D. ( frac{left(I_{1}-I_{2}right) omega_{1}}{I_{1}+I_{2}} )
11
865A thin wire of length ( L ) and uniform
linear mass density ( rho ) is bent into a
circular loop with centre at ( boldsymbol{O} ) as shown
in figure. Calculate the moment of in
inertia of the loop about the axis ( X X )
11
866A bullet of mass ( 20 mathrm{g} ) is fired from a rifle with a velocity of ( 800 m s^{-1} . ) After passing through a mud wall ( 100 mathrm{cm} )
thick, velocity drops to ( 100 mathrm{ms}^{-1} ). What
is the average resistance of the wall? (Neglect friction due to air and work of
gravity)
11
867A solid cylinder starts rolling down on an inclined plane from its top and ( V ) is
the velocity of its centre of mass on reaching the bottom of inclined plane. If a block starts sliding down on an
identical inclined plane but smooth,
from its top, then the velocity of block on reaching the bottom of inclined plane is :
A ( cdot frac{V}{sqrt{2}} )
B. ( sqrt{2} V )
c. ( sqrt{frac{3}{2}} V )
D. ( sqrt{frac{2}{3}} V )
11
868Two persons of equal height are
carrying a long uniform wooden plank of length ( l . ) They are at distance ( frac{l}{4} ) and ( frac{l}{6} )
from nearest end of the rod. The ratio of
normal reaction at their heads is-
( mathbf{A} cdot 2: 3 )
B. 1: 3
( c cdot 4: 3 )
D. 1: 2
11
869For a bowling ball, how far apart are the
center of gravity and center of mass?
A. They are at almost exactly the same location.
B. They are at opposite sides of the object.
C. They are both at the surface of the object.
D. They mean the same thing, so they’re at the same location, as always.
E. None of the other answers is correct.
11
870A cord is wound around the
circumference of a bicycle wheel
(without tyre) of diameter 1 m. A mass
of ( 2 k g ) is tied to the end of the cord and
it is allowed to fall from rest. The weight
falls ( 2 m ) in ( 4 s ). The axle of the wheel is
horizontal and the wheel rotates with its
plane vertical. The angular acceleration produced is:
( left(operatorname{take} g=10 m s^{-2}right) )
A ( cdot 0.5 ) rads( ^{-2} )
c. 2 rads ( ^{-2} )
D. 4 rads ( ^{-2} )
11
871Write Sl unit of angular momentum.11
872Two point masses ( m ) and ( 3 m ) are placed
at distance. The moment of inertia of the
system about an axis passing through the center of mass of system and perpendicular to the line joining the point masses is
A ( cdot frac{3}{5} m r^{2} )
в. ( frac{3}{4} m r^{2} )
c. ( frac{3}{2} m r^{2} )
D. ( frac{6}{7} m r^{2} )
11
873Two skaters ( A ) and ( B ) of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?
A. Both have moved 3 metres
B. A moves 2.5 metres and B moves 3.5 metres.
C. A moves 3.5 metres and ( B ) moves 2.5 metres
D. A moves 2 metres and B moves 4 metres
11
874A horizontal plane supports a fixed vertical cylinder of radius ( R ) and a particle is attached to the cylinder by a horizontal thread ( A B ) as shown in
figure. A horizontal velocity ( boldsymbol{v}_{0} ) is
imparted to the particle, normal to the thread, then during subsequent motion:
A. Angular momentum of particle about ( O ) remain constant
B. Angular momentum of particle about ( B ) remains constant
c. Momentum of particle remains constant
D. Kinetic energy of particle remains constant
11
875A uniform rod of length one meter is
bent at its midpoint to make ( 90^{0} ). The
distance of centre of mass from the
centre of rod is(in cm)?
A . 20.2
в. 13.4
c. 15
D. 35.36
11
876A uniform disc of mass ( M ) and radius ( R )
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull ( T ) is exerted on the cord, the tangential acceleration of a point on the rim is
A ( cdot frac{T}{M} )
в. ( frac{M}{T} )
c. ( frac{2 T}{M} )
D. ( frac{M}{2 T} )
11
877Assertion
For the planets orbiting around the sun, angular speed, linear speed and K.E. changes with time, but angular
momentum remains constant.
Reason
No torque is acting on the rotating planet. So its angular momentum is
constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
878stands at the end of diving board, as
shown. The board is uniform, massive
and solid. There is no vibration or
motion of any kind. The board is firmly
attached to two supports at point ( boldsymbol{P}_{1} )
and ( P_{2} . ) The professor now begins to walk slowly in (right) from the end of
the board towards ( P_{1} . ) While he is
walking, how should you describe the force on the board by the support at
point ( P_{2} ? ) (i.e. Over at the far right hand
end)
A. upwards and increasing magnitude.
B. upwards and decreasing magnitude
c. downwards and increasing magnitude.
D. downwards and decreasing magnitude
11
879A sphere is released on a smooth
inclined plane from the top. When it
moves down its angular momentum is:
B. conserved about the point of contact only
c. conserved about the centre of the sphere only
D. conserved about any point on a fixed line parallel to the inclined plane and passing through the centre of the ball
11
880The mass ( 100 g ) and ( 300 g ) at a given time have velocities ( 10 hat{i}-7 hat{j}-3 hat{k} ) and ( mathbf{7} hat{mathbf{i}}-mathbf{9} hat{mathbf{j}}+mathbf{6} hat{boldsymbol{k}} ) respectively. Determine
velocity of ( boldsymbol{C O} boldsymbol{M} )
11
881A uniform thin rod of mass ( m ) and
length ( l ) is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the
smooth surface and the rod starts
falling. Find the velocity of centre of mass of the rod at the instant when it
makes and angle ( theta ) with horizontal.
11
882Thin threads are tightly wound on the ends of a uniform solid cylinder of mass
m. The free ends of the threads are
attached to the ceiling of an elevator car. The car starts going up with an
acceleration ( overrightarrow{boldsymbol{w}}_{mathbf{0}} )
Find the acceleration ( vec{w}^{prime} ) of the cylinder
relative to the car:
A ( cdot vec{w}^{prime}=frac{2}{3}left(g-vec{w}_{0}right) )
B ( cdot vec{w}^{prime}=frac{3}{2}left(g-vec{w}_{0}right) )
c. ( vec{w}^{prime}=2 frac{3}{2}left(g-vec{w}_{0}right) )
D・ ( vec{w}^{prime}=2 frac{2}{3}left(g-vec{w}_{0}right) )
11
883The instantaneous angular position of a point on a rotating wheel is given by the equation ( boldsymbol{theta}(boldsymbol{t})=2 boldsymbol{t}^{3}-boldsymbol{6} boldsymbol{t}^{2} . ) The torque on
the wheel becomes zero at :
( mathbf{A} cdot t=1 s )
B. ( t=0.5 s )
c. ( t=0.25 s )
( mathbf{D} cdot t=2 s )
11
884The acceleration of the system will be
A ( frac{g}{2} )
в. ( frac{g}{4} )
c. ( frac{7 g}{24} )
( D cdot g )
8
11
885A rod PQ of mass ‘m’ and length ‘I’
rotated about and axis through ‘p’ as
shown in figure.Find the moment of
A ( cdot frac{3 g}{2 L} )
B. ( frac{m l^{2}}{3} )
c. ( frac{m l^{2}}{3} cos ^{2} theta )
D. ( frac{m l^{2}}{3}+m l^{2} )
11
886A ceiling fan is rotating at the rate of
( 3.5 r p s ) and its moment of inertia is
( 1.25 k g m^{2} . ) If the current is switched off
the fan comes to rest in ( 5.5 s . ) The torque acting on the fan due to friction is:
A . ( 2.5 mathrm{Nm} )
B. ( 5 mathrm{Nm} )
( mathrm{c} .7 .5 mathrm{Nm} )
D. 10 Nm
11
887A square plate of mass ( M ) and edge ( L )
is shown in the fig. The moment of
inertia of the plate about the axis in the
plane of plate and passing through one
of its vertex making an angle ( 15^{0} ) with the horizontal is
A. ( frac{M L^{2}}{12} )
B. ( frac{11 M L^{2}}{24} )
( c cdot frac{7 M L^{2}}{12} )
D. none of these
11
888A man hangs from a rope attached to a hot-air balloon. The mass of the man is
greater than the mass of the balloon
and its contents. The system is stationary in air. If the man now climbs up to the balloon using the rope, the
centre of mass of the ‘man plus balloon
system wiii
A. remain stationary
B. move up
c. move down
11
889Using the formula for the moment of
inertia of a uniform sphere, the moment
of inertia of a thin spherical layer of
mass ( m ) and radius ( R ) relative to the
axis passing through its centre is ( boldsymbol{I}= ) ( frac{2}{x} m r^{2} . ) Find the value of ( x )
11
890If ( I ) is the moment of inertia of a
circular ring about a tangent of ring in its plane then the moment of inertia of the same ring about a tangent of ring perpendicular to its plane is:
A ( cdot frac{2 I}{3} )
в. ( frac{3 I}{2} )
c. ( frac{4 I}{3} )
D. ( frac{3 I}{4} )
11
891In the figure shown, a cubical block is held stationary against a rough wall by
applying force, ‘ ( boldsymbol{F}^{prime} ), then incorrect
statement among the following is
A. frictional force ( f=M g )
B. ( F=N, N ) is normal reaction
C. ( F ) does not apply any toque
D. ( N ) does not apply any torque
11
892Two rings each of mass ‘ ( m^{prime} ) and radius
( r^{prime} ) are placed such that their centres
are at a common point and their planes
are normal to each other. The moment of
inertia of the system about an axis passing through the centre and perpendicular to plane of one of ring is:
A ( cdot 2 m r^{2} )
B. ( m r^{2} )
c. ( frac{1}{2} m r^{2} )
D. ( frac{3}{2} m r^{2} )
11
893The unit vector perpendicular to the plane containing ( overrightarrow{boldsymbol{A}}, overrightarrow{boldsymbol{B}} ) such that ( overrightarrow{boldsymbol{A}}= )
( 4 hat{i}-hat{j}-hat{k} ) and ( vec{B}=4 hat{i}+hat{j}-4 hat{k} ) is:
( frac{5 hat{i}-5 hat{j}+5 hat{k}}{sqrt{3}} )
B. ( frac{5 hat{i}+12 hat{j}+8 hat{k}}{sqrt{233}} )
c. ( frac{hat{i}+3 hat{j}+hat{k}}{11} )
D. ( 5 hat{i}-5 hat{j}+5 hat{k} )
11
894The moment of force of ( 5 N ) about a
point ( boldsymbol{P} ) is ( 20 mathrm{Nm} ). Calculate the
distance of point of application of the
from the point ( boldsymbol{P} )
( A .3 m )
в. ( 0.6 m )
( c .4 m )
D. ( 10 m )
11
895Assertion
If there is no external torque acting on a body about its center of mass, then the velocity of the center of mass remains constant.
Reason
The linear momentum of an isolated
system remains constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
11
896A planet of mass ( m ) is in an elliptical
orbit about the sun ( left(boldsymbol{m}<<boldsymbol{M}_{text {sun }}right) ) with
an orbital period. If ( A ) be the area of orbit, then its angular momentum would be:
( ^{mathrm{A}} cdot frac{2 m A}{T} )
в. ( m A T )
c. ( frac{m A}{2 T} )
D. ( 2 mathrm{mAT} )
11
897Which of the following pairs do not
match?
A. Rotational power – Joule
B. Torque – Newton meter
D. Angular acceleration – Radian/sec ( ^{2} )
11
898A light rod of length ( 1 mathrm{m} ) is pivoted at its
centre and two masses of ( 5 mathrm{kg} ) and ( 2 mathrm{kg} ) are hung from the ends as shown in figure. Find the initial angular acceleration of the rod assuming that it was horizontal in the beginning.
11
899A particle is moving with a constant speed in a circular path. The ratio of average velocity to its instantaneous velocity when the particle describe an angle ( frac{pi}{2} ) is?
A. ( 3 / 2 pi )
B. ( frac{2 sqrt{2}}{pi} )
( c cdot frac{2}{pi} )
D.
11
900The moment of inertia of a metre stick
of mass ( 300 g ), about an axis at right
angles to the stick and located at ( 30 mathrm{cm} )
mark, is
( mathbf{A} cdot 8.3 times 10^{5} g mathrm{cm}^{2} )
в. ( 5.8 g mathrm{cm}^{2} )
C. ( 3.7 times 10^{5} mathrm{g} mathrm{cm}^{2} )
D. None of these
11
901A man ( m=80 k g ) is standing on a
trolley of mass ( 320 mathrm{kg} ) on a smooth surface. If man starts walking on trolley along rails at a speed of ( 1 boldsymbol{m} / boldsymbol{s}, ) then
after 4 sec, his displacement relative to
ground is
A . ( 4 m )
B. ( 4.8 m )
c. ( 3.2 m )
D. ( 6 m )
11
902A body of mass 2 kg moving with velocity of ( 6 mathrm{m} / mathrm{s} ) strike another body of same mass at rest and sticks to it. The
amount of heat evolved during collision is:
A . 18 J
B. 36 J
c. 9 J
D. 3
11
903Two coherent sources separated by
distance d are radiating in phase having wavelength ( lambda ). A detector moves
in a big circle around the two sources in
the plane of the two sources. The angular position of ( n=4 ) interference maxima is given as
A ( cdot sin ^{-1} frac{n lambda}{d} )
B. ( cos ^{-1} frac{4 lambda}{d} )
c. ( tan ^{-1} frac{d}{4 lambda} )
D. ( cos ^{-1} frac{lambda}{4 d} )
11
904Centre of gravity is the point
A. where the weight of the object is supposed to be present or concentrated.
B. where the weight of the object is perpendicular to the surface area of the object
C. where maximum no of molecules presents
D. none of the above
11
905A circular hoop of mass ( M ) and radius
( R ) is suspended from a nail in the wall.
Its moment of inertia about an axis
along the nail will be:
A. Zero
В. ( M R^{2} )
( mathrm{c} cdot 2 mathrm{M} R^{2} )
D. ( frac{M R^{2}}{2} )
11
906A gymnast takes turns with her arms ( & )
legs stretched. When she pulls her arms
& legs in
A. The angular velocity decreases
B. The moment of inertia decreases
c. The angular velocity stays constant
D. The angular momentum increases
11
907A tennis ball has a mass of 57 g and a diameter of ( 7 mathrm{cm} . ) Find the moment of
inertia about its diameter. Assume the
ball is a thin spherical shell:
A . ( 4.65 times 10^{-5} )
В. ( 9.65 times 10^{-5} )
c. ( 4.65 times 10^{-3} )
D. ( 9.65 times 10^{-3} )
11
908A block of mass ( M ) with a semicircular
track of radius ( R ) rests on a horizontal
frictionless surface. A uniform cylinder
of radius ( r ) and mass ( m ) is released
from rest from the top point ( boldsymbol{A} ). The
cylinder steps on the semicircular frictionless track. The distance travelled
by the block when the cylinder reaches
the point ( boldsymbol{B} ) is :
A ( cdot frac{M(R-r)}{M+m} )
В ( cdot frac{m(R-r)}{M+m} )
c. ( frac{(M+m) R}{M} )
D. None of the above
11
909Four particles ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} ) and ( boldsymbol{D} ) with
( operatorname{masses} boldsymbol{m}_{boldsymbol{A}}=boldsymbol{m}, boldsymbol{m}_{B}=2 boldsymbol{m}, boldsymbol{m}_{C}=3 boldsymbol{m} )
and ( m_{D}=4 m ) are at the corners of a
square. They have accelerations of
equal magnitude with directions as
shown. The acceleration of the centre of
mass of the particles is
A ( cdot frac{a}{5}(hat{i}-hat{j}) )
B・ ( frac{a}{5}(hat{i}+hat{j}) )
( c, ) zer
D. ( a(hat{i}+hat{j}) )
11
910If the moment of inertia of a circular
disc about an axis tangentially and
parallel to its surface be ( I ), then the moment of inertia about the axis
tangential but perpendicular to the surface will be :
A ( cdot frac{6}{5} I )
в. ( frac{3}{4} I )
c. ( frac{3}{2} I )
D. ( frac{5}{4} )
11
911A billiard ball is struck by a cue. The line of action of applied impulse is horizontal and passes through the
center of the ball. The initial velocity ( V_{0} ) of the ball, radius ( R ), mass ( m ) and
coefficient of friction ( mu ) between ball
and table are known. The ball moves distance ( frac{12 V_{0}^{2}}{X mu g} ) before it ceases to slip on the table. What is the value of ( X ? )
A .49
в. зб
( c cdot 25 )
( D cdot 64 )
11
912Three rings each of mass ( m ) and radius
are so placed that they touch each
other. The radius or gyration of the
system about the axis as shown in the
figure is:
A ( cdot sqrt{frac{6}{5}} )
B. ( sqrt{frac{5}{6}} )
c. ( sqrt{frac{6}{7}} )
D. ( sqrt{frac{7}{6}} )
11
913Calculate the velocity of a body of a mass 2 kg whose linear momentum is 5
N s.
A ( .2 .5 mathrm{ms}^{-1} )
B. ( 10 mathrm{ms}^{-1} )
c. ( 5 m s^{-1} )
D. ( 2 m s^{-1} )
11
914A ring rolls without slipping on the
ground. Its centre ( C ) moves with a
constant speed ( u . P ) is any point on the
ring. The speed of ( P ) with respect to the
ground is ( boldsymbol{v} ) This question has multiple correct options
A ( .0 leq v leq 2 u )
B. ( v=u ), if ( C P ) is horizontal
c. ( v=u ), if ( C P ) makes and angle of ( 30^{circ} ) with horizontal and ( P ) is below the horizontal level of ( C )
D. ( v=sqrt{2} u ), if ( C P ) is horizontal
11
915Fill in the blank.
The distance between any two given points of a rigid body in
time regardless of external forces
exerted on it.
A. increases
B. remains constant
c. decrease
D. depend of the external force
11
916against the inner surface of a
larger sphere of radius 6 R. The masses of large and small spheres are ( 4 mathrm{M} ) and
M respectively. This arrangement is placed on a horizontal table as shown.
There is no friction between any
surfaces of contact. The small sphere is
now released. The coordinates of the
centre of the large sphere when the
smaller sphere reaches the other
extreme position is
A ( cdot(L-2 R, 0) )
B. ( (L+2 R, O) )
c. ( (2 R, 0) )
D. ( (2 R-L )
11
917A chain couples and rotates two wheels in a bicycle. The radii of bigger and smaller wheels are ( 0.5 m ) and ( 0.1 m )
respectively. The bigger wheel rotates at
the rate of 200 rotations per minute, then the rate of rotation of smaller
wheel will be:
A. 1000 rpm
в. ( frac{50}{3} ) грт
c. 200 rpm
D. 40 rp
11
918An electron collides with a free
molecule initially in its ground state. The collision leaves the molecule in an
excited state that is metastable and
does not decay to the ground state by radiation. Let ( K ) be the sum of the
initial kinetic energies of the electron and the molecule, the ( vec{P} ) the sum of their initial momenta. Let ( K^{prime} ) and ( vec{P} )
represent the same physical quantities after the collision. Then.
( mathbf{A} cdot K=K^{prime}, vec{P}=vec{P} )
B . ( K^{prime}<K, vec{P}=vec{P}^{prime} )
C . ( K=K^{prime}, vec{P} neq vec{P}^{prime} )
D . ( K^{prime} neq K, vec{P} neq vec{P}^{prime} )
11
919A sphere has to purely roll upwards. At an instant when the velocity of sphere is
( v, ) frictional force acting on it is
A. downwards and ( mu ) mg cos ( theta )
B. downwards and ( frac{2 m g sin theta}{7} )
c. upwards and ( mu m g cos theta )
D. upwards and ( frac{2 m g sin theta}{7} )
11
920A system consisting of two masses connected by a mass less rod lie along the ( x- ) axis. ( A 0.4 k g ) mass is at a
distance ( x=2 m ) while a 0.6 kg mass is
at a distance ( boldsymbol{x}=mathbf{7} ) m. The ( boldsymbol{x} )
coordinate of the centre of mass is
( mathbf{A} cdot 5 m )
B. ( 3.5 m )
c. ( 4.5 mathrm{m} )
D. ( 4 m )
11
921Center of gravity is usually located where
A. less mass is concentrated
B. less weight is concentrated
c. more mass is concentrated
D. more weight is concentrated
11
922Consider an “L”-shaped object where the vertical leg extends from the origin to
(0,5) and the horizontal segment
extends from the origin to (3,0)
Assume that the object has uniform
linear density throughout. Where is the location of the center of
( operatorname{mass}(boldsymbol{C o} boldsymbol{M}) ? )
A ( cdot(1.5,1.5) )
B . (1.5,2.5)
( mathbf{c} cdot(2.5,2.5) )
D. The center of mass for an “L” is undefined because there is no single point on the object where it can be supported, such that it will not rotate
E. None of these
11
923A uniform solid right circular cone of
base radius ( mathrm{R} ) is joined to a uniform
solid hemisphere of radius ( R ) and of the
same density, as shown. The centre of
mass of the composite solid lies at the
centre of base the cone. The height of
the cone is
( mathbf{A} cdot 1.5 mathrm{R} )
B. ( sqrt{3} ) R
( c cdot 3 R )
D. ( 2 sqrt{3} ) R
11
924can imagine 2 similar objects rotating around a sphere at the same velocity but at different orbits. One object would
rotate around the sphere faster than the other, right? What is puzzling to me is that if I think of both objects going now in a straight line one could not say that one object was going faster than the other. Can someone help me through this? Is there a subtlety here?
11
925Drum B undergoes
A. translational motion
B. rotational motion
c. rotational as well as transaltional motion
D. none of the above
11
926M.I of hemisphere about axis ( 2, ) which is
parallel to diameter but passing
through centre of mass, will be
( ^{mathrm{A}} cdot frac{83}{320} m R^{2} )
( ^{mathbf{B}} cdot frac{2}{5}^{m R^{2}} )
( c cdot frac{m R^{2}}{5} )
( frac{2}{3}^{m R^{2}} )
11
927A uniform metre rule balances ho
rizontally on a knife edge placed at the ( 58 c m ) mark when a weigh of ( 29 g f ) is
suspended from one end.
(i)Draw a diagram of the arrangement
(ii)What is the weight of the rule?
11
928A flywheel of moment of inertia
( 0.4 K g / m^{2} ) and radius ( 0.2 m ) is free to
rotate about a central axis. If a string is wrapped around it and it is pulled with a force of ( 10 N ) then its angular velocity
after ( 4 s ) will be
A. ( 5 r a d / s )
c. ( 10 r a d / s )
D. ( 0.8 mathrm{rad} / mathrm{s} )
11
929Assuming the earth to be a homogeneous sphere, determine the
density of the earth from the following data:
( g=9.8 mathrm{m} / mathrm{s}^{2}, mathrm{G}=6.673 times 10^{-11} mathrm{Nm}^{2} / mathrm{kg}^{2} )
( R=6400 mathrm{km} )
11
930Two men of equal masses stand at
opposite ends of the diameter of a
turntable disc of a certain mass,
moving with constant angular velocity.
The two men make their way to the
middle of the turntable at equal rates. In
doing so will
A. kinetic energy of rotation has increased while angular momentum remains same.
B. kinetic energy of rotation has decreased while angular momentum remains same.
C. kinetic energy of rotation has decreased but angular momentum has increased.
D. both, kinetic energy of rotation and angular momentum have decreased.
11
931If ( overline{boldsymbol{F}} ) is the force and ( bar{r} ) is the radius
vector, then the torque is :
A ( cdot bar{r} times bar{F} )
в. ( bar{r} bar{F} )
c. ( |bar{r}| .|bar{F}| )
D ( cdot frac{|bar{r}|}{|bar{F}|} )
11
932A ( 2.0 m ) diameter propeller is rotating at
( 2500 r p m )
Which of the following values best represents the tangential velocity of the tip of the propeller blade?
A ( .262 m / s )
в. ( 524 m / s )
c. ( 1,050 m / s )
D. ( 15,700 mathrm{m} / mathrm{s} )
E . ( 2500 mathrm{m} / mathrm{s} )
11
933Calculate total moment of the two
A. ( 2 N m ) (clockwise)
B. ( 2 N ) m(anti clockwise)
c. ( 4 N m ) (clockwise)
D. ( 4 N m ) (anti clockwise)
11
934Which of the following relations is
correct?
A ( cdot v=w^{2} r )
B . ( v=w r^{2} )
c. ( v=w r )
( mathbf{D} cdot v=w^{2} r^{2} )
11
935The centre of gravity of a rod (of length
L), whose linear mass density varies as
the square of the distance from one end
is at:
A ( cdot frac{3 L}{5} )
В ( cdot frac{2 L}{5} )
c. ( frac{L}{3} )
D. ( frac{3 L}{4} )
11
936A nut is opened by a wrench of length ( 10 mathrm{cm} . ) If the least force required is
( 5.0 N, ) find the moment of force needed
to turn the nut.
( A .50 N m )
в. ( 0.5 N mathrm{cm} )
c. ( 5 N m )
D. ( 0.5 N ) m
11
937The radius of gyration of a disc of mass ( 100 g ) and radius ( 5 c m ) about an axis passing through its centre of gravity and perpendicular to the plane is (in ( mathrm{cm} )
A . 0.5
B . 2.
( c .3 .54 )
D. 6.54
11
938Four particles each of mass ( boldsymbol{m} ) are
placed at the corners of a square of side length ( l ). The radius of gyration of the system about an axis perpendicular to the square and passing through its
center is:
A ( frac{l}{sqrt{2}} )
B. ( frac{l}{2} )
c. ( l )
D. ( (sqrt{2}) l )
11
939Two spheres of mass ( M ) and ( 4 M ) are connected by a rod whose mass is negligible, and the distance between the centers of each sphere is ( d )
The ( 4 M ) sphere is moved a distance ( d / 3 ) towards the smaller sphere. How far has the Center of Mass for the
entire object moved?
A. The Center of Mass has not moved, because both spheres still have their original masses
в. ( d / 15 )
( c cdot d / 5 )
D. ( 4 d / 15 )
E . ( 8 d / 15 )
11
940Three bodies, a ring, a solid cylinder and
a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies
are identical. Which of the bodies
reaches the ground with maximum velocity?
11
941Consider a uniform disc of mass ( 4 mathrm{kg} ) performing pure rolling with velocity 5 ( mathrm{m} / mathrm{s} ) on a fixed rough surface
A. Kinetic energy of upper half will be 37.5 J
B. Kinetic energy of upper half will be less than 37.5
c. Kinetic energy of upper half will be more than 37.5 j
D. Kinetic energy of upper half will be more than 75
11
942When a ceiling fan is switched off, its angular velocity reduces by ( 50 % ) while it makes 36 rotations. How many more
rotations will it make before coming to rest? (Assume uniforms angular retardation)
A . 48
B . 36
c. 12
D. 18
11
943Three point particles of masses ( 1.0 k g )
( 1.5 k g ) and ( 2.5 k g ) are placed at three corners of a right angle triangle of sides
4.0 ( c m, 3.0 c m ) and ( 5.0 c m ) as shown in
the figure. The centre of mass of the
system is at a point :
A. ( 1.5 mathrm{cm} ) right and ( 1.2 mathrm{cm} ) above ( 1 mathrm{kg} ) mass
B. ( 2.0 mathrm{cm} ) right and ( 0.9 mathrm{cm} ) above ( 1 mathrm{kg} ) mass
c. ( 0.6 mathrm{cm} ) right and ( 2.0 mathrm{cm} ) above ( 1 mathrm{kg} ) mass
D. ( 0.9 mathrm{cm} ) right and ( 2.0 mathrm{cm} ) above ( 1 mathrm{kg} ) mass
11
944A thin horizontal disc of radius ( R= )
( 10 mathrm{cm} ) is located within a cylindrical
cavity filled with oil whose viscosity ( boldsymbol{eta}=mathbf{0 . 0 8} boldsymbol{P} ) (figure shown above). The
clearance between the disc and the
horizontal planes of the cavity is equal
to ( h=1.0 m m . ) Find the power
developed by the viscous forces acting on the disc when it rotates with the
angular velocity ( omega=60 mathrm{rad} / mathrm{s} ). The end
effects are to be neglected. Round off to closest integer.
11
945An object can have
A. more than one center of gravity.
B. only one center of gravity
C . always two center of gravity
D. none of the above
11
946A rigid body in the shape of a ( V ) has two equal arms made of uniform rods.What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?
( ^{A} cdot cos ^{-1}left(frac{1}{3}right) )
B. ( cos ^{-1}left(frac{1}{2}right) )
c. ( cos ^{-1}left(frac{1}{4}right) )
D. ( cos ^{-1}left(frac{1}{6}right) )
11
947Conservation of linear momentum is
equivalent to
A. Newton’s first law of motion
B. Newton’s second law of motion
c. Newton’s third law of motion
D. Newton’s law of gravitation
11
948Then the displacement of the centre of mass ( mathrm{m} ) at time ( mathrm{t} ) is :
A ( frac{F t^{2}}{2 m} )
B. ( frac{F t^{2}}{3 m} )
c. ( frac{F t^{2}}{4 m} )
D. ( frac{F t^{2}}{m} )
11
949A rod of mass ( M ) and length ( L ) is placed
on a horizontal plane with one end hinged about the vertical axis. horizontal force of ( boldsymbol{F}=frac{boldsymbol{m} boldsymbol{g}}{mathbf{3}} ) is applied
( boldsymbol{L} )
at a distance ( frac{-}{3} ) from the hinged end.
The angular acceleration of the rod will
be:-
11
950A ring rolls without slipping on the
ground. Its centre ( C ) moves with a
constant speed ( u . P ) is any point on the
ring. The speed of ( P ) with respect to the
ground is ( boldsymbol{v} ) This question has multiple correct options
A ( .0 leq v leq 2 u )
B. ( v=u ), if ( C P ) is horizontal
c. ( v=u ), if ( C P ) makes and angle of ( 30^{circ} ) with horizontal and ( P ) is below the horizontal level of ( C )
D. ( v=sqrt{2} u ), if ( C P ) is horizontal
11
951A body of mass ( M ) at rest explodes into
three pieces, two of which of mass ( M / 4 )
each are thrown off in perpendicular directions with velocities of ( 3 m / s ) and ( 4 m / s ) respectively. The third piece will be thrown off with a velocity of
A. ( 1.5 mathrm{m} / mathrm{s} )
в. 2.0 ( m / s )
( c .2 .5 mathrm{m} / mathrm{s} )
D. 3.0 ( m / s )
11
952A large number of particles are placed around the origin, each at a distance ( mathrm{R} ) from the origin. The distance of the center of mass of the system from the origin is.
( mathbf{A} cdot+R )
в. ( leq R )
( c cdot>R )
( D . geq R )
11
953Electrons in a TV tube move horizontally
South to North. Vertical component of earth’s magnetic field points down. The electron is deflected towards which
direction? ( [boldsymbol{F}=boldsymbol{q}(overrightarrow{boldsymbol{v}} times overrightarrow{boldsymbol{B}})] )
A. west
B. No deflection
c. East
D. North to South
11
954A uniform rod of mass ( mathrm{m} ) and length Lis held at rest by a force ( F ) applied at it’s end as shown in the vertical plane. The ground is sufficiently rough. Find
(a) Force ( F )
(b) Normal reaction exerted by the
ground
(c) Frictional force exerted by the ground (magnitude and dirtection)
11
955Two particles each of the same mass move due north and due east
respectively with the same velocity ( ^{prime} V^{prime} ) The magnitude and direction of the velocity of the center of mass is:
A ( cdot frac{V}{sqrt{2}} N E )
в. ( sqrt{2} V N E )
c. ( 2 V S W )
D. ( frac{V}{2} S W )
11
956A metal rod of uniform thickness and of
length ( 1 m ) is suspended at its ( 25 c m )
division with the help of a string. The rod remains horizontally straight when a block of mass ( 2 k g ) is suspended to
the rod at its ( 10 mathrm{cm} ) division from same
end. The mass of the rod is:
A. ( 0.4 mathrm{kg} )
B. ( 0.8 mathrm{kg} )
c. ( 1.2 mathrm{kg} )
D. ( 1.6 mathrm{kg} )
11
and radius ( 20 mathrm{cm} . ) A steady pull of ( 25 mathrm{N} )
is applied on the cord as shown in the
figure. The fly wheel is mounted on a horizontal axle with frictionless
bearings. Find the workdone by the pull when ( 2 mathrm{m} ) of the cord is unwound.
A. 30
3. 40
c. 50
)
11
958the angular acceleration of the ball about its centre of mass is ( =frac{x mu g cos theta}{2 R} )11
959The translation distances ( (d x, d y) ) is called as
A. Translation vector
B. Shift vector
c. Both A and B
D. Neither A nor B
11
960Two points ( P ) and ( Q ), diametrically opposite on a disc of radius ( R ) have
linear velocities ( v ) and ( 2 v ) as shown in
figure. The angular speed of the disc is
( overrightarrow{r R} )
Find the value of ( x )
11
961For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken
A. the centre of the system
B. the centre of mass of the system
c. any point on the system
11
962Consider following statements. Choose
the correct ones:
This question has multiple correct options
A. ( mathrm{CM} ) of a uniform semicircular disc of radius ( mathrm{R} ) is ( 2 R pi )
from the centre.
B. ( mathrm{CM} ) of a uniform semicircular ring of radius ( 2 R / 3 ) is ( 4 R / 3 pi ) from the centre.
C. ( mathrm{CM} ) of a solid hemisphere of radius ( mathrm{R} ) is ( 4 R / 3 pi ) from the centre.
D. ( mathrm{CM} ) of a solid hemisphere shell of radius ( mathrm{R} ) is ( R / 2 ) from the centre.
11
963Two bodies of different masses have
same K.E. The one having more momentum is
A. Heavier body
B. Iighter body
c. both none
D. both
11
964A mass ‘m’ is fixed at ( x=a ) on a
parabolic wire with its axis vertical and
vertex at the origin as shown in the
figure. The equation of parabola is ( x^{2}= )
4ay. The wire frame is rotating with
constant angular velocity ( omega ) about ( Y )
axis. The acceleration of the bead is
( A cdot frac{a}{4} omega^{2} )
B. ( a omega^{2} )
c. zero
( D )
11
965What is the speed in rpm if the apparent weight of the person at the highest point is zero?
A. 1.87 rpm
B. 2.87 rpm
c. 3.32 rpm
D. 2.08 rpm
11
966Core condition for state of equilibrium in principle of moment is:
A. Distance between two objects in a beam balance should be same
B. Resultant of force should be zero
c. weight of both the object on beam balance should be same
D. Tension should be equal on both sides
11
967Moment of momentum is called:
A. Torque
B. Impulse
c. couple
D. Angular momentum
11
968A uniform ladder of length ( 5 m ) is placed against the wall as shown in the figure. If coefficient of friction ( mu ) is the same for
both the walls. what is the minimum
value of ( mu ) for it not to slip?
A ( cdot mu=1 / 2 )
B. ( mu=1 / 4 )
c. ( mu=1 / 3 )
D. ( mu=1 / 5 )
11
969A particle of mass ‘ ( m^{prime} ) is rigidly
attached at ( ^{prime} A^{prime} ) to a ring of mass ( ^{prime} 3 m^{prime} )
and radius ‘ ( r .^{prime} ) The system is released
from rest and rolls without sliding. The angular acceleration of ring just after
release is
( ^{A} cdot frac{g}{4 r} )
в. ( frac{g}{6 r} )
( c )
( frac{g}{2 r} )
11
970rest on a rough horizontal table. A
horizontal force ( F ) is applied normal to one of the face at a point, at a height ( 3 b / 4 ) above the base. What should be
the coefficient of friction ( (mu) ) between
cube and table so that it will tip about
an edge before it starts slipping?
‘ ( mu>frac{2}{3} )
3. ( mu>frac{1}{3} )
( c_{mu>frac{3}{2}} )
( D )
11
971Two point masses ( m ) and ( M ) are
separated by a distance ( L ). The distance
of the center of mass of the system from
( boldsymbol{m} ) is :
( mathbf{A} cdot L(m / M) )
в. ( L(M / m) )
c. ( _{Lleft(frac{M}{m+M}right)} )
D. ( Lleft(frac{m}{m+M}right) )
11
972In the figure shown a planet moves in an
elliptical orbit around the sun. Compare
the speeds, linear and angular
momenta at the points ( A ) and ( B )
11
973The system is said to be in equilibrium when
A ( cdot stackrel{F_{1}}{longrightarrow}-stackrel{F_{2}}{longrightarrow}=0 )
B. ( stackrel{F_{1}}{longrightarrow}-stackrel{F_{2}}{longrightarrow}=+v e )
c. ( stackrel{F_{1}}{longrightarrow}-stackrel{F_{2}}{longrightarrow}=-v e )
D. All
11
974Which of the following statements about angular momentum is correct?
A. It is moment of inertia
B. It is directly proportional to moment of inertia
c. . tis a scalar quantity
D. All of these
11
975A thin uniform rod of length ( L ) is bent at
its midpoint as shown in the figure. The distance of the center of mass from the
point ( ^{prime} boldsymbol{O}^{prime} ) is
A ( cdot frac{L}{2} cos frac{theta}{2} )
B. ( frac{L}{4} sin frac{theta}{2} )
c. ( frac{L}{4} cos frac{theta}{2} )
D. ( frac{L}{2} sin frac{theta}{2} )
11
976A body of mass 2 g, moving along the positive ( x- ) axis in gravity free space
with velocity ( 20 mathrm{cms}^{-1} ) explodes at ( x= ) ( mathbf{1} mathbf{m}, boldsymbol{t}=mathbf{0} ) into two pieces of masses ( frac{mathbf{2}}{mathbf{3}} )
( mathrm{g} ) and ( frac{4}{3} ) g. After ( 5 mathrm{s} ), the lighter piece is at the point ( (3 m, 2 m,-4 m) . ) Then the position of the heavier piece at this moment, in metres is
в. (1.5,-2,-2)
begin{tabular}{l}
c. (1.5,-1,-1) \
hline
end{tabular}
D. None of these
11
977A uniform disc of radius ( R ) is spinned to
the angular velocity ( omega ) and then
carefully placed on a horizontal surface.
How long will the disc be rotating on the surface if the friction coefficient is
equal to ( k ) ? The pressure exerted by the
disc on the surface can be regarded as uniform.
( mathbf{A} cdot_{t}=frac{5 R omega_{0}}{4 k g} )
B. ( t=frac{3 R omega_{0}}{4 k g} )
( mathbf{c} cdot_{t}=frac{3 R omega_{0}}{8 k g} )
D. None of these
11
978A body weighs ( 8 g ) when placed in one
pan and ( 18 g ) when placed on the other pan of a false balance. If the beam is
horizontal when both the pans are
empty, the true weight of the body is:
A ( cdot 13 g )
в. ( 12 g )
c. ( 15.5 g )
D. ( 15 g )
11
979If ( overrightarrow{boldsymbol{A}}=mathbf{5} hat{boldsymbol{i}}+mathbf{7} hat{boldsymbol{j}}-boldsymbol{3} hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=mathbf{1 5} hat{boldsymbol{i}}+ )
( 21 hat{j}+a hat{k} ) are parallel vectors then the
value of ( boldsymbol{a} ) is:
( A cdot-3 )
B. 9
( c cdot-9 )
D. 3
11
980Two thin rods each of mass ( m ) and
length 1 are joined to form L shape as
shown. The moment of inertia of rods
about an axis passing through free end
(O) of a rod end and perpendicular to
both the ends is
A ( cdot frac{5 m l^{2}}{3} )
B. ( frac{m l^{2}}{6} )
c. ( frac{5}{7} M R^{2} )
D. ( frac{7}{12} M R^{2} )
11
981A rod of mass ( m ) spins with an angular speed ( omega=sqrt{g / l}, ) Find its
a. Kinetic energy of rotation.
b. kinetic energy of translation
c. Total kinetic energy.
11
982Two particles move on a circular path (one just inside and the other just
outside) with the angular velocity ( boldsymbol{w} )
and ( 5 w ) starting from the same point.
Then
This question has multiple correct options
A. They cross each other at regular intervals of time ( 2 pi / 4 w ) when their angular velocity are oppositely directed
B. They cross each other at point on the path subtending an angle of ( 60^{circ} ) at the center if their angular velocity are oppositely directed
C. They cross at intervals of time ( pi / 3 w ) if their angular velocities are oppositely directed
D. They cross each other at point on the path subtending ( 90^{circ} ) at the centre if their angular velocity are in the
same sense
11
983The angular velocity ( (omega ) of a particle is
related to the linear velocity ( v ) of the particle moving in a circular motion or radius R using the formula
( mathbf{A} cdot v=R omega )
B. ( v=2 R omega )
c. ( v=R omega^{2} )
D. ( v=R sqrt{(} omega) )
11
984The centre of mass of a rigid body always lies inside the body. Is this statement true or false?
A. True
B. False
11
985Masses ( 8,2,4,2 mathrm{kg} ) are placed at the corners ( A, B, C, D ) respectively of a square ABCD of diagonal 80 cm. The distance of center of mass from A is:
A. 20 cm
B. 30cm
c. ( 40 mathrm{cm} )
D. 60cm
11
986A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be :
A ( cdot frac{5}{3} )
B. ( frac{3}{5} )
c. ( frac{15}{13} )
D. ( frac{13}{15} )
11
987A mass ‘ ( m^{prime} ) moves with velocity ( v= ) ( sqrt{3} m / s ) and collides with another mass
( 2 m ) initially at rest. After collision first mass move with velocity ( frac{v}{sqrt{3}} ) in the
direction perpendicular to initial
direction of motion. Speed of second mass (in ( mathrm{m} / mathrm{s} ) ) after collision is
11
988The forces at the support point
A. 780 N
B. 220 N
c. ( 1920 mathrm{N} )
D. 1140 N
11
989( Q ) Type your ques
same material, A is solla but b is
hollow. These are connected by an idea
spring and this system is kept over a
smooth plank such that center of mass of two balls coincide with mid point of
the plank. Initially the spring is
compressed by a certain amount and
the plank is in horizontal position. Now
we release the system then,
A. Plank will rotate clock wise
B. Plank will rotate anti clock wise
C. Plank will not rotate
It will depend upon st
11
990Let ( I_{A} ) and ( I_{B} ) be the moments of inertia
of two solid cylinders of identical geometrical shape and size about their axes, the first made of aluminum and
the second of iron then:
A ( cdot I_{A}I_{B} )
D. The relation between ( I_{A} ) and ( I_{B} ) depends on the actual shape of the bodies
11
991When sand is poured on a rotating disc, its angular velocity will be:-
A . Decrease
B. Increase
c. Remain constant
D. None of these
11
992Find a unit vector perpendicular to ( vec{A}= ) ( mathbf{2} hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}+hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}-hat{boldsymbol{j}}+hat{boldsymbol{k}} ) both
A ( .4 hat{i}-hat{j}-5 hat{k} )
B. ( frac{1}{sqrt{42}}(4 hat{i}-hat{j}-5 hat{k}) )
c. ( frac{1}{sqrt{21}}(4 hat{i}-hat{j}-5 hat{k}) )
D. ( frac{1}{sqrt{14}}(2 hat{i}-hat{j}-3 hat{k}) )
11
993In a free space a rifle (fixed) of mass ( M )
shoots a bullet of mass ( m ) at a
stationary block of mass ( M ) distance ( D ) away from it. When the bullet has
moved through a distance ( d ) towards the
block the centre of mass of the bullet-
block system is at a distance of:
A ( cdot frac{(D-d) m}{M+m} ) from the block
B. ( frac{m d+M D}{M+m} ) from the rifle
c. ( frac{2 d m+D M}{M+m} ) from the rifle
D. ( (D-d) frac{M}{M+m} ) from the bullet
11
994A disc of mass ( m ) and radius ( R ) moves
in the ( x ) -y plane as shown in figure. The
angular momentum of the disc about
the origin ( O ) at the instant shown is:
( ^{mathrm{A}} cdot_{-}^{5}^{m R^{2} omega hat{k}} )
( ^{mathrm{B}} cdot frac{7}{3}^{m R^{2} omega hat{k}} )
C ( -frac{9}{2} m R^{2} omega hat{k} )
( stackrel{0}{2}^{m} m^{2} omega )
11
995If the earth is treated as a sphere of
radius ( R ) and mass ( M, ) its angular
momentum about the axis of its
rotation with period ( boldsymbol{T} ) is
A ( cdot frac{4 pi M R^{2}}{5 T} )
в. ( frac{2 pi M R^{2}}{5 T} )
( ^{mathrm{c}} cdot frac{M R^{2} T}{T} )
D. ( frac{pi M R^{3}}{T} )
11
996A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
The plank is pulled to the right by a constant force ( F ). If the sphere does not
slip over the plank, then This question has multiple correct options
A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force ( F )
11
997A straw is placed on the corner of a
table of length 3cm3cm.
11
998Distinguish between centre of mass and centre of gravity?11
999A man and a child are holding a uniform rod of length ( L ) in the horizontal direction in such a way that one fourth weight is supported by the child. If the child is at one end of the rod then the
distance of man from another end will
be:
A ( cdot frac{3 L}{4} )
в. ( frac{L}{4} )
c. ( frac{L}{3} )
D. ( frac{2 L}{3} )
11
1000A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the downward vertical.
A ( .30^{circ} )
B . ( 45^{circ} )
( c cdot 60^{circ} )
D. ( 90^{circ} )
11
1001If the area of parallelogram, whose diagonals are represented by ( (3 hat{i}+hat{j}+hat{k}) ) and ( (hat{i}-hat{j}-hat{k}), ) is in the
form of ( x sqrt{2} ) square unit, the value of ( x )
is :
A . 4
B. 2
( c cdot 3 )
D. 6
11
1002A constant torque of ( 25 mathrm{N} mathrm{m} ) is needed
to keep a wheel make 10 revolutions in 20 secs. The average power exerted by
this torque is
A . 19.6 watts
B. 62.8 Watts
c. 35 watts
D. 70 Watts
11
1003A uniform ring of mass ( m, ) with the
outside radius ( r_{2}, ) is fitted tightly on a
shaft of radius ( r_{1} . ) The shaft is rotated
about its axis with a constant angular
acceleration ( beta . ) Find the moment
of elastic forces in the ring as a
function of the distance ( r ) from the
rotation axis.
A ( cdot N=frac{1}{2} frac{m beta}{left(r_{2}^{2}-r_{1}^{2}right)}left(r_{2}^{4}-r^{4}right) )
B. ( N=frac{1}{2} frac{m beta}{left(r_{2}^{2}+r_{1}^{2}right)}left(r_{2}^{4}-r^{4}right) )
C ( quad N=frac{1}{2} frac{m beta}{left(r_{2}^{2}+r_{1}^{2}right)}left(r_{2}^{4}+r^{4}right) )
D. None of these
11
1004In the figure, the disc D does not slip on
the surface S. The pulley P has mass,
and the string does not slip on it. The
string is wound around the disc. Then,
which of the following statement(s) is/are true?
his question has multiple correct options
A. The acceleration of the block B is double the acceleration of the centre of ( D )
B. The force of friction exerted by D on S acts to the left
c. The horizontal and the vertical sections of the string have the same tension
D. The sum of the kinetic energies of D and B is less than the loss in the potential energy of B as it moves down
11
1005A uniform circular disc has radius ( boldsymbol{R} )
and mass ( m . ) A particle also of mass ( m )
is fixed at a point ( A ) on the edge of the
disc as shown in the figure. The disc can rotate freely about a fixed
horizontal chord ( P Q ) that is at a
distance ( R / 4 ) from the centre ( C ) of the
disc. The line ( A C ) is perpendicular to
( P Q . ) Initially the disc is held vertical
with the point ( A ) at its highest position.
If is then allowed to fall so that it starts
rotating about ( P Q . ) The linear speed of
the particle as it reaches its lowest position is ( sqrt{n g R}, ) where ( n ) is an integer
Find the value of ( n )
11
1006A body of mass ( m_{1}=4 k g ) moves at
( mathbf{5 i} boldsymbol{m} / boldsymbol{s} ) and another body of mass
( boldsymbol{m}_{2}=2 k g ) moves at ( 10 i m / s . ) The
kinetic energy of centre of mass is
A ( cdot frac{200}{3} J )
в. ( frac{500}{3} J )
c. ( frac{400}{3} J )
D. ( frac{800}{3} J )
11
1007The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size ( boldsymbol{theta} ) and
A ( cdot frac{4}{3} R frac{sin (theta / 2)}{theta} )
B. ( R frac{sin (theta / 2)}{theta} )
c. ( frac{4}{3} R cos left(frac{(theta)}{2}right) )
D ( cdot frac{2}{3} R cos (theta) )
11
1008It becomes easier to open or close a door turning about its hinges if the force is applied at the:
A. Two third of the door
B. Free edge of the door
c. Middle of the door
D. Point near the hinges
11
1009A square of side ( 4 mathrm{cm} ) and uniform
thickness is divided into four squares.
The square portion ( boldsymbol{A}^{prime} boldsymbol{A} boldsymbol{B}^{prime} boldsymbol{D} ) is removed
and the removed portion is placed over
the square ( boldsymbol{B}^{prime} boldsymbol{B C}^{prime} ) D. The new position
of centre of mass is
( A cdot(2 mathrm{cm}, 2 mathrm{cm} )
B. ( (2 mathrm{cm}, 3 mathrm{cm}) )
c. ( (2 mathrm{cm}, 2.5 mathrm{cm}) )
( mathrm{D} cdot(3 mathrm{cm}, 3 mathrm{cm}) )
11
1010An object will not turn when:
A. The forces are acting on it at different positions
B. Every forces is creating different turning effects
C. Every moment has the same amplitude
D. All the forces are acting at its centre of gravity
11
1011A block moving in air breaks in two
parts and the parts separate
A. the total momentum must be conserved
B. the total kinetic energy must be conserved
c. the total momentum must change
(B) both are correct
D. option (A) and
11
1012A uniform disc of mass ( m ) and radius ( R )
rolls without slipping up a rough
inclined plane at an angle of ( 30^{circ} ) with the horizontal. If the coefficient of static
and kinetic friction are each equal to ( mu )
and the forces acting on the disc are gravity and contact force, then find the direction and magnitude of the friction force acting on it.
11
1013A large number of particles are placed around the origin, each at a distance ( boldsymbol{R} )
from the origin. The distance of the
centre of mass of the system from the origin is:
( mathbf{A} cdot=R )
в. ( geq R )
( c cdot>R )
( mathrm{D} cdot leq R )
11
1014Shown in the figure is a very long semicylindrical conducting shell of radius ( mathrm{R} ) and carrying a current i. An infinitely
long straight current carrying conductor lies along the axis of the semi – cylinder. If the current flowing
through the straight wire be ( i_{0} ), then the
force per unit length on the conducting
wire is :
A ( cdot frac{mu_{0} i times i_{0}}{pi^{2} R} )
В ( cdot frac{mu_{0} i times i_{0}}{pi R^{2}} )
c. ( frac{mu_{0} i_{o}^{2} times i}{pi^{2} R} )
D. None of these
11
1015The moment of inertia of a hollow
cubical box of mass ( M ) and side a
about an axis passing through the centres of two opposite faces is equal to
A ( cdot frac{5 M a^{2}}{3} )
в. ( frac{5 M a^{2}}{6} )
c. ( frac{5 M a^{2}}{12} )
D. ( frac{5 M a^{2}}{18} )
11
1016A boy sitting firmly over a rotating stool (constant angular velocity) has his arms folded. If he stretches his arms,
his angular momentum about the axis of rotation.
A. increases
B. decreases
c. remains unchanged
D. None of the above
11
1017A rod of mass ( m ) and length ( l ) is
connected with a light rod of length ( l )
The composite rod is made to rotate with angular velocity ( omega ) is shown in the
figure. Find the total kinetic energy.
11
1018The moment of inertia of a uniform
circular disc about its diameter is 200 gm ( c m^{2} ). Then its moment of inertia
about an axis passing through its center and perpendicular to its circular face is
A ( cdot 100 mathrm{gm} mathrm{cm}^{2} )
в. 200 gm ( c m^{2} )
( mathrm{c} cdot 400 mathrm{gm} mathrm{cm}^{2} )
D. 1000 gm ( c m^{2} )
11
1019A sphere rolls without sliding on a
rough inclined plane (only mg and contact forces are acting on the body).
The angular momentum, of the body:
B. is conserved about the point of contact
c. is conserved about a point whose distance from the inclined plane is greater than the radius of the sphere
D. is not conserved about any point
11
1020State the law of conservation of angular
momentum
11
1021The moment of a force of ( 10 N ) about a
fixed point ( boldsymbol{O} ) is ( mathbf{5} boldsymbol{N} boldsymbol{m} . ) Calculate the
distance of the point ( O ) from the line of action of the force.
A. ( 5 m )
в. ( 1 m )
( c .50 m )
D. ( 0.5 m )
11
1022Three identical. spheres of mass in each are placed at the corners of an equilateral triangle of side 2 in. Taking one of the corner as the origin, the
position vector of the centre of mass is
( mathbf{A} cdot sqrt{3}(hat{i}-hat{j}) )
B. ( frac{i}{sqrt{3}}+hat{j} )
( c cdot frac{i+3}{3} )
D. ( hat{i}+frac{j}{sqrt{3}} )
11
1023( (n-1) ) equal point masses each of
mass ( mathrm{m} ) are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the positive
vector of centre of mass:
A ( cdot frac{1}{n-1} a )
в. ( -frac{1}{(n-1)} a )
c. ( (n-1) a )
D. ( -left(frac{n-1}{a}right) )
11
1024Assertion
Two cylinders, one hollow (metal) and the other solid (wood), with the same
mass and identical dimensions are
simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane
first.
Reason
By the principle of conversation of
energy the total kinetic energies of both the cylinders are identical when they
reach the bottom of the incline.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
1025A heavy plank is moving with horizontal
acceleration ( a=2 m / s^{2} . ) A hollow
cylinder of mass ( boldsymbol{m}=mathbf{3} k boldsymbol{g} ) and
radius ( =25 mathrm{cm} ) is on the upper surface
of the plank and moves without slipping. Find the angular acceleration (about the axis in ( r a d / s^{2} ) ) of the hollow
cylinder?
11
1026In translatory motion, The axis of frame
of object remains always parallel to the corresponding axis of ?
A. Mover’s frame of reference
B. observer’s frame of reference
c. Rotator’s frame of reference
D. None of the above
11
1027A rope brake is fitted to a flywheel of
diameter ( =1 mathrm{m} . ) The flywheel runs at 220
r.p.m. It is required to absorp ( 5.25 mathrm{kW} ) of
brake power. Difference in the two pulls ( (T-S) ) is :
( mathbf{A} cdot 456 N )
B. ( 654 N )
( c .564 N )
D. ( 465 N )
11
1028People can spin a ball on their finger
This is due to
A. the centre of gravity of the ball is on his finger.
B. the resultant force is passing through the centre of gravity of the ball.
c. the resultant force is passing through the centre of the ball
D. both A and B
11
1029Two spheres of masses ( 2 mathrm{M} ) and ( mathrm{M} ) are kept at a distance R apart. Due to mutual force of attraction, they
approach each other. When they are at a separation R/2. Find the acceleration of centre of mass.
11
1030Find the tension in the string
( A cdot frac{M g}{3} )
в. ( frac{M g}{4} )
с. ( M g )
( D cdot frac{M g}{2} )
11
1031The position of the center of gravity of the pot before filling it with water will be
at its base.
A. True
B. False
11
1032A solid sphere of mass ( m ) is lying at rest on a rough horizontal surface. The coefficient of friction between the
ground and sphere is ( mu . ) The maximum
value of ( F, ) so that the sphere will not slip, is equal to
( A )
в.
( c )
( D )
11
1033A uniform disc of radius ( R ) is put over
another uniform disc of radius ( 2 R )
made of same material having same thickness. The peripheries of the two discs touches each other. Locate the
centre of mass of the system taking
center of large disc at origin.
11
1034A circular thin disc of mass 5 kg has a diameter ( 1 mathrm{m} . ) The moment of inertia
about an axis passing through the edge and perpendicular to the plane of the disc is
A ( cdot(8 / 15) k g-m^{2} )
В ( cdot 8 k g-m^{2} )
( mathbf{c} cdot(15 / 8) k g-m^{2} )
D. ( 1 k g-m^{2} )
11
1035A steel girder of length ( l ) rests freely on two supports (figure shown above). The moment of inertia of its cross-section is
equal to ( I . ) Neglecting the mass of the
girder and assuming the sagging to be slight, if the deflection ( lambda ) due to the
force ( boldsymbol{F} ) applied to the middle of the ( operatorname{girderis} lambda=frac{1}{(40+x)} frac{F l^{3}}{E I}, ) find the
value of ( boldsymbol{x} )
11
( m_{1} ) and ( m_{2}, ) the coetticient of triction
between the body ( m_{1} ) and the horizontal
plane is equal to ( k, ) and a pulley of mass
( m ) is assumed to be a uniform disc. The
thread does not slip over the pulley. At
the moment ( t=0 ) the body ( m_{2} ) starts
descending. Assuming the mass of the thread and the friction in the axle of the
pulley to be negligible, find the work performed by the friction forces
acting on the body ( m_{1} ) over the first ( t ) seconds after the beginning of motion.
( ^{mathbf{A}} cdot_{A}=-frac{k m_{1}left(m_{1}-k m_{1}right) g^{2} t^{2}}{m+2left(m_{1}+m_{2}right)} )
B. ( A=-frac{k m_{1}left(m_{1}+k m_{1}right) g^{2} t^{2}}{m+2left(m_{1}-m_{2}right)} )
c. ( A=frac{k m_{1}left(m_{1}+k m_{1}right) g^{2} t^{2}}{m+2left(m_{1}+m_{2}right)} )
D. None of these
11
1037A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant
force ( F ) starting from rest. As the time increases:
A . its angular velocity increases, but force on hinge remains constan
B. its angular velocity remains same, but force on hinge increases
c. its angular velocity increases and force on hinge increases
D. its angular velocity remains same and force on hinge is constant
11
1038A couple produces:
A. no motion
B. linear and rotational motion
C . purely rotational motion
D. purely linear motion
11
1039A body is projected vertically upwards.
In this
A. it is a violation of law of conservation of linear
momentum
B. momentum of the body alone gets conserved
C. momentum of the body, earth and air molecules together remains constant
D. violates law of conservation of energy.
11
1040What is the moment of inertia of each of
the following uniform objects about the
axes indicated?
A. ( A ) 2.50-kg sphere, 31.0 -cm in diameter about an axis through its center, if the sphere is solid.
B. A 2.50-kg sphere, 31.0-cm in diameter about an axis through its center, if the sphere is a thin-walled hollow shell.
C. An 8.00 -kg cylinder of length 17.0 -cm and diameter ( 20.0-mathrm{cm} ) about the central axis of the cylinder, if the cylinder is thin-walled and hollow.
D. An 8.00-kg cylinder of length 17.0-cm and diameter 20.0-cm about the central axis of the cylinder, if the cylinder is solid.
11
1041A disc of mass ( mathrm{m} ) and radius ( mathrm{R} ) has a
concentric hole of a radius r. Its
moment of inertia about an axis
through its centre and perpendicular to its plane is :
A ( cdot frac{1}{2} mleft(R^{2}+r^{2}right) )
B . ( frac{1}{2} mleft(R-r^{2}right) )
C ( cdot frac{1}{2} mleft(R^{2}-r^{2}right) )
D ( cdot frac{1}{2} mleft(R+r^{2}right) )
11
1042Assertion
STATEMENT-1: Two particles undergo rectilinear motion along different straight lines. Then the centre of mass
of system of given two particles also always moves along a straight line.
Reason
STATEMENT-2: If direction of net
momentum of a system of particles having nonzero net momentum) is fixed, the centre of mass of given system moves along a straight line.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True
11
1043STATEMENT-1
Two cylinders, one hollow (metal) and
the other solid (wood) with the same
mass and identical dimensions
are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the
inclined plane first.
STATEMENT-2
By the principle of conservation of
energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
11
1044Two solid discs of radii ( r ) and ( 2 r ) roll
from the top of an inclined plane without slipping. Then
A. The bigger disc will reach the horizontal level first
B. The smaller disc will reach the horizontal level first
c. The time difference of reaching of the discs at the horizontal level will depend on the inclination of the plane
D. Both the discs will reach at the same time
11
1045A uniform solid cylinder of mass ( 2 k g )
and radius ( 0.2 m ) is released from the
rest at the top of a semicircular track of
radius ( 0.7 m ) cut in block of mass ( M= )
( 3 k g ) as shown. The block is resting on a
smooth horizontal surface and the
cylinder rolls down without slipping. The
distance moved by the block when the cylinder reaches the bottom of the track is:
( mathbf{A} cdot 0.3 m )
B. ( 0.5 m )
c. ( 0.7 m )
D. ( 0.2 m )
11
1046Three vectors satisfy the relation ( vec{A} ). ( vec{B}=0 ) and ( vec{A} bullet vec{C}=0, ) then ( vec{A} ) is
parallel to
A . ( vec{c} )
в. ( vec{B} )
c. ( vec{B} times vec{C} )
D. ( vec{B} cdot vec{C} )
11
1047Moment of inertia of thin uniform rod of
length ( l ) is equal to:
( ^{A} cdot frac{m l^{2}}{6} )
в. ( frac{m l^{2}}{12} )
c. ( frac{m l^{2}}{4} )
D. ( frac{m l^{2}}{24} )
11
1048Find frequency. ( left(operatorname{in} s^{-1}right) )
A . 31.85
B. 32
c. 32.58
D. 35.025
11
1049When the velocity of a body is doubled
A. kinetic energy is doubled
B. acceleration is doubled
c. momentum is doubled.
D. potential energy is doubled
11
1050Find out relation between ( boldsymbol{I}_{1} ) and ( boldsymbol{I}_{2} )
Where ( I_{1} ) and ( I_{2} ) moment of inertia of a
rigid body mass ( m ) about an axis as
shown in the figure.
11
1051A circular disc rolls on a horizontal floor
without slipping and the centre of the disc moves with a uniform velocity ( v )
Which of the following values of the velocity at a point on the rim of the disc can have?
This question has multiple correct options
( A )
В. ( -v )
( c cdot 2 v )
D.
11
1052Two objects of same mass ( m ) are
attached at end of a light rod of length ( l )
and rotating about axis ( O O^{prime} ) as shown
in the figure. The moment inertia of the
system about the axis ( O O^{prime} ) is
A ( frac{m l^{2}}{12} )
B. ( frac{5 m l^{2}}{18} )
c. ( frac{5 m l^{2}}{24} )
D. ( frac{5 m l^{2}}{36} )
11
1053Starting from rest a wheel rotates with
uniform angular acceleration ( 2 pi r a d / s^{2} )
After ( 4 s, ) if the angular acceleration ceases to act, its angular displacement
in the next ( 4 s ) is:
B. ( 16 pi ) rad
( mathbf{c} cdot 24 pi quad r a d )
D. ( 32 pi ) rad
11
1054Establish the relation between torque
and angular acceleration Hence define moment of inertia.
11
1055On a large tray of mass ( mathrm{M} ), an ice cube of mass ( mathrm{m} ), edge ( mathrm{L} ) is kept. If the ice melts completely, the center of mass of the
system comes down by:
( ^{mathbf{A}} cdot frac{m L}{2(M+m)} )
в. ( frac{(M-m) L}{2(M+m)} )
c. ( frac{(M+2 m) L}{2(M+m)} )
D ( cdot frac{2 M L}{2(M+m)} )
11
1056If ( vec{A} times vec{B}=0, vec{B} times vec{C}=0, ) then ( vec{A} times )
( vec{C}= )
A. ( A C )
в. ( frac{A B^{2}}{C} )
c. ( Z ) ero
D. Noneofthese
11
1057Calculate the moment of inertia of a
uniform disc of mass M and radius R
11
1058A circular ring of diameter ( 40 mathrm{cm} ) and mass I kg is rotating about an axis normal to its plane and passing through the (time with a frequency of 10 rotations per second. Calculate the
angular momentum about its axis of
rotation.
11
1059The surface density (mass/area) of a
circular disc of radius ( a ) depends on the
distance from the center of ( rho(r)=A+ )
Br. Find its moment of inertia about
the line perpendicular to the plane of the disc through its centre.
11
1060The average angular velocity of the
spinning motion of the Earth in rads( ^{-1} )
will be :
A ( cdot frac{pi}{43,200} )
в. ( frac{2 pi}{43,200} )
c. ( frac{pi}{86,400} )
D. ( frac{4 pi}{86,400} )
11
1061A particle moves in x-y under the action of the force ( overrightarrow{mathbf{F}} ) Such that ( mathbf{x} ) and ( mathbf{y} )
components of linear momentum, ( overrightarrow{mathbf{P}} ) at any time ( t ) are 2 cos ( t ) and ( 2 sin t . ) Find the angle between ( overrightarrow{mathbf{F}} & overrightarrow{mathbf{P}} ) at a given time
( A cdot 60^{circ} )
B. 300
( c cdot 0^{0} )
D. ( 90^{circ} )
11
1062Particle 1 with mass ( M ) has ( x ) position
defined by the function ( x_{1}(t)= )
( 2 t(t+3) ) where units are in meters
time is in seconds, and are abbreviated
in the function. Particle 2 has mass ( 2 M )
and ( x ) position defined by ( x(t)= )
( (t-1)(t-2) / 2 )
Considering the system of these two particles, what is the velocity of the
center of mass of the system at ( t=2 ? )
A. ( 5 m / s )
в. ( 9 m / s )
c. ( 10 m / s )
D. ( 10.5 m / s )
E ( .16 mathrm{m} / mathrm{s} )
11
1063Find the position of centre of mass of
the uniform lamina shown in Fig.
11
1064What is the position of centre of gravity
of a cylinder?
A. At the center of base circle
B. At the center of top circle
c. cannot be determined
D. At the mid point on the axis of cylinder
11
1065Find the centre of mass of a triangular lamina.11
1066A mass slides down an inclined plane and reaches the bottom with a velocity
( v . ) If the same mass is in the form of a
disc and rolls down the same inclined
plane, what will be its velocity at the bottom?
A ( . v )
B. ( sqrt{frac{2}{3}} )
( c cdot sqrt{2} v )
D. ( frac{v}{sqrt{2}} )
11
1067A disc of mass ( 100 g ) and radius ( 10 mathrm{cm} ) has a projection on its circumference. The mass of projection is negligible. A ( 20 g ) bit of putty moving tangential to
the disc with a velocity of ( 5 m s^{-1} ) strikes the projection and sticks to it. The angular velocity of disc is
A ( cdot 14.29 ) rad ( s_{1} )
B. 17.3 rad ( s_{-1} )
c. 12.4 rad ( s_{-1} )
D. 9.82 rad ( s_{1} )
11
1068Which of the following statement best
describe torque?
A. is the vector product of force and lever arm length.
B. is a scalar and has no direction associated with it
C. is always equal to force.
D. is always greater for shorter lever arms.
E. must always equal zero
11
1069A circular disc of mass ( M_{1} ) and radius
( R, ) initially moving with a constant
angular speed ( omega_{0} ) is gently placed coaxially on a stationary circular disc of
mass ( M_{2} ) and radius ( R ), as shown in
Figure. There is a frictionless force
between the two discs
f disc ( M_{2} ) is placed on a smooth surface, then determine the final
angular speed of each disc.
11
1070A ( 1 mathrm{m} ) long uniform beam is being
balanced as shown below. Calculate
force G.
A. 3.0 N
B. 4.5 ( mathrm{N} )
( c cdot 5.0 N )
D. 6.0 N
11
1071If the translatory kinetic energy of a rolling solid sphere is ( 35 J ), then its total kinetic energy is:
A . ( 42 J )
B. ( 49 J )
c. 56.5
D. ( 63 J )
11
1072Which of the following statement is not true in the context of above system
A. centre of mass reference frame is an inertial frame
B. kinetic energy of the system is minimum in centre of mass frame.
c. at the instant of maximum deformation both the blocks are instantaneously at rest in centre of mass reference frame
D. acceleration of centre of mass is constant is ground frame
11
1073The resultant moment of all the forces
acting on the body about the point of rotation should be
A. Greater than one
B. Smaller than one
c. zero
D. one
11
1074Consider a vector ( boldsymbol{F}=mathbf{4} hat{mathbf{i}}-mathbf{3} hat{mathbf{j}} ). Another
vector which is perpendicular to ( overrightarrow{boldsymbol{F}} ) is:
A . ( 4 hat{i}+3 hat{j} )
B. ( 6 hat{i} )
( c .7 k )
D. ( 3 hat{i}-4 hat{j} )
11
1075Using the relationship between
moments of inertia as ( boldsymbol{I}_{boldsymbol{x}}+boldsymbol{I}_{boldsymbol{y}}=boldsymbol{I}_{boldsymbol{z}} )
where sub indices ( x, y, ) and ( z ) define three mutually perpendicular axes passing through one point, with axes 1 and 2 lying in the plane of the plate, the moment of inertia of a thin uniform
round disc of radius ( R ) and mass ( m )
relative to the axis coinciding with one of its diameters is ( I=frac{m R^{2}}{x} . ) Find the
value of ( boldsymbol{x} )
11
1076Consider a uniform rod of mass ( boldsymbol{M}= )
( 4 m ) and length ( l ) pivoted about its
centre. A mass ( m ) moving with velocity ( boldsymbol{v} ) making angle ( boldsymbol{theta}=frac{boldsymbol{pi}}{boldsymbol{4}} ) to the rod’s long
axis collides with one of the rod and
sticks to it. The angular speed of the rod-mass system just after the collision
is:
A ( frac{3}{7 sqrt{2}} frac{v}{l} )
B. ( frac{3 sqrt{2}}{7} frac{v}{l} )
c. ( frac{4}{7} frac{v}{l} )
D. ( frac{3}{7} frac{v}{l} )
11
1077Find the accelerations of the point ( boldsymbol{B} )
A ( cdot 6.5 mathrm{cm} / mathrm{s}^{2} )
в. ( 2.5 mathrm{cm} / mathrm{s}^{2} )
( mathrm{c} cdot 5 mathrm{cm} / mathrm{s}^{2} )
D. ( 2 mathrm{cm} / mathrm{s}^{2} )
11
1078A small body of mass ( m ) tied to a non-
stretchable thread moves over a smooth
horizontal plane. The other end of the
thread is being drawn into a hole ( boldsymbol{O} )
(figure shown above) with a constant velocity. Find the thread tension as a
function of the distance ( r ) between
the body and the hole if at ( r=r_{0} ) the
angular velocity of the thread is equal to
( omega_{0} )
11
1079A solid sphere of mass ( mathrm{m} ) and radius ( boldsymbol{R} )
is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.
11
1080A uniform rod of length ( l=1 m ) is kept
as shown in the figure. ( boldsymbol{H} ) is a horizontal
smooth surface and ( W ) is a vertical
smooth well. The rod is release from this
position. What is the angular angular acceleration of the rod just after the released?
A. ( frac{6 g cos theta}{l} )
B. ( frac{3 g cos theta}{l} )
( c .6 g cos theta )
D. ( frac{2 g cos theta}{l} )
11
1081A particle initially at rest starts moving from point ( A ) on the surface of a fixed
smooth hemisphere of radius r as
shown. The particle looses its contact
with hemisphere at point B. ( C ) is centre of the hemisphere. The equation
relating ( boldsymbol{alpha} ) and ( boldsymbol{beta} ) is:
A. ( 3 sin alpha=2 cos beta )
B. ( 2 sin alpha=3 cos beta )
( c .3 sin beta=2 cos alpha )
D. ( 2 sin beta=3 cos alpha )
11
1082In the case of explosion of a bomb
a) KE changes
b) the mechanical energy conserves
c) linear momentum changes
d) chemical energy changes
A. a ( & ) b are true
B. ( c & ) d are true
( c . ) a ( & mathrm{c} ) are true
D. a & dare true
11
1083An object will not undergo rotational
motion when:
A. the forces are acting on it at different positions
B. every forces is creating different turning effects
C. every moment has the same amplitude
D. all the forces are acting at its centre of gravity
11
1084Express 42 seconds as a percent of 6 minutes.11
1085Distinguish between dot product and cross product.11
1086State and prove low of conservation of
momentum.
11
1087A smooth tube of certain mass is
rotated in a gravity-free space and realeased. The two balls shown in the
figure move towards the ends of the tube. For the whole system, which of the following quantities is not conserved
A. Angular momentum
B. Linear momentum
c. Kinetic energy
D. Angular speed
11
1088A man has constructed a toy as shown
in figure. If the density of the material of the sphere is 12 times than of the cone
then determine the position of the
centre of mass. [Centre of mass of a
( boldsymbol{h} )
cone of height ( h h ) is at height of ( frac{-f r o m}{4} ) from
its base.
11
1089A mercury thermometer is placed in a gravity free half without touching. As temperature rises mercury expands and ascend in thermometer. If height
ascend by mercury in thermometer is ( h ) then by what height centre of mass of mercury and thermometer system descend?
11
1090toppr
spool has mass ( m ), edge radius ( K ) and
is wound up to a radius ( r, ) its moment of
inertia about its own axis is ( boldsymbol{I} ). The free
end of the thread is attached as shown
in figure. So that the thread is parallel
to the inclined plane. ( T ) is the tension in
the thread. Which of the following is
correct?
This question has multiple correct options
A. The linear acceleration of the spool axis down the
slope is ( frac{m g sin theta-T}{m} )
B. Angular accelerations is ( frac{T r}{2 I} )
C. The linear acceleration of the spool axis down the
plane is ( frac{T r^{2}}{I} )
D. The acceleration of the spool axis down the slope is
( frac{frac{1}{1} theta}{m r^{2}} )
11
1091A cubical block of mass ( m ) and side ‘a
is moving horizontally on a smooth horizontal surface with a velocity ( v_{0} )
The block collides with a ridge ( P ) and starts rotating about ( P ). Find the
minimum value of ( boldsymbol{v}_{0} ) needed to
overcome the ridge.
11
1092negligible mass rests on a horizontal
plane as known. The diameter of the
base is ( a ) and the side of the cylinder
makes an angle ( theta ) with the horizontal.
Water is then slowly poured into the
cylinder. The cylinder topples over when
the water reaches a certain height ( h )
given by.
A ( . h=2 a tan theta )
B ( cdot h=a tan ^{2} theta )
( mathbf{c} cdot h=a tan theta )
D. ( h=frac{a}{2} tan theta )
11
1093If ( l=50 mathrm{kg}-m^{2}, ) then how much torque
will be applied to stop it in 10 sec. Its initial angular speed is 20 rad sec.
A . ( 100 mathrm{N}-mathrm{m} )
B . ( 150 mathrm{N}-mathrm{m} )
c. ( 200 mathrm{N}-mathrm{m} )
D. ( 250 mathrm{N}-mathrm{m} )
11
1094A ring of mass ( m ) and radius r rolls on an inclined plane. A torque is produced in the ring due to
A. mgsintheta and the radius of the ring
B. the perpendicular distance between the force and the point of contact and the force ( m g ) acting on it
c. the perpendicular distance between the force and the point of contact and the normal force acting on the object
D. the perpendicular distance between the force and the point of contact and the force ( m g sin theta ) acting on it
11
1095A disc of mass ( 2 k g ) and diameter ( 2 m ) is
performing rotational motion. Find the work done, if the disc is rotating from ( 300 r p m ) to ( 600 r p m )
A . ( 1479 J )
в. ( 147.9 J )
c. ( 14.79 J )
D. ( 1.479 J )
11
1096Conservation of momentum in a
collision between particles can be understood from
A. Conservation of energy
B. Newton’s first law only
c. Newton’s second law only.
D. Both Newton’s second and third law.
11
1097A log of wood of length ( l ) and mass ( M ) is floating on the surface of river perpendicular to the banks. One end of the log touches the banks. A man of
mass ( m ) standing at the other end
walks towards the bank. Calculate the
displacement of the log when he reaches the nearer end of the log.
11
1098A wooden plank rests in equilibrium on
two rocks on opposite sides of a narrow
stream. Three forces ( P, Q ) and ( R ) act on
the plank. How are the sizes of the
forces related?
( mathbf{A} cdot mathbf{P}+mathbf{Q}=mathbf{R} )
B. ( P+R=Q )
( mathbf{c} cdot mathrm{P}=mathrm{Q}=mathrm{R} )
D. ( P=Q+R )
11
1099A disc of mass ( mathrm{M} ) and radius ( mathrm{R} ) is
reshaped in the form of ring of same
gyration increased by a factor:
11
1100The mass of a metal scale of uniform
thickness is ( 1.6 k g ) and its length is ( 2 m ) This scale is placed on the horizontal surface of the table such that ( frac{1}{4}^{t h} ) of its length is beyond the edge of the table. The maximum mass that can be
suspended to this scale at a distance of 10cm from the free end of the scale so
that scale does not turn down is:
A . ( 1 k g )
в. ( 2 k g )
( c cdot 2 cdot 4 k g )
D. 3.2 2 k
11
1101A hollow sphere is held suspended. Sand is now poured into it in stages. The centre of gravity of the sphere with the sand
A. Rises continuously
B. Remains unchanged in the process
c. Firstr rises and then falls to the original position
D. First falls and then rises to the original position
11
spriere or radius K are to be balanced al
the edge of a heavy table such that the centre of the sphere remains at the maximum possible horizontal distance
from the vertical edge of the table
without toppling as indicated in the
figure. If the mass of each block is ( mathrm{M} )
and of the sphere is ( M / 2, ) then the maximum distance ( x ) that can be
achieved is?
( mathbf{A} cdot 8 L / 15 )
в. ( 5 L / 6 )
c. ( (3 L / 4+R) )
( D )
11
1103A sphere of mass ( M ) and radius ( r ) slips
on a rough horizontal plane. At some
instant it has translation velocity ( boldsymbol{v}_{0} ) and rotational velocity about the centre
( v_{0} / 2 r . ) The translation velocity after the
sphere starts pure rolling
A ( cdot 6 v_{0} / 7 ) in forward direction
B. ( 6 v_{0} / 7 ) in backward direction
( c cdot 7 v_{0} / 6 ) in forward direction
D. ( 7 v_{0} / 6 ) in backward direction
11
1104Two balls of equal masses are projected upward simultaneously, one from the ground with speed of ( 50 mathrm{m} / mathrm{s} ) and other from a ( 40 mathrm{m} ) high tower with initial speed of ( 30 mathrm{m} / mathrm{s} ). Find the maximum height attained by their center of mass.11
1105A disc of mass ( M ) and radius ( R ) rolls on
a horizontal surface and then rolls up
an inclined plane as shown in figure. If the velocity of the disc is ( v, ) height to
which the disc will rise will be
( mathbf{A} cdot frac{3 v^{2}}{2 g} )
B. ( frac{3 v^{2}}{4 g} )
c. ( frac{v^{2}}{4 g} )
( frac{v^{2}}{2 g} )
11
1106A non-uniform thin rod of length ( L ) is placed along ( x- ) axis as such its one of
ends at the origin. The linear mass
density of rod is ( lambda=lambda_{0} x . ) The distance
of centre of mass of rod from the origin
is:
A ( . L / 2 )
B. ( 2 L / 3 )
c. ( L / 4 )
D. L/5
11
1107A student initially at rest on a frictionless frozen pond throws a ( 2 mathrm{kg} ) hammer in one direction. After the
throw, the hammer moves off in one
direction while the student moves in the
other direction.Then:
A. the hammer will have the momentum with greater magnitude
B. the student will have the momentum with greater magnitude
c. the hammer will have the greater kinetic energy
D. the student will have the greater kinetic energy
11
1108From a uniform disk of radius ( mathrm{R} ), a
circular hole of radius R/2 is cut out.
The centre of the hole is at R/2 from the
centre of the original disc. Locate the
centre of gravity of the resulting flat body.
11
1109The position vector of three particles of
masses ( boldsymbol{m}_{1}=mathbf{1} boldsymbol{k} boldsymbol{g}, boldsymbol{m}_{2}=boldsymbol{2} boldsymbol{k} boldsymbol{g} ) and
( boldsymbol{m}_{3}=mathbf{3} boldsymbol{k} boldsymbol{g} operatorname{are} overrightarrow{boldsymbol{r}}_{1}=(hat{boldsymbol{i}}+boldsymbol{4} hat{boldsymbol{j}}+ )
( hat{boldsymbol{k}}) boldsymbol{m}, overrightarrow{boldsymbol{r}}_{2}=(hat{boldsymbol{i}}+hat{boldsymbol{j}}+hat{boldsymbol{k}}) boldsymbol{m} ) and ( overrightarrow{boldsymbol{r}}_{3}= )
( (2 hat{i}-hat{j}-2 hat{k}) mathrm{m} ) respectively. Find the position vector of their center of mass.
A ( cdot frac{1}{2}(hat{i}+hat{j}-hat{k}) m )
B ( cdot frac{1}{2}(hat{i}+3 hat{j}-hat{k}) m )
c ( cdot frac{1}{2}(hat{i}+hat{j}-3 hat{k}) m )
D ( cdot frac{1}{2}(3 hat{i}+hat{j}-hat{k}) m )
11
1110A rod of mass ( m ) and length ( l ) is
connected with a light rod of length ( l )
The composite rod is made to rotate
with angular velocity ( omega ) is shown in the figure. Find the Translational kinetic
energy.
11
1111A ring of radius ( R ) rolls without sliding
with a constant velocity. If the radius of curvature of the path followed by any particle of the ring at the highest point
of its path is ( x R ). Find ( x )
11
1112A parallelopiped has edges described by the ( hat{i}+2 hat{j}, 4 hat{j} ) and ( hat{j}+3 hat{k} . ) Then the
volume is:
A . 1
B. 12
( c cdot 15 )
D. 28
11
1113Does the center of mass of a system of
two particles lie on the lines joining the particles?
11
1114Four identical rods each of mass ( M ) are
joined to form as square frame, the moment of inertia of the system about one of the diagonals is
A. ( frac{13 M l^{2}}{3} )
в. ( frac{2 M l^{2}}{3} )
c. ( frac{M l^{2}}{6} )
D. ( frac{13 M l^{2}}{6} )
11
1115Calculate the torque developed (in ( mathrm{Nm} ) by an airplane engine whose
output is ( 2000 H P ) at an angular
velocity of 2400 rev / min.
11
1116A cord is wrapped around the rim of a
pull of ( 50 N ) in applied on the cord as shown in the figure. The wheel is mounted on a frictionless bearing on the horizontal shaft through its centre.
The moment of inertia of the wheel is
( 4 k g m^{2} )
(a) Compute angular acceleration of the whee
(b) If a mass having a weight ( 50 N ) hangs from the cord as shown in the figure. Compute the angular acceleration of the wheel. Why is this not the same as in part (a)?
11
1117Component of reaction at the hinge in
the horizontal direction is
( ^{A} cdot frac{F}{4} )
B. ( F )
c. ( frac{F}{3} )
D. ( frac{F}{2} )
11
1118The moment of the torque of a force
along a turning point is the force multiplied by the distance
to the force from turning point. Fill in
the blank.
A. Perpendicular
B. Horizontal
c. Both A and B
D. None
11
1119Four particle of mass ( 5,3,2,4 k g ) are at
the points ( (1,6),(-1,5),(2,-3),(-1,-4) . ) Find
the coordinates of their center of mass.
11
1120A gun recoils backward after firing a
bullet
A. To follow the law of inertia
B. To conserve momentum
c. To conserve mass
D. The statement is wrong
11
1121The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size ( theta ) and
radius ( boldsymbol{R} ) is given by
( A )
( B frac{sin (theta / 2)}{theta} )
( ^{mathrm{c}} cdot frac{4}{3} R cos left(frac{theta}{2}right) )
D ( cdot frac{2}{3} R cos (theta) )
11
1122If a string attached to a fixed pulley of radius R moves through a distance ( x ) and the pulley rolls without slipping
through an angle ( theta, x ) and ( theta ) are related
by
( A cdot x>R theta )
B. ( x=R theta )
( c cdot x<R theta )
D. 2R ( theta )
11
1123A long slender rod of mass ( 2 mathrm{kg} ) and
length 4 m is placed on a smooth
horizontal table. Two particles of
masses ( 2 k g ) and ( 1 k g ) strike the rod
simultaneously and stick to the rod
after collision as shown in Figure. Velocity of the centre of mass of the rod
after collision is
A ( .12 mathrm{m} / mathrm{s} )
B. ( 9 mathrm{m} / mathrm{s} )
c. ( 6 m / s )
D. ( 3 mathrm{m} / mathrm{s} )
11
1124The motion of centre of mass depends
on
A. total external forces
B. total internal forces
c. sum of ( (a) ) and ( (b) )
D. None of these
11
1125Two points of a rod move with velocities
( 3 v & v ) perpendicular to the rod and in the same direction, separated by a distance ‘r’. The angular velocity of rod is :
A ( cdot frac{3 v}{r} )
в. ( frac{4 v}{r} )
c. ( frac{5 v}{r} )
D. ( frac{2 v}{r} )
11
1126The wheel of radius ( r=300 mathrm{mm} ) rolls to
the right without slipping and has a
velocity ( V_{0}=3 m / s ) of its centre 0. The
speed of the point ( A ) on the wheel for the
instant represented in the figure is :-
( A cdot 4.36 m / )
B. ( 5 m / s )
( c cdot 3 m / s )
( mathbf{D} cdot 1.5 mathrm{m} / mathrm{s} )
11
1127A boy of mass ( mathrm{m} ) is standing on a block of mass M kept on a rough surface. When the boy walks from left to right on
the block, the centre of mass(boy ( + )
block) of the system.
A. Remains stationary
B. Shifts towards left
c. shifts towards right
D. Shifts toward right if ( mathrm{M}>mathrm{m} ) and toward left if ( mathrm{M}<mathrm{m} ).
11
1128A fly wheel rotating at 600 rev/min is brought under uniform deceleration and
stopped after 2 minutes, then what is
angular deceleration in rad/sec ( ^{2} ) ?
11
1129A wheel of radius 0.5 m rolls without sliding on a horizontal surface, starting from rest, the wheel moves with
constant acceleration ( 6 ~ r a d / s^{2} ). The distance travelled by the centre of the wheel from ( t=0 ) to ( t=3 s ) is:
A . 27 m
в. ( 13.5 mathrm{m} )
( c .18 m )
D. zero
11
1130Select and write the most appropriate answer from the given alternatives for the following:A particle rotates in U.C.M. with tangential velocity ( v ) along a horizontal circle of diameter ( D ). Total
angular displacement of the particle in
time ‘t’ is
A. ( v t )
B. ( left(frac{v}{D}right)-t )
c. ( frac{v t}{2 D} )
D. ( frac{2 v t}{D} )
11
1131A point mass ( m ) is rigidly attached at
the circumference of uniform Ring of same mass. It is at same horizontal
position as centre of ring. The minimum coefficient of friction between ring and
ground so that there is pure rolling of
ring on surface just after system is
released is:
A . ( 3 / 5 )
B. 2/3
( c cdot 1 / 3 )
D. ( 2 / 7 )
11
1132Two blocks of masses ( 10 k g ) and ( 4 k g ) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulsive force
gives a velocity of ( 14 m s^{-1} ) to the
heavier block in the direction of the
lighter block. The velocity of centre of mass of the system at that moment is
A ( .30 m s^{-1} )
B. ( 20 m s^{-1} )
( mathrm{c} cdot 10 mathrm{ms}^{-1} )
( mathbf{D} cdot 5 m s^{-1} )
11
1133A table fan, rotating at a speed of 2400
rpm is switched off and the resulting
variation of the rpm with time is shown
in the figure. The total number of revolutions of the fan before it comes to
rest is:
A. 420
B. 280
( c cdot 480 )
D. 380
11
1134A wheel of radius ( 10 mathrm{cm} ) can rotate freely
about an axis passing through its centre. A force ( 20 N ) acts tangentially at
the rim of wheel. If moment of inertia of
wheel is ( 0.5 k g m^{2}, ) its
angular acceleration is:
A ( cdot 2 ) rad/s^
B . ( 2.5 mathrm{rad} / mathrm{s}^{2} )
11
1135Show that if a rod held at angle ( theta ) to the horizontal and released, its lower end
will not slip if the friction coefficient
between rod and ground is greater than ( frac{3 sin theta cos theta}{1+3 sin ^{2} theta} )
11
1136Area of parallelogram, whose diagonals ( operatorname{are} 3 hat{i}+hat{j}-2 hat{k} ) and ( hat{i}-3 hat{j}+4 hat{k} ) will be
:
A. 14 unit
B. ( 5 sqrt{3} ) unit
c. ( 10 sqrt{3} ) unit
D. ( 20 sqrt{3} ) unit
11
1137Two skaters ( A ) and ( B ) of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?
A. Both have moved 3 metres
B. A moves 2.5 metres and B moves 3.5 metres.
C. A moves 3.5 metres and ( B ) moves 2.5 metres
D. A moves 2 metres and B moves 4 metres
11
1138The work done by the frictional force at the instant of pure rolling is
( ^{text {A }} cdot frac{mu m g a t^{2}}{2} )
B. ( mu ) mgat ( ^{2} )
( mathrm{c},_{mu m g} frac{a t^{2}}{alpha} )
D. zero
11
1139Assertion
Centre of mass of a rigid body always lies inside the body.
Reason
Centre of mass and centre of gravity coincide if gravity is uniform.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
1140A hollow smooth uniform sphere ( A ) of mass m rolls without sliding on a smooth horizontal surface. It collides
head on elastically with another stationary smooth solid sphere ( B ) of the same mass ( mathrm{m} ) and same radius. The
ratio of kinetic energy of ( B ) to that of ( A ) just after the collision is :
( A cdot 1: 1 )
в. 2: 3
( c .3: 2 )
D. 4: 3
11
1141A thin ring has mass ( 0.25 mathrm{kg} ) and radius
( 0.5 m . ) Its M.I. about an axis passing
through its centre and perpendicular to its plane is ( ldots )
( mathbf{A} cdot 0.0265 g-c m^{2} )
В. ( 0.0625 mathrm{kg}-mathrm{m}^{2} )
c. ( 0.625 k g-m^{2} )
D. ( 6.25 mathrm{kg}-mathrm{m}^{2} )
11
1142Four point masses are placed at the
corners of a square of side ( 2 m ) as shown
in figure. Find the centre of mass of the
system w.r.t the centre of square
11
1143A locomotive is propelled by a turbine whose axle is parallel to the axes of
wheels. The turbine’s rotation direction
coincides with that of wheels. The
moment of inertia of the turbine rotor
relative to its own axis is equal to ( boldsymbol{I}= )
( 240 k g cdot m^{2} . ) If the additional force
exerted by the gyroscopic forces on the rails when the locomotive moves along
a circle of radius ( R=250 m ) with
velocity ( boldsymbol{v}=mathbf{5 0} boldsymbol{k m} / boldsymbol{h} ) is ( boldsymbol{F}_{boldsymbol{a d d}}= )
( frac{x}{10} k N . m, ) find the value of ( x . ) The gauge
is equal to ( l=1.5 m . ) The angular
velocity of the turbine equals ( n= )
1500 rpm
11
1144Find the value of ( ^{prime} a^{prime} ) for which the vector
( boldsymbol{A}=mathbf{3} hat{mathbf{i}}+mathbf{3} hat{boldsymbol{j}}+mathbf{9} hat{boldsymbol{k}} ) and ( overline{boldsymbol{B}}=hat{boldsymbol{i}}+boldsymbol{a} hat{boldsymbol{j}}+boldsymbol{3} hat{boldsymbol{k}} )
are parallel
11
1145A sphere is released on a smooth
inclined plane from the top. When it
moves down, its angular momentum is
B. conserved about the point of contact only
C. conserved about the centre of the sphere only
D. conserved about any point on a line parallel to the inclined plane and passing through the centre of the ball
11
1146Two particles of masses ( 2 mathrm{kg} ) and ( 4 mathrm{kg} ) are approaching towards each other with acceleration ( 1 mathrm{m} / mathrm{s}^{2} ) and ( 2 mathrm{m} / mathrm{s}^{2} )
respectively, on a smooth horizontal surface. Them find the acceleration of
centre of mass of the system and
direction of acceleration of ( C O M )
11
1147A bullet of mass ( mathrm{X}, ) moving with a velocity ( V ), strikes a wooden block of mass ( Z ) and gets embedded. If the block
is free to move, its velocity after impact will be.
A ( cdot frac{X}{X+Z} mathrm{v} )
в. ( frac{X+Z}{Z} vee )
c. ( frac{x}{x-Z} V )
D. ( frac{X+Z}{X} V )
11
1148If ( overrightarrow{boldsymbol{F}} ) is the force acting on a particle
having position vector ( vec{r} ) and ( vec{tau} ) be the torque of this force about the origin, then :
A ( cdot vec{r} . vec{tau}=0 ) and ( vec{F} cdot vec{tau} neq 0 )
В . ( vec{r} . vec{tau} neq 0 ) and ( vec{F} . vec{tau}=0 )
c. ( vec{r} . vec{r}>0 ) and ( vec{F} . vec{tau}<0 )
D . ( vec{r} . vec{r}=0 ) and ( vec{F} . vec{tau}=0 )
11
1149Motion of centre of mass11
1150A disc of radius ( 0.2 m ) is rolling with
slipping on a flat horizontal surface, as shown in figure. The instantaneous
centre of rotation is: (the lowest contact
point is 0 and centre of disc is ( C ) )
A . zero
B. ( 0.1 m ) above 0 on line 0 C
c. ( 0.2 m ) below o on line oc
D. ( 0.2 m ) above 0 on line 0 c
11
its axis at an angular speed of 20 rad/s. Find the linear speed of point of the rim.
11
1152Four rod each of mass ( mathrm{m} ) from a square
length of diagonal b rotates about its
diagonal. Its moment of inertia is:-
11
1153A rigid body rotates about a stationary
axis according to the law ( boldsymbol{theta}=boldsymbol{a t}-boldsymbol{b} boldsymbol{t}^{3} )
awhere ( a=6 frac{r a d}{s} ) and ( b=2 frac{r a d}{s^{3}} . ) Then
mean value of angular velocity ( ( omega ) ) over
the interval ( t=0 ) and the moment when
it comes to rest is:
A ( .4 mathrm{rad} / mathrm{s} )
c. 8 rad ( / s )
D. 6 rad ( / ) s
11
1154An insect sits on the end of a long board
of length 5 m. The board rests on a frictionless horizontal table. The insect
wants to jump to the opposite end of the board. What is the minimum take-off speed (in ( mathrm{m} / mathrm{s} ) ) of insect relative to
ground, that allows the insect to do the trick? The board and the insect have
equal masses. ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
11
1155Two blocks of masses ( 10 mathrm{kg} ) and ( 4 mathrm{kg} ) are connected by a spring of negligible mass and placed on a frictionless horizontal surface.An impulse gives a velocity of ( 14 mathrm{m} / mathrm{s} ) to the heavier block in
the direction of the lighter block.the velocity of the center of mass is :
( A cdot 5 m / s )
B. 20 ( mathrm{m} / mathrm{s} )
( c cdot 30 m / s )
D. ( 10 mathrm{m} / mathrm{s} )
11
1156Immediately after the right string is
cut, what is the linear acceleration
of the middle of the rod?
11
1157( N ) similar slabs of cubical shape of
edge ( b ) are lying on the ground. Density
of material of the slab is ( rho . ) Work done to
arrange them one over the other is :
(Given acceleration due to gravity ( =g) )
A ( cdotleft(N^{2}-1right) b^{3} rho g )
в. ( (N-1) b^{4} rho g )
c. ( frac{1}{2}left(N^{2}-Nright) b^{4} rho g )
D. ( left(N^{2}-Nright) b^{4} rho g )
11
1158A straight road has two sections ( A B ) (highly rough) and ( B C( ) slightly rough),a body of mass m rolling without friction in ( A B ) at ( t=0 . ) After some time it enters
the section ( B C ) then in this section,
A . friction start acting
B. pure rolling in BC
C. forward slipping takes place
D. none of the above
11
1159A ball of mass ( 50 g ) moving at a speed of ( 2.0 m / s ) strikes a plane surface at an
angle of incidence ( 45^{circ} ) The ball is
reflected by the plane at equal angle of reflection with the same speed.
Calculate
(a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the
momentum of the ball
11
1160A solid sphere starts rolling down on an inclined plane from a vertical height
( 3.5 m . ) The velocity of centre of mass of sphere on reaching the bottom of inclined plane is :
A ( .2 .45 mathrm{ms}^{-1} )
в. ( 4.9 mathrm{ms}^{-1} )
( mathbf{c} cdot 7 m s^{-1} )
D. ( 9.8 m s^{-1} )
11
1161A plastic circular disc of radius ( R ) is
placed on a thin oil film, spread over a flat horizontal surface. The torque
required to spin the disc about its central vertical axis with a constant
angular velocity is proportional to
( mathbf{A} cdot R^{2} )
B . ( R^{3} )
( c cdot R^{4} )
D. ( R^{6} )
11
1162Any point on the circumference of a
rigid body which is rolling without slipping undergoes :
A. a circular path
B. an elleptic path
c. a cycloid path
D. an parabolic path
11
1163A stationary body explodes into two
fragments of masses ( boldsymbol{m}_{1} ) and ( boldsymbol{m}_{2} . ) If
momentum of one fragment is ( p ), the minimum energy of explosion is
( ^{mathbf{A}} cdot frac{p^{2}}{2left(m_{1}+m_{2}right)} )
в. ( frac{p^{2}}{2(sqrt{m_{1} m_{2}})} )
c. ( frac{p^{2}left(m_{1}+m_{2}right)}{2 m_{1} m_{2}} )
D. ( frac{p^{2}}{2left(m_{1}-m_{2}right)} )
11
1164A uniform disc of mass ( mathrm{m} ) and radius ( mathrm{R} )
is projected horizontally with velocity ( v_{0} ) on a rough horizontal floor so that it starts off with a purely sliding motion at
( t=0 . ) After ( t_{0} ) seconds it acquires a pure rolling motion. Calculate the velocity of
the centre of mass of the disc at ( t_{0} )
A ( cdot v=(2 / 4) v_{0} )
B. ( v=(2 / 3) v_{0} )
( c cdot v=(3 / 3) v_{0} )
( D cdot v=(4 / 3) v_{0} )
11
1165State whether true or false.
A couple tends to produce motion in a straight line.
A. True
B. False
11
1166The net external force acting on the disk
when its centre of mass is at
displacement x with respect to its equilibrium position is
4. ( k x )
3. ( 2 k x )
( c cdot-frac{2 k x}{3} )
D. ( -frac{4 mathrm{kx}}{3} )
11
1167Which of the following quantities is zero, when a uniform object is being supported at its center of gravity?
A . Mass
B. Weight
c. Force
D. Moment
11
1168A ladder ( A B, 2.5 m ) long and of weight ( 150 N ) has its centre of gravity ( 1 m ) from ( A ) is lying flat on ground. ( A ) weight
of ( 40 N ) is attached to the end ( B ). The
work required (in joule) to raise the ladder from the horizontal position to vertical position so that the bottom end ( A ) is resting in a ditch 1 m below the ground level will be :
A . 60
B. 30
c. 20
D. 120
11
1169A bomb at rest explodes in air in two equal fragments. If one of the fragments starts moving vertically upwards with
velocity ( v_{0}, ) then the other fragment will
move:
A. vertically up with velocity ( v_{0} )
B. vertically downwards with velocity ( v_{0} )
c. in any arbitrary direction
D. none of these
11
1170If the velocity of centre of mass of a
rolling body is ( V ) then velocity of highest point of that body is :
A. ( sqrt{2} V )
в. ( V )
c. ( 2 V )
D. ( frac{V}{sqrt{2}} )
11
1171A system consists of two identical
small balls of mass 2 kg each
connected to the two ends of a 1 m long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at angular speed of 9 rad/s. An impulsive force of
average magnitude ( 10 N ) acts on one of the masses in the direction of its
velocity for ( 0.20 s . ) Calculate the new
angular velocity of the system.
11
1172For the cube-rod-sphere combination shown, the density of the material is uniform throughout the object. A thin rod of length, ( d ), connects the centers of the two objects. Where is the center of mass?
A. Inside the cube
B. closer to the cube than to the sphere
c. At the midpoint between the cube and the sphere
D. closer to the sphere than to the cube
E. Inside the sphere
11
1173A uniform solid sphere is placed on a
smooth horizontal surface. An impulse
( I ) is given horizontally to the sphere at a height ( h=frac{4 R}{5} ) above the centre line. ( m )
and ( R ) are mass and radius of sphere
respectively.
(a) Find angular velocity of sphere ( & ) linear velocity of centre of mass of the
sphere after impulse.
(b) Find the minimum time after which
the highest point ( B ) will touch the
ground
(c) Find the displacement of the centre of mass during this interval.
11
1174A constant torque of ( 50 mathrm{N} mathrm{m} ) is needed
to keep a wheel moving at a constant angular speed of 20 rads/s. The amount of work performed by this torque in 5 minutes
B. 100 KJ
c. 300 KJ
D. 30 KJ
11
1175In neutral equilibrium,
A. center of gravity is neither raised nor lowered.
B. center of gravity is raised.
C. center of gravity is lowered
D. None
11
1176A ball of radius ( boldsymbol{R}=mathbf{1 0 . 0} ) cm rolls
without slipping on a horizontal plane
so that its centre moves with constant
acceleration ( a=2.50 mathrm{cm} / mathrm{s}^{2} ; t=2.00 s )
after the beginning of motion its portion corresponds to that shown in Fig. Find:
(a) the velocities of the points ( A, B ) and
( O )
(b) the accelerations of these points.
11
1177A uniform metre stick of mass 200 g is suspended from the ceiling through two vertical strings equal lengths fixed at the ends. A small object of mass 20 g is placed on the stick at a distance ( 70 mathrm{cm} )
from the left end. Find the tensions in
the two strings.
11
1178A solid sphere is rolling without slipping on a level surface at a constant
speed of ( 2.0 m s^{-1} . ) How far can it roll up
a ( 30^{circ} ) ramp before it stops?
( mathbf{A} cdot 56 mathrm{cm} )
B . ( 26 mathrm{cm} )
( c .53 mathrm{cm} )
D. 84
11
1179What is the center of mass of an object?
A. The mean position of the mass in an object.
B. The geometric center of an object.
C. The furthest away position of the mass in an object.
D. The same as the center of gravity.
E. The closest position of the mass in an object.
11
1180The altitude of a parallelopiped whose three coterminous edges are the vectors, ( overline{boldsymbol{A}}=hat{boldsymbol{i}}+hat{boldsymbol{j}}+hat{boldsymbol{k}} ; overline{boldsymbol{B}}=mathbf{2} hat{boldsymbol{i}}+boldsymbol{4} hat{boldsymbol{j}}-hat{boldsymbol{k}} )
( & bar{C}=bar{i}+bar{j}+3 hat{k} ) with ( bar{A} ) and ( bar{B} ) as the
sides of the base of the parallelopiped is
A. ( 2 / sqrt{19} )
в. ( 4 / sqrt{19} )
c. ( 2 sqrt{38} / 19 )
( D . ) none
11
1181The topmost and bottom most
velocities of a disc are ( v_{1} ) and ( v_{2} ) in the
same direction. The radius is R. What is
the angular velocity of the disc
A ( cdot frac{left(v_{1}-v_{2}right)}{R} )
в. ( frac{left(v_{1}-v_{2}right)}{2 R} )
c. ( frac{left(v_{1}+v_{2}right)}{2 R} )
D. ( _{text {a }} frac{left(v_{1}+v_{2}right)}{R} )
11
1182A square plate ( A B C D ) of mass ( m ) and
side ( l ) is suspended with the help of two
ideal strings ( P ) and ( Q ) as shown
determine the acceleration ( left(text { in } m / s^{2}right) ) of
corner ( A ) of the square just at the
moment the string ( Q ) is cut ( (g= )
( left.10 m / s^{2}right) )
11
1183Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.11
1184A small piece of space junk is at rest in outer space. A very small asteroid strikes it, exerting a force on it that is NOT directed through the piece of space junk’s center of mass. Which of the following describes the motion of the piece of space junk DURING the asteroid strike?
A. Because the asteroid is small, the space junk remains at rest
B. The piece of space junk spins, but does NOT move linearly
c. The piece of space junk moves at constant velocity linearly, but does NOT spin
D. The piece of space junk accelerates linearly, but does NOT spin
E. The piece of space junk accelerates linearly, AND spins
11
1185A train of mass ( M ) is moving on a
circular track of radius ( R ) with a
constant speed ( v ). The length of the train is half of the perimeter of the track. The linear momentum of the train will be
A . zero
в. ( frac{2 M v}{pi} )
c. ( M v R )
D. ( M v )
11
1186Name the factors affecting the turning effect of a body11
1187A circular hole of radius ( frac{x}{2} ) is cut from a
circular disc of radius ( R ). The disc lies
in the XY-plane and its centre coincides
with the origin. If the remaining mass of
the disc is ( M ) then,
(1)determine the initial mass of the
disc.
(2)determine its moment of inertia
11
1188A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be :
A ( cdot frac{5}{3} )
B. ( frac{3}{5} )
c. ( frac{15}{13} )
D. ( frac{13}{15} )
11
1189A thin circular ring of mass ( M ) and
a constant angular velocity ( omega . ) Two
objects, each of mass ( boldsymbol{m}, ) are attached gently to the opposite ends of the
diameter of the ring. The wheel now rotates with an angular velocity
( mathbf{A} cdot frac{omega M}{(M+m)} )
B. ( frac{omega(M-2 m)}{(M+2 m)} )
( ^{mathbf{c}} cdot frac{omega M}{(M+2 m)} )
D. ( frac{omega(M+2 m)}{M} )
11
1190A disc of mass ( m ) and radius ( R ) rolls
down an inclined plane of height ( h ) without slipping. Find out the velocity of the disc when it reaches the bottom
of the incline? The moment of inertia for
a disk is ( (1 / 2) m R^{2} )
A ( cdot sqrt{g h} )
в. ( sqrt{frac{4}{3} g h} )
c. ( sqrt{2 g h} )
D. ( 2 sqrt{g h} )
E ( .2 sqrt{2 g h} )
11
1191A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 ( mathrm{m} / mathrm{s} . ) The total kinetic energy of rolling sphere would be (in J)
A ( .1 .4 times 10^{-4} J )
B. ( 0.75 times 10^{-3} J )
c. ( 5.75 times 10^{-3} J )
D. ( 4.9 times 10^{-5} J )
11
1192The diagram below (Fig.) shows a uniform bar supported at the middle
point ( O . A ) weight of ( 40 g f ) is placed at a
distance ( 40 mathrm{cm} ) to the left of the point ( O )
How can you balance the bar with a
weight of ( 80 g f ? )
A. By placing the weight of ( 80 g f ) at a distance ( 10 mathrm{cm} ) to the right of the point ( O )
B. By placing the weight of ( 40 g f ) at a distance ( 20 mathrm{cm} ) to the right of the point ( O )
C. By placing the weight of ( 160 g f ) at a distance ( 10 mathrm{cm} ) to the right of the point ( O )
D. By placing the weight of ( 80 g f ) at a distance ( 20 mathrm{cm} ) to the of the point ( O )
11
1193The ratio of the angular speed of hours hand and second hand of a clock is
A . 1: 1
B. 1: 60
c. 1: 720
D. 3600 : 1
11
1194Centre of mass of two body system
divides the distance between two
bodies, is proportional to
A. Inverse of square of the mass
B. Inverse of mass
c. The ratio of the square of mass
D. The ratio of mass
11
1195( sum_{i=3}^{infty} )11
1196A uniform metre rule balances
horizontally on a knife edge placed at the ( 58 c m ) mark when a weight of ( 20 g f ) is suspended from one end. What is the weight of the rule?
A. ( 10500 g f )
в. ( 105 g f )
c. ( 1.05 g f )
D. ( 11.6 g f )
11
1197If ( bar{A} times bar{B}=bar{C} ) which of the following
statement is not correct?
A. ( bar{C} ) T ( bar{A} )
в. ( bar{C} ) Т ( bar{B} )
c. ( bar{C} ) T ( bar{A} times bar{B} )
D. ( bar{C} top bar{A}+bar{B} )
11
1198A ring ( (R), ) a disc ( (D), ) a solid sphere ( (S) ) and a hollow sphere with thin walls (H), all having the same mass and radii, start together from rest at the top of an inclined plane and roll down without slipping. This question has multiple correct options
A. All of them will reach the bottom of the incline together.
B. The body with the maximum radius will reach the bottom first.
c. They will reach the bottom in order ( mathrm{S}, mathrm{D}, mathrm{H}, mathrm{R} )
D. All of them will have the same kinetic energy at the bottom of the incline
11
1199A plate in the form of a semicircle of
radius ( R ) has a mass per unit area of ( k r )
where ( k ) is a constant and ( r ) is the
distance form the centre of a straight
edge. By dividing plate into
semicircular rings find the centre of
mass of the plate from the centre of its straight edge.
A ( cdot frac{4 R}{3 pi} )
B. ( frac{2 R}{pi} )
c. ( frac{3 R}{2 pi} )
D. ( frac{3 R}{4 pi} )
11
1200A circular disc is rotating about its own natural axis. A constant opposing torque ( 2.75 N m ) is applied on the disc due to which it comes to rest in 28
rotations. If moment of inertia of disc is
( 0.5 k g m^{2}, ) the initial angular velocity of
disc is:
A . 210 rpm
в. 280 rpm
c. ( 360 r p m )
D. 420 rpm
11
1201Where does the center of gravity of the
atmosphere of the lie?
11
1202Two solid cylinders ( P ) and ( Q ) of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder
( P ) has most of its mass concentrated
near its surface, while ( Q ) has most of its
mass concentrated near the axis. Which
statement(s) is (are) correct?
A. Both cylinders ( P ) and ( Q ) reach the ground at the same time
B. Cylinder ( P ) has larger linear acceleration than cylinder
( Q )
C. Both cylinders reach the ground with same translational kinetic energy.
D. Cylinder ( Q ) reaches the ground with larger angular speed
11
1203Two particles of masses ( 1 k g ) and ( 2 k g ) are placed at a distance at a distance of
( 3 m . ) Moment of inertia of the particles about an axis passing through their centre of mass and perpendicular to the
line joining them is ( left(operatorname{in} k g-m^{2}right) )
( mathbf{A} cdot mathbf{6} )
B. 9
c. 8
D. 12
11
1204A torque of ( 0.5 N m ) is required to drive a screw into a wooden frame with the help of a screw driver. If one of the two forces
of couple produced by screw driver is
( mathbf{5 0} N, ) the width of the screw driver is:
( mathbf{A} cdot 0.5 mathrm{cm} )
B. ( 0.75 mathrm{cm} )
( c cdot 1 c m )
D. ( 1.5 mathrm{cm} )
11
1205Two particles having masses in ( mathrm{m} ) and ( 2 mathrm{m} ) are travelling along ( mathrm{x} ) -axis on a
smooth surface with velocities ( u_{1} ) and
( u_{2}, ) collide .If their velocities after
collision are ( v_{1} ) and ( v_{2}, ) then the ratio of
velocities of their centre of mass before
and after impact is
A. 2:
B. 2:3
( c cdot 1: )
D. 1: 2
11
1206The grinding stone of a flour mill is
rotating at 600 rad/sec. for this power of ( 1.2 k ) watt is used. The effective
torque on stone in ( N-m ) will be
( A )
B. 2
( c cdot 3 )
D. 4
11
1207Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The
centre of mass has an acceleration
A . zero
B . ( frac{1}{2} a )
( c cdot a )
D. 2a
11
1208Linear Acceleration of all the points in
rigid body is-
A. same
B. different
c. may be same may be different
D. none of these
11
1209The maximum angular deflection of the
rod from the vertical after the collision
is
( ^{mathbf{A}} cdot_{theta}=cos ^{-1}left(1-frac{5 v_{0}^{2}}{16 g l}right) )
B. ( quad theta=sin ^{-1}left(1-frac{3 v_{0}^{2}}{16 g l}right) )
( mathbf{c} cdot_{theta}=cos ^{-1}left(1-frac{3 v_{0}^{2}}{16 g l}right) )
D ( quad theta=sin ^{-1}left(1-frac{5 v_{0}^{2}}{16 g l}right) )
11
1210A pulley fixed to the ceiling carries a
thread with bodies of masses ( m_{1} ) and
( m_{2} ) attached to its ends. The masses of
the pulley and the thread are negligible, friction is absent. Find the acceleration
( boldsymbol{w}_{C} ) of the centre of mass of this system
A ( cdot frac{left(m_{1} m_{2}right)^{2} vec{g}}{left(m_{1}-m_{2}right)^{2}} )
B. ( frac{left(m_{1}+m_{2}right)^{2} vec{g}}{left(m_{1}-m_{2}right)^{2}} )
c. ( frac{left(m_{1} m_{2}right)^{2} vec{g}}{left(m_{1}+m_{2}right)^{2}} )
D. ( frac{left(m_{1}-m_{2}right)^{2} vec{g}}{left(m_{1}+m_{2}right)^{2}} )
11
1211The centre of gravity of an object is whether it is placed near the
surface of the Earth or near the surface
of the Moon.
A. same
B. different
c. depend on the situation
D. none
11
1212A solid cylinder is rolling down on an inclined plane without slipping. The length of the plane is ( 30 m ) and its angle
of inclination is ( 30^{circ} . ) If the cylinder starts from rest then its velocity at the bottom of the inclined plane is:
A ( cdot 14 m s^{-1} )
B. ( 28 m s^{-1} )
( mathbf{c} cdot 7 m s^{-1} )
D. ( 35 m s^{-1} )
11
1213State whether true or false:
The position of centre of gravity of a body remains unchanged even when the body is deformed.
A. True
B. False
c. Ambiguous
D. Data insufficient
11
1214Equal volume of two solution having pH ( =2 ) and ( p H=10 ) are mixed together at 90C. Then pH of resulting solution is :
(Take ( left.K w text { at } 90 C=10^{-12}right) )
A. ( 2+log 2 )
B. 10 ( log 2 )
c. 7
( D cdot 6 )
11
1215The position of a particle is given by ( vec{r}=(hat{i}+2 hat{j}-hat{k}) ) and momentum ( vec{P}= )
( (3 hat{i}+4 hat{j}-2 hat{k}) . ) The angular momentum is perpendicular to
A. X-axis
B. Y-axis
c. z-axis
D. Line at equal angles to all the three axes
11
1216A horizontal circular platform of radius
( 0.5 m ) and mass ( 0.45 k g ) is free to rotate
about its axis. Two massless spring toyguns, each carrying a steel ball of mass ( 0.05 k g ) are attached to the platform at a distance ( 0.25 m ) from the centre on its
either sides along its diameter (see figure). Each gun simultaneously fires the ball horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the ball have horizontal speed of ( 9 m s^{-1} ) with respect to the ground. The rotational speed of
the platform in ( r a d s^{-1} ) after the balls
leave the platform is :
11
1217is applied to unwind a screw.
A. single force
B. Couple
c. Parallel force
D. None of these
11
1218Find the friction force.11
1219The time ( t ) (after entering in rough
surface) after which ring starts pure
rolling
A. ( frac{v_{0}}{2 mu_{0}} )
в. ( underline{v_{0}} )
( g )
c. ( frac{v_{0}}{mu g g g g} )
D. None of these
11
1220The principle involved in the construction of beam balance is :
A. Principle of moments
B. Principle of inertia
c. Principle of superposition
D. Principle of velocity
11
1221A particle of mass ( m ) is subjected to an attractive central force of magnitude
( k / r^{2}, k ) being a constant. If at the instant when the particle is at an extreme position in its closed orbit, at a
distance ( a ) from the centre of force, its
speed is ( (k / 2 m a), ) if the distance of other extreme position is ( b ). Find ( a / b )
( A cdot 4 )
B. 3
( c cdot 5 )
D. 6
11
1222In a complete circular motion, first half circle is covered with 6.The other half circle is covered in two equal times
intervals at speed 4 and 2 respectively.The average speed during the circular motion is
( A cdot 2 )
B. 3
( c cdot 4 )
D. 5
11
1223The condition of no-slip in rotation of a
pulley attached to a mass using a
string refers to
( mathbf{A} cdot v=R omega ; v ) is the linear velocity, ( omega ) is the angular
velocity and ( mathrm{R} ) is the radius
B. ( a=R alpha ; a ) is the linear acceleration, ( alpha ) is the angular acceleration and ( mathrm{R} ) is the radius
C ( . v=R omega ) and ( a=R alpha ; v ) is the linear velocity, ( omega ) is the
angular velocity, ( alpha ) is the angular acceleration and ( mathrm{R} ) is
( ^{mathrm{D}} T=M frac{v^{2}}{R} ; T ) is the tension in the string, ( v ) is the linear
velocity, and ( R ) is the radius
11
1224A thin horizontal uniform rod ( A B ) of
mass ( M ) and length ( l ) can rotate freely about a vertical axis passing through
its end ( A ). At a certain moment the end
( B ) starts experiencing a constant force
( boldsymbol{F} ) which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle ( varphi ) counted relative to the initial position.
A ( cdot omega=sqrt{frac{6 F sin varphi}{M l}} )
B. ( omega=sqrt{frac{3 F sin varphi}{M l}} )
c. ( omega=sqrt{frac{6 F cos varphi}{M l}} )
D. None of these
11
1225Two particle of equal masses have velocities ( vec{V}_{1}=2 i m / s ) and the second particle has velocity ( 2 hat{j} ) m/s. The first particle has an acceleration ( overrightarrow{a_{1}}=(3 hat{i}+ )
( mathbf{3} hat{boldsymbol{j}}) frac{m}{s^{2}} ) while the acceleration of the other particle is zero. The center of mass of the particle moves in a :
A . circle
B. parabola
c. straight line
D. ellipse
11
1226Vector ( underset{A}{A} ) has a magnitude of 6 units and is in the direction of ( +x a x i s . ) Vector
( vec{B} ) has a magnitude of 4units lies in
the ( x ) -y plane making an angle of ( 30^{circ} ) with ( +x-a x i s . ) Find the vector
product ( underset{A}{A} times frac{ }{B} )
11
1227(i) Where is the centre of gravity of a uniform ring situated?
(ii) “The position of the centre of gravity of a body remains unchanged even when the body is deformed”. State whether this statement is true or false.
11
1228Indicate the minimum number of
tosses by each skater required to avoid
collision.
Number of tosses by ( A= ) Number of tosses by B =
11
1229Average torque on a projectile of mass
( m, ) initial speed ( u ) and angle of
projection ( theta ) between initial and final positions ( mathrm{P} ) and ( mathrm{Q} ) as shown in the figure about the point of projection is:
A ( cdot frac{m u^{2} sin 2 theta}{2} )
в. ( m u^{2} cos theta )
c. ( mu^{2} sin theta )
D. ( frac{m u^{2} cos theta}{2} )
11
1230What is the torque of the force ( overrightarrow{boldsymbol{F}}= ) ( (2 hat{i}-3 hat{j}+4 hat{k}) N, ) acting at the point ( vec{r}=(3 hat{i}+2 hat{j}+3 hat{k}) m ) about the origin
( (operatorname{in} N-m) )
A . ( 6 hat{i}-6 hat{j}+12 hat{k} )
B . ( 17 hat{i}-6 hat{j}-13 hat{k} )
c. ( -6 hat{i}+6 hat{j}-12 hat{k} )
D. ( -17 hat{i}+6 hat{j}-13 hat{k} )
11
1231Moment of inertia of a uniform circular
disc about a diameter is ( l ). Its moment
of inertia about an axis perpendicular
to its plane and passing through a point on its rim will be:
11
1232A uniform metre rule of weight ( 10 g f ) is
pivoted at its 0 mark. How can it be
made horizontal by applying a least force?
A. By applying a force ( 10 g f ) downwards at the ( 100 mathrm{cm} ) mark
c. By applying a force ( 5 g f ) upwards at the 100 cm mark.
D. By applying a force ( 5 g f ) downwards at the 100 cm mark.
11
1233What is the difference between the
centre of gravity and the centre of
mass?
11
1234When a body starts to roll on an inclined plane, its potential energy is converted into
A. Translation kinetic energy only
B. Translation and rotational kinetic energy
C. Rotational energy only
D. None of these
11
1235A thin circular disk is in the ( x y ) plane as
shown in the figure. The ratio of its
moment of inertia about ( z ) and ( z^{prime} ) axes
will be
A . 1: 2
B. 1: 4
c. 1: 3
D. 1: 5
11
1236toppr
force, but otherwise the sled will not
have external forces interacting with its horizontal motion).
In order to push the sled without
making it rotate, where should you
push?
Refer to the diagram to help you conceptualize the situation. All objects
in the system you are about to push
have some mass, through their
quantities are unknown. The sled is
motionless initially and the surface is
completely flat. Assume you are going
to push on the side that is closer to you,
as shown in the diagram.
A. Directly between the two dogs depicted in the diagram
B. Somewhere closer to the black dog
c. Somewhere closer to the white dog
D. At the center of mass of the two dogs
11
1237The M.I of a thin rod of length ( l ) about
the perpendicular axis trough its center
is ( I_{0} . ) The M.I of the square structure
made by four such rods about a perpendicular axis to the the plane and through the center will be :-
A ( .4 I_{0} )
в. ( frac{8}{3} I_{0} )
c. ( frac{4}{3} I_{0} )
D. ( 6 I_{0} )
11
1238Two particles having mass ( mathrm{M} ) and ( mathrm{m} ) are moving in circular paths having radii R and r. If their time periods are same then the ratio of their angular velocities will be:
A. MR : mrr
B. ( M: m )
c. ( R: r )
D. 1:
11
1239A thin disc of radius ( mathrm{R} ) and mass ( mathrm{M} ) has
charge q uniformly distributed on it. It rotates with angular velocity ( omega . ) The ratio of magnetic moment and angular momentum for the disc is?
A ( cdot frac{q}{2 M} )
в. ( frac{R}{2 M} )
c. ( frac{q^{2}}{2 M} )
D. ( frac{2 M}{q} )
11
1240Calculate the ratio of the angular
momentum of the earth about its axis
due to its spinning motion to that about the sun due to its orbital motion.

of the orbit of the earth about the sun is
equal to ( 1.5 times 10^{8} mathrm{km} )

11
1241The mass of block is ( m_{1} ) and that of
liquid with the vessel is ( m_{2} . ) The block is
suspended by a string(tension ( boldsymbol{T} ) )
partially in the liquid. The reading of the weighing machine placed below the
vessel:
A ( cdot ) can be ( left(m_{1}+m_{3}right) g )
B. can be greater than ( left(m_{1}+m_{2}right) g )
C . is equal to ( left(m_{1} g+m_{5} g-Tright) )
D. can be less than ( left(m_{1}+m_{2}right) g )
11
1242Assertion
Speed of a particle moving in a circle varies with time as, ( boldsymbol{v}=(mathbf{4} boldsymbol{t}-mathbf{1 2}) . ) Such
type of circular motion is not possible.
Reason

Speed cannot change linearly with time.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion is incorrect and Reason is correct

11
1243When a particle moves in a circle with a
uniform speed
A. Its velocity and acceleration are both constant
B. Its velocity is constant but the acceleration changes
C. Its acceleration is constant but the velocity changes
D. Its velocity and acceleration both change
11
1244The angular momentum of a system as
particle is conserved
A. when no external force acts upon the system
B. when no external torque acts upon the system
C. when no external impulse acts upon the system
D. when axis of rotation remains same
11
1245A particle is located at ( (3 m, 4 m) ) and moving with ( overrightarrow{boldsymbol{v}}=(4 hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} . ) Find
its magnitude of angular velocity about origin at this instant in rad/sec
11
1246The unit vector perpendicular to ( vec{A}= ) ( mathbf{2} hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}+hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}-hat{boldsymbol{j}}+hat{boldsymbol{k}} ) is:
A ( cdot frac{4 hat{i}-hat{j}-5 hat{k}}{sqrt{42}} )
B. ( frac{4 hat{i}-hat{j}+5 hat{k}}{sqrt{42}} )
c. ( frac{4 hat{i}+hat{j}+5 hat{k}}{sqrt{42}} )
( frac{4 hat{i}+hat{j}-5 hat{k} hat{k}}{sqrt{42}} )
11
1247A uniform circular disc placed on a
rough horizontal surface has initially
velocity ( v_{0} ) and an angular velocity ( omega_{0} ) as
shown in the figure. The disc comes to
rest after moving some distance in the direction of motion. Then ( frac{v_{0}}{r omega_{0}} ) is
A . ( 1 / 2 )
B.
( c cdot 3 / 2 )
D. 2
11
1248Consider a mass ( mathrm{m} ) attached to a string of length I performing vertical circle.find an expression for velocity at any point and tension at any point.11
1249A tank of size ( 10 m times 10 m times 10 m ) is ful
of water and built on the ground. If ( g= )
( 10 m s^{-2}, ) the potential energy of the
water in the tank is
A ( .5 times 10^{7} J )
В. ( 1 times 10^{8} J )
c. ( 5 times 10^{4} J )
D. ( 5 times 10^{5} J )
11
1250Student 1 is
grips wrench here
(wrench turns winch clockwise)
A. correct, because the torque that the wrench must exert to lift the block depend on the wrench’s length
B. correct, because the torque that the wrench must exert to lift the block doesn’t depend on the wrench’s length
C. incorrect, because the torque that the wrench must exert to lift the block doesn’t depend on the wrench’s length
D. incorrect, because using a longer wrench decreases the torque it must exert on the winch.
11
1251If the body is moving in a circle of
radius ( r ) with a constant speed ( v ). Its angular velocity is :
A ( cdot v^{2} / r )
B. ( v r )
c. ( v / r )
D. ( r / v )
11
1252An object comprises of a uniform ring of
radius ( R ) and a uniform chord ( A B ) (not
necessarily made of the same material) as shown. Which of the following cannot
be the centre of mass of the object?
( mathbf{A} cdot(mathrm{R} / 3, mathrm{R} / 3) )
в. ( (R / 2, R / 2) )
c. ( (mathrm{R} / 4, mathrm{R} / 4) )
D. none of the above
11
1253A thin uniform rod of length ( L ) is bent at its mid point as shown in figure. The distance of the centre of mass from the
point ( boldsymbol{L} ) is
A ( cdot frac{L}{4} )
в. ( frac{L}{4} sin (theta / 2) )
c. ( frac{L}{4} cos (theta / 2) )
D. ( frac{L}{2} cos (theta / 2) )
11
1254An automobile engine develops ( 100 k W )
when rotating at a speed of ( mathbf{1 8 0 0} ) rev/min. The torque it delivers is
A . ( 3.33 N-m )
B . ( 200 N-m )
c. ( 530.5 N-m )
D. ( 2487 N-m )
11
1255( A, B ) and ( C ) are the three forces each of
magnitude ( 4 N ) acting in the plane of
paper as shown in the figure. The point
O lies in the same plane. Which force
has the least moment about ( O ) ?
( A cdot A )
в. ( B )
( c . C )
D. all the above
11
1256A sphere of mass ( M ) and radius ( r )
shown in the figure, slips on rough
horizontal plane. At some instant it has
translational velocity ( v_{0} ) and rotational
velocity about centre ( boldsymbol{v}_{mathbf{0}} / 2 boldsymbol{r} . ) The
percentage change of translational
velocity after the sphere start pure
rolling:
A. ( 14.28 % )
B . ( 7.14 % )
c. ( 21.42 % )
D. None
11
1257Two particles having mass ratio ( n: 1 )
are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of
mass of the system is :
A ( cdot(n-1)^{2} g )
( ^{text {B }}left(frac{n+1}{n-2}right)^{2} )
( ^{mathbf{c}} cdotleft(frac{n-1}{n+2}right)^{2} )
D. ( left(frac{n-1}{n+2}right) g )
11
1258Find the centre of mass of a uniform
solid cone.
11
1259rove: ( (overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}}) times(overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}})=2(overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}) )11
1260Find the position of the centre of mass
of the ( T ) -shaped plate from ( O ) in figure.
11
1261A smooth horizontal disc rotates with a
constant angular velocity ( omega ) about a stationary vertical axis passing through
its centre, the point ( O . A t ) a moment ( t= )
0 a disc is set in motion from that point
with velocity ( v_{0} . ) Find the angular
momentum ( boldsymbol{M} )
( (t) ) of the disc relative to the point ( O ) in the reference frame fixed
to the disc. Make sure that this angular momentum is caused by the Coriolis force.
11
1262Find the center of mass of a uniform ( L )
shaped lamina (a thin flat plate) with
dimensions as shown in Fig. The mass
of lamina is ( 3 mathrm{kg} )
11
1263The moment of inertia of a flywheel is ( 0.2 k g m^{2} ) which is initially stationary. constant external torque ( 5 N m ) acts on the wheel. The work done by this torque
during 10 sec is:
A . ( 1250 J )
B. ( 2500 J )
c. ( 5000 J )
D. ( 6250 J )
11
1264From a semi-circular disc of mass ( M )
and radius ( R_{2} . ) A semi-circular disc of
radius ( R_{1} ) is removed as shown in the
figure. If the mass of original uncut disc
is ( M, ) find the momentum of inertia of
residual disc about an axis passing
through centre ( O ) and perpendicular to
the plane of the disc.
( ^{mathbf{A}} cdot frac{M}{2 R_{2}^{2}}left(R_{2}^{4}-R_{1}^{4}right) )
В ( cdot frac{M}{R_{2}^{2}}left(R_{2}^{4}-R_{1}^{4}right) )
( ^{mathbf{c}} cdot frac{M}{R_{2}^{2}}left(frac{R_{2}^{4}}{4}-R_{1}^{4}right) )
D ( frac{M}{2 R_{2}^{2}}left(R_{2}^{4}-frac{R_{1}^{4}}{4}right) )
11
1265Determine the tension in the left string immediately after the right string is cut11
1266If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time?
A ( cdot omega_{1}>omega_{2} )
в. ( omega_{1}=omega_{2} )
( mathrm{c} cdot omega_{2}>omega )
D. None of these
11
1267An object of radius ‘R’ and mas ‘M’ is rolling horizontally without slipping with speed ‘V’. It the rolls up the hill to a
maximum height ( boldsymbol{h}=mathbf{3} boldsymbol{v}^{2} / mathbf{4} boldsymbol{g} ). The
moment of inertia of the object is:
(ge eceleration due to gravity)
( ^{mathbf{A}} cdot frac{2}{5} M R^{2} )
в. ( frac{M R^{2}}{2} )
c. ( M R^{2} )
D. ( frac{3}{2} M R^{2} )
11
1268The potential energy of a conservative
system is given by ( V(x)=left(x^{2}-3 xright) )
joule where ( x ) is measured in metre. Then its equilibrium position is at
A . ( 1.5 mathrm{m} )
B. 2 ( m )
( c cdot 3 m )
( D cdot 1 mathrm{m} )
E. 5 m
11
1269A bomb of mass ( m=1 mathrm{kg} ) thrown
vertically upwards with a speed ( u= )
( 100 mathrm{m} / mathrm{s} ) explodes into two parts after
( boldsymbol{t}=mathbf{5} ) s. ( mathbf{A} ) fragment of ( operatorname{mass} boldsymbol{m}_{mathbf{1}}=mathbf{4 0 0} mathbf{g} )
moves downwards with a speed ( v_{1}=25 )
( mathrm{m} / mathrm{s}, ) then speed ( boldsymbol{v}_{2} ) and direction of
another mass ( m_{2} ) will be?
A. ( 40 mathrm{m} / mathrm{s} ) downwards
B. 40 m/s upwards
c. ( 60 mathrm{m} / mathrm{s} ) upwards
D. ( 100 mathrm{m} / mathrm{s} ) upwards
11
1270Assertion
We can calculate angular momentum of bodies of all shapes by the product of moment of inertia and angular velocity
Reason The basic equation of torque i.e.,torque is equal to rate of change of angular momentum is valid for both inertial and
non inertial frames.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
1271The vertical forces that the ground
exerts on a stationary van are shown.
The van is ( 2.50 mathrm{m} ) long with the wheels
at a distance of ( 0.600 mathrm{m} ) from the front
of the van and ( 0.400 mathrm{m} ) from the rear of
the van.

What is the horizontal distance of the
van’s centre of gravity from the front of the van?
A. ( 0.540 mathrm{m} )
B. 0.960 m
c. ( 1.14 mathrm{m} )
D. ( 1.36 mathrm{m} )

11
1272If the body is moving in a circle of
radius ( r ) with a constant speed ( v ). Its angular velocity is:
A ( cdot frac{v^{2}}{r} )
B. ( v r )
c. ( frac{v}{r} )
D. ( frac{r}{v} )
11
1273In the case of different rolling bodies
match the ratio of rotational kinetic
energy to the total kinetic energy
( begin{array}{ll}text { List-I } & text { List-II } \ text { a) hollow sphere } & text { e) } 2: 5 \ text { b) solid cylinder } & text { f) } 1: 2end{array} ) c) solid sphere
d) hollow cylinder
( A )
( a-h ; b-g ; c-e ; d-f )
в. ( a-h ; b-g ; c-f ; d-e )
c. ( a-e ; b-g ; c-h ; d-f )
D. ( a-e ; b-g ; c-f ; d-h )
11
1274From a uniform circular disc of mass
( M ) and radius ( R ) a small disc of radius
( R / 2 ) is removed is such away that both have a common tangent. Find the distance of center of mass of remaining
part from the center of original disc.
( mathbf{A} cdot R / 20 )
в. ( R / 16 )
c. ( R / 6 )
D. ( frac{3}{4} R )
11
1275Two rings of the same radius ( R ) and
mass ( M ) are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system
about an axis passing through the common centre and perpendicular to the plane of one of the rings is:
( ^{A} cdot frac{M R^{2}}{2} )
в. ( M R^{2} )
c. ( frac{3 M R^{2}}{2} )
D. ( 2 M R^{2} )
11
1276A uniform meter rule balances
horizontally on a knife edge placed at the ( 58 mathrm{cm} ) mark when a weight of 20 gf is suspended from one end.
11
1277Two blocks each of the mass ( m ) are
attached to the ends of massless rod
which pivots as shown in fig. Initially the rod is held in the horizontal position
and then released. Calculate the net
torque on this system above pivot.
( mathbf{A} cdotleft(m l_{2} g-m l_{1} gright) hat{k} )
B. ( left(m l_{1} g+m l_{2} gright) hat{k} )
( mathbf{c} cdotleft(m l_{1} g-m l_{2} gright) hat{k} )
D. ( -left(m l 1 g+m l_{2} gright) hat{k} )
11
1278an axis passing through the centroid
and perpendicular to plane of the
triangle PQR.
11
1279A uniform disc of radius ( R ) is put over
another uniform disc of radius ( 2 R )
made of same material having same thickness. The peripheries of the two discs touches each other. Locate the
centre of mass of the system taking centre of large disc at origin.
11
1280The maximum value of ( mathbf{V}_{0} ) for which the
disk will roll without slipping is
( ^{4} cdot mu g sqrt{frac{M}{k}} )
( ^{3} cdot mu mathrm{g} sqrt{frac{mathrm{M}}{2 mathrm{k}}} )
( ^{c} cdot operatorname{ag} sqrt{frac{3 M}{k}} )
( mu_{g} sqrt{frac{5 mathrm{M}}{2 mathrm{k}}} )
11
1281Which of the following statements is
not correct regarding conservation laws?
A. A conservation law is a hypothesis based on observations and experiments
B. Conservation laws do not have a deep connection with symmetries of nature.
c. A conservation law cannot be proved
D. Conservation of energy, linear momentum, angular momentum are considered to be fundamental laws of physics
11
1282A windmill is pushed by four external
forces as shown. Calculate force ( F )
required to make to windmill stand still.
( A cdot-2 N )
B. – -4 N
( c cdot-6 N )
D . -16 N
11
1283Masses ( 8 mathrm{kg}, 2 mathrm{kg}, 4 mathrm{kg} & 2 mathrm{kg} ) are placed
at the corners ( P, Q, R & S ) respectively of a square PQRS of side 80cm. The
distance of ( x ) co-ordinate centre of mass
from P will be?
( mathbf{A} cdot 20 mathrm{cm} )
B. 30cm
c. ( 40 mathrm{cm} )
D. ( 60 mathrm{cm} )
11
1284The centre of gravity of the floating ship.
A. Coincides with the metacentre
B. Lies below the metacentre
C. Lies above the metacentre
D. None of the above
11
1285A cylinder is sandwiched between two
planks. Two constant horizontal forces
( F ) and ( 2 F ) are applied on the planks as
shown. If there is no slipping at the top
and bottom of cylinder, then
This question has multiple correct options
A . acceleration of the centre of mass of cylinder is ( frac{21 F}{26 M} )
B. acceleration of the centre of mass of cylinder is ( frac{13 F}{26 M} )
C. acceleration of the top plank is ( frac{F}{2 G M} )
D. acceleration of the top plank is ( frac{F}{13 M} )
11
1286A yo-yo is relased from your hand with the string wrapped around your finger. If you hold your hand still, the
acceleration of the yo-yo is :
A. downward, much greater than g
B. downward, much less than g
c. upward, much less than ( g )
D. upward, much greater thang
11
1287The ratio of moments of inertia of two
solid spheres of same mass but densities in the ratio 1: 8 is:
A . 1: 4
B . 4: 1
c. 2: 1
D. 8: 1
11
1288A disk has rotational inertia ( 1.22 times 10^{-3} )
( mathrm{kg}-mathrm{m}^{2} ) and is attached to an electric drill whose motor delivers a torque of
( 15.8 mathrm{N}-mathrm{m} )
The angular momentum of the disk 33 ms after the motor is turned on is:
A. ( 0.256 mathrm{kg}-mathrm{m}^{2} / mathrm{s} )
B . 1.012 ( mathrm{kg}-mathrm{m}^{2} / mathrm{s} )
c. ( 0.158 mathrm{kg}-mathrm{m}^{2} / mathrm{s} )
D. 0.521 ( mathrm{kg}-mathrm{m}^{2} / mathrm{s} )
11
1289If radius of earth is increased, without
change in its mass, will the length of
day increase, decrease or remain same?
11
1290A thin metal disc of radius ( 25 mathrm{cm} ) and
mass ( 2 mathrm{kg} ) starts from rest and rolls
down on an inclined plane. If its
rotational kinetic energy is ( 8 J ) at the foot of the inclined plane, then the linear velocity of centre of mass of disc is :
A. ( 2 mathrm{m} / mathrm{s} )
в. ( 4 mathrm{m} / mathrm{s} )
c. ( 6 m / s )
D. ( 8 m / s )
11
1291Is it possible to choose ( r, ) so that a is greater than ( frac{boldsymbol{F}}{boldsymbol{M}} ) ? How?11
1292Three particles of masses ( 50 g, 100 g )
and ( 150 g ) are placed at the vertices of
an equilateral triangle of side ( 1 m ) (as
shown in the figure). The ( (x, y) ) coordinates of the centre of mass will
be :
( ^{mathbf{A}} cdotleft(frac{7}{12} m, frac{sqrt{3}}{8} mright) )
B ( cdotleft(frac{sqrt{3}}{4} m, frac{5}{12} mright) )
( ^{mathbf{c}} cdotleft(frac{7}{12} m, frac{sqrt{3}}{4} mright) )
D. ( left(frac{sqrt{3}}{8} m, frac{7}{12} mright) )
11
1293A ball Of ( 0.1 k g ) strikes a wall at right
angle with a speed of ( 6 m / s ) and rebounds along its original path at
( 4 m / s . ) The change in momentum in Newton – sec is-
A ( cdot 10^{3} )
B. ( 10^{2} )
c. 10
D.
11
1294A ball of mass ( m ) is released from ( A )
inside a smooth wedge of mass ( m ) as
shown in the figure. What is the speed
of the wedge when the ball reaches
point ( B ? )
( A )
B ( cdot sqrt{2 g R} )
( c )
D. ( sqrt{frac{3}{2} g R} )
11
1295The moment of inertia of an uniform
axis is 8 units. The moment of inertia
about the axis tangential to one of plane circular faces, i.e., about diameter of the circular base is (length of
cylinder is 3 times it’s radius)
A. 52 units
B. 26 units
c. 104 units
D. 49 units
11
1296Calculate moment of inertia of a ring of mass 500 g and radius ( 0.5 mathrm{m} ) about an axis of rotation coinciding with its diameter and tangent perpendicular to its plane.11
1297Two particles are shown in figure. At
( t=0, ) a constant force ( F=6 N ) starts
acting on the 3 kg mass. Find the velocity of the centre of mass of these
particles at ( t=5 s )
( mathbf{A} cdot 5 m / s )
B. ( 4 m / s )
( mathrm{c} .6 mathrm{m} / mathrm{s} )
D. ( 3 m / s )
11
1298Given solid sphere is in pure rolling on a
rough surface. Pick correct statement(s): (Take ( left.pi=frac{22}{7}right) )
This question has multiple correct options
A. There are two points in sphere having velocity in vertical direction
B. There is no point in sphere having velocity in vertical direction
C . Ratio of distance travelled by A and O is ( frac{14}{11} ) in one
complete round
D. Ratio of distance travelled by A and O is 1 in one complete round
11
1299The moment of inertia of a solid cylinder
about its own axis is the same at its
moment of inertia about an axis
passing through its cenre of gravity and perpendicular to its length. The relation between its length ( L ) and radius ( R ) is
В. ( L=sqrt{3} R )
c. ( L=3 R )
D. ( L=R )
11
1300The position vector of a particle of mass ( boldsymbol{m}=mathbf{6 k g} ) is given as ( overrightarrow{boldsymbol{r}}=left[left(boldsymbol{3} boldsymbol{t}^{2}-boldsymbol{6} boldsymbol{t}right) hat{boldsymbol{i}}+right. )
( left.left(-4 t^{3}right) hat{j}right] ) m. Find
(i) the force ( (vec{F}=m vec{a}) ) acting on the
particle.
(ii) the torque ( (vec{tau}=vec{r} times vec{F}) ) with respect
to the origin, acting on the particle.
(iii) the momentum ( (vec{p}=m vec{v}) ) of the
particle.
(iv) the angular momentum ( (vec{L}=vec{r} times vec{p}) ) of the particle with respect
to the origin.
A ( cdotleft(text { i) }(36 hat{i}-144 t hat{j}) N text { (ii) }left(-288 t^{3}+864 t^{2}right) hat{k} text { (iii) }(36 t-right. )
36)( hat{i}-72 t^{2} hat{j}(text { iv })left(-72 t^{4}+288 t^{3}right) hat{k} )
B . (i) (63 ( i-144 t hat{j}) N ) (ii) ( left(-288 t^{3}+864 t^{2}right) hat{k} ) (iii) ( (36 t- ) 36)( hat{i}-72 t^{2} hat{j}(text { iv })left(-72 t^{4}+288 t^{3}right) hat{k} )
C . (i) (36 ( hat{i}-144 text { tj }) N ) (ii) ( left(-28 t^{3}+84 t^{2}right) hat{k} ) (iii) ( (36 t- ) 36)( hat{i}-72 t^{2} hat{j}(text { iv })left(-72 t^{4}+288 t^{3}right) hat{k} )
D . (i) (36 ( hat{i}-144 t hat{j}) N ) (ii) ( left(-288 t^{3}+864 t^{2}right) hat{k} ) (iii) ( (3 t- ) 6)( hat{i}-72 t^{2} hat{j} ) (iv) ( left(-72 t^{4}+288 t^{3}right) hat{k} )
11
1301The moment of inertia of a disc of
radius ( 0.5 mathrm{m} ) about its geometric axis is ( 2 mathrm{kg}-m^{2} . ) If a string is tied to its circumference and a force of 10 Newton is applied, the value of torque with respect to this axis will be :-
A. 2.5 N-m
B. 5 N-m
( c cdot 10 N-m )
D. 20 N-m
11
1302Which of the following instruments make use of principle of moments
during operation?
A . Ruler
B. Vernier calipers
c. spring balance
D. Simple balance
11
1303The moment of inertia of a sphere of
mass ( M ) and radius ( R ) about an axis passing through its centre is ( frac{2}{5} M R^{2} ) The radius of gyration of the
sphere about a parallel axis tangent to
the sphere is:
A ( cdot frac{7}{5} R )
B. ( frac{3}{5} R )
( ^{C} cdot frac{sqrt{7}}{sqrt{5}} R )
D. ( frac{sqrt{3}}{sqrt{5}} R )
11
1304In which of the following cases of rolling body, translatory and rotational kinetic energies are equal
A. Circular ring
B. Circular plate
c. Solid sphere
D. solid cylinder
11
1305What is the final speed of the sphere’s
centre of mass in ground frame when eventually pure rolling sets in
( A cdot frac{5}{-11} )
7
( v )
B. 2 ( 7^{v} )
( c cdot 7 )
( v )
( v )
( D cdot 7 )
( 2^{v} )
11
1306A wheel is made to roll without slipping,
towards right, by pulling a string
wrapped around a coaxial spool as
shown in figure. With what velocity(in
( mathrm{m} / mathrm{s}) ) the string should be pulled so that
the centre of the wheeel moves with a
velocity of ( 3 mathrm{m} / mathrm{s} ? )
11
1307Two people carry a heavy electric motor
(M) by placing it on a board ( 2.0 mathrm{m} ) long
that weighs 200 N. one person A lifts at one end with a force of ( 400 mathrm{N} ). and the
other ( mathrm{B} ) lifts the opposite end with a force of 600 N. The distance from ( A )
where the centre of gravity of the motor
is located is
( A cdot 1 m )
B. 1.25 m
( c cdot 0.8 m )
D. ( 0.75 mathrm{m} )
11
1308A flywheel is in the form of a uniform circular disc of radius ( 1 mathrm{m} ) and mass 2
kg. The work which must be done on it to increase its frequency of rotation from 5 rev / ( s ) to 10 rev / s is
approximately
A ( cdot 1.5 times 10^{2} J )
B. ( 3.0 times 10^{2} J )
c. ( 1.5 times 10^{3} J )
D. ( 3.0 times 10^{3} J )
11
1309Angular momentum of a system a particles changes, when
A. Force acts on a body
B. Torque acts on a body
C. Direction of velocity changes
D. None of these
11
1310The dimensions of torque are
( mathbf{B} cdotleft[M L^{2} T^{-2}right] )
c. ( left[M^{2} L^{2} T^{-2}right] )
D. ( left[M L T^{-1}right] )
11
1311The centre of mass of system of particles?
A. Coincides with the ca
B. Never Coincides with the CG
c. coincides with the cG in uniform gravitational field
D. None of the above
11
1312Two discs have same mass and
thickness. Their materials are of
densities ( pi_{1} ) and ( pi_{2} . ) The ratio of their
moment of inertia about central axis will be
( mathbf{A} cdot pi_{1}: pi_{2} )
в. ( pi_{1} pi_{2}: ) ।
( mathbf{D} cdot pi_{2}: pi_{1} )
11
1313Two bodies of masses ( m_{1} ) and ( m_{2} ) are
separated by a distance ( R ). The distance
of the centre of mass of the bodies from
the mass ( m_{1} ) is
A ( cdot frac{m_{2} R}{m_{1}+m_{2}} )
В. ( frac{m_{1} R}{m_{1}+m_{2}} )
c. ( frac{m_{1} m_{2}}{m_{1}+m_{2}} R )
D. ( frac{m_{1}+m_{2}}{m_{1}} R )
11
1314A solid sphere is rolling purely on a rough horizontal surface with speed of center ( u=12 mathrm{m} / mathrm{s} ). It collides
inelastically with a smooth vertical wall at a certain moment, with the coefficient of restitution being ( frac{1}{2} . ) How long (in sec) after the collision, does the sphere begin pure rolling? [coefficient of friction between the sphere and the ground is ( frac{mathbf{3}}{mathbf{3 5}} )
11
1315Assertion
A disc rolls without slipping on a horizontal ground with uniform speed has 0 acceleration of lowest point.
Reason
velocity of the lowest point of the same
disc is zero
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
11
1316An ice cube of edge length ( 20 mathrm{cm} ) is
floating in a tank of base area ( 2500 mathrm{cm}^{2} )
filled with water to ( 22 c m ) height. The displacement of centre of mass of whole system (in ( mathrm{cm} ) ), when ice cube melts completely will be
( left(rho_{i c e}=900 k g / m^{3}, rho_{omega}=right. )
( left.mathbf{1 0 0 0 k g} / boldsymbol{m}^{3}, boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{mathbf{2}}right) )
A . 1
в. 1.5
( c cdot 1.32 )
D. 1.44
11
1317Newton’s second law of motion and work
done in rotation of a rigid body can be
expressed as
A. Newton’s law cannot be expressed in rotation, work done in rotation is ( W=tau ) theta
B. Force and work done are expressed as ( tau=I alpha ) and ( W=tau ) theta
c. Force can be expressed as ( tau=I alpha, ) while work done will
be zero
D. Force will be zero, since no net displacement is present
11
1318The linear velocity of a rotating body is given by ( overrightarrow{boldsymbol{v}}=overrightarrow{boldsymbol{omega}} times overrightarrow{boldsymbol{r}}, ) where ( overrightarrow{boldsymbol{omega}} ) is the
angular velocity and ( vec{r} ) is the radius vector. The angular velocity of a body is ( vec{omega}=hat{i}-2 hat{j}+2 hat{k} ) and the radius vector
( vec{r}=4 hat{j}-3 hat{k}, ) then ( |vec{v}| ) is:
B. ( sqrt{31} ) units
c. ( sqrt{37} ) units
D. ( sqrt{41} ) units
11
1319( A 2 mathrm{kg} ) disc of radius ( 0.5 mathrm{m} ) accelerates from rest to 25 rad/s in 5 seconds. The
average power exerted on the disc is
A. 78.1 watts
B. 15.6 Watts
c. 28.1 watts
D. 40.6 watts
11
1320Fill in the blanks with the correct words:
when a body is in translational motion,
all its parts, move (equal/unequal) distances in a given time.
11
1321The COM of body in pure rotation does-
A. translation
B. rotation
D. none of these
11
1322Two thin uniform circular rings each of
radius ( 10 m ) and mass ( 0.1 k g ) are arranged such that they have Common centre and their planes are perpendicular to each other. The M.I. of the system about an axis passing through their common centre and perpendicular to the plane of either of the ring in ( k g m^{-2} ) is:
A. 1.5
в. 4.5
c. 15
D. 18
11
1323A body is moving on a rough horizontal plate in a circular path being tide to a nail (at the centre) by a string, while the body is in motion the friction force of the body
A. changes direction
B. changes magnitude
c. changes both magnitude and direction
D. none of he above
11
1324Assertion
A hollow shaft is found to be stronger
than a solid shaft made of same
material.
Reason
The torque required to produce a given twist in hollow cylinder is greater than
that required to twist a solid cylinder of same size and material.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
1325Three bodies, a ring, a solid cylinder
and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies
are identical. Which of the bodies
reaches the ground with maximum
velocity?
A. The ring body
B. The solid sphere body
c. The solid cylinder body
D. can’t’tind out
11
1326The centre of mass of a uniform thin
hemispherical shell of radius R is located at a distance?
A ( cdot frac{pi R}{2} )
в. ( frac{2 R}{3} )
c. ( frac{R}{2} )
D. ( frac{4 R}{3 pi} )
11
1327A uniform semicircular ring of radius ( boldsymbol{R} )
,and mass ( M ) is rotating about a vertical axis (passing through its circumference mid point) with angular
velocity ( omega ) then its angular momentum is given as ( frac{8 M R^{2}}{11 k} omega ) then the value of ( k ) is
11
1328Assertion
It is harder to open and shut a door if we
apply force near the hinge
Reason
Torque is maximum if force is applied at the hinge of the door
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
1329Due to slipping, points ( \$ A \$ ) and ( \$ B \$ ) on
the rim of the disc have the velocities
shown. Distance between centre of disc
and point on disc which is having zero
velocity.
A . ( 0.04 mathrm{m} )
B. ( 0.05 mathrm{m} )
c. ( 0.06 mathrm{m} )
D. None
11
1330Three identical spheres each of mass 1
kg are placed touching one another with their centres in a straight line. Their
centres are marked as ( A, B, C ) respectively. The distance of centre of
mass of the system from A is.
A ( cdot frac{A B+A C}{2} )
в. ( frac{A B+B C}{2} )
c. ( frac{A C-A B}{3} )
D. ( frac{A B+A C}{3} )
11
1331What are the coordinate of the centre of
mass of the three particles system
shown in figure?
11
1332The net torque on the body is zero that
means the distance between the force
and the rotational axis is zero
A. The first part of the statement is false and other part is true
B. The first part of the statement is false and other part is false too
C. The first part of the statement is true and other part is false
D. The first part of the statement is true and other part is true too
11
1333On the basis of above paragraph, find the relation between angular
momentum and torque:
( mathbf{A} cdot tau Delta theta=J )
в. ( tau=int J d theta )
c. ( int tau cdot d t=J )
D. ( int J cdot d t=tau )
11
1334A dancer is rotating on smooth horizontal floor with an angular
momentum ( L ). The dancer folds her
hands so that her momentof inertia
decreases by ( 25 % ). The new angular momentum is.
A ( cdot frac{3 L}{4} )
в. ( frac{L}{4} )
c. ( frac{L}{2} )
D. ( L )
11
1335A circular arc ( (A B) ) of thin wire frame of radius ( R=sqrt{2} pi mathrm{cm} ) and mass ( M )
makes an angle of ( 90^{circ} ) at the origin.Find the y co-ordinate of the CM. Taking 0 as the origin in ( mathrm{cm} )
11
1336the velocity of the CM of the rod.
A ( cdot frac{5}{7} v_{0} ) at ( tan ^{-1} frac{4}{3} ) below horizontal
B. ( frac{5}{7} v_{0} ) at ( tan ^{-1} frac{3}{4} ) below horizontal
C. ( frac{5}{6} v_{0} ) at ( tan ^{-1} frac{3}{4} ) below horizontal
D. ( frac{5}{6} v_{0} ) at ( tan ^{-1} frac{4}{3} ) below horizontal
11
1337A body of mass m moves in a circular
path with uniform angular velocity. The motion of the body has constant
A. Acceleration
B. Velocity
c. Momentum
D. Kinetic energy
11
1338Solid sphere, hollow sphere, solid cylinder and hollow cylinder of same mass and same radii simultaneously start rolling down from the top of an inclined plane. The body that takes
longest time to reach the bottom is:
A. Solid sphere
B. Hollow sphere
c. solid cylinder
D. Hollow cylinder
11
1339Two brass solid spheres have radiii in the ratio ( 1: 2 . ) About the axis passing through their centres, the ratio of thier moments of inertia of is:
A .1: 4
B. 1: 8
c. 1: 16
D. 1: 32
11
1340Two bodies of mass ( 1 mathrm{kg} ) and ( 3 mathrm{kg} ) have position vectors ( hat{mathbf{i}}+hat{mathbf{2}} boldsymbol{j}+hat{boldsymbol{k}} ) and ( -hat{mathbf{3}} boldsymbol{i}- )
( hat{mathbf{2}} boldsymbol{j}+hat{boldsymbol{k}}, ) respectively. The center of mass of this system has a position vector:
( mathbf{A} cdot-hat{i}+hat{j}+hat{k} )
( mathbf{B} cdot-hat{2} i+hat{2 k} )
c. ( -hat{2} i-hat{j}+hat{k} )
D. ( 2 i-hat{j}-hat{2} k )
11
1341The position of centre of mass of a system consisting of two particles of
masses ( m_{1} ) and ( m_{2} ) separated by a
distance ( L ) apart, from ( m_{1} ) will be
A ( cdot frac{m_{1} L}{m_{1}+m_{2}} )
В. ( frac{m_{2} L}{m_{1}+m_{2}} )
c. ( frac{m_{2}}{m_{1}} L )
D. ( frac{L}{2} )
11
1342A solid sphere of radius ( R ) has moment
of inertia ( I ) about its geometrical axis. If
it is melted into a disc of radius ( r ) and
thickness ( t ). If its moment of inertia
about the tangential axis (which is perpendicular to plane of the disc), is also equal to ( I, ) then the value of ( r ) is
equal to:
A.
B.
c. ( frac{3}{sqrt{15}} R )
( D )
11
1343Assertion
Moment of inertia is always constant.
Reason

Angular moment is conserved that is
why moment of inertia is constant.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect

11
1344A car is moving at a speed of 72 Km/hour. The diameter of its wheels is
( 50 mathrm{cm} . ) If its wheels come to rest after
20 rotations as a result of the
application of brakes, then the angular retardation produced in the car will be
A . -25.5 radians / ( s^{2} )
B. 0.25 radians / ( s^{2} )
C. 2.55 radians / ( s^{2} )
D.
11
1345Difference between mass and weight.11
1346the horizontal and vertical components
of the force exerted on the beam at the
wall
A. Horizontal component is ( 500 N ) towards left and vertical component ( 75 N ) downwards
B. Horizontal component is ( 500 N ) towards right and vertical component ( 75 N ) upwards
C. Horizontal component is ( 625 N ) towards left and vertical component ( 150 N ) upwards
D. Horizontal component is ( 625 N ) towards right and vertical component ( 150 N ) downwards
11
1347Obtain the relation between linear
velocity and angular velocity
11
1348A body of mass 100 g is moving with a velocity of ( 15 mathrm{m} / mathrm{s} ). The momentum associated with the ball will be:
A. ( 0.5 mathrm{kg} mathrm{m} / mathrm{s} )
B. ( 1.5 mathrm{kg} mathrm{m} / mathrm{s} )
c. ( 2.5 mathrm{kg} mathrm{m} / mathrm{s} )
D. 3.2 Ns
11
1349When a bullet is fired from a gun
a) Kinetic Energy of bullet is more than
that of gun
b) acceleration of bullet is more than
that of gun
c) momentum of bullet is more that of
gun
d) velocity of bullet is more than that of
gun
A. only a ( & ) b are true
B. only b & c are true
( mathrm{c} cdot mathrm{a}, mathrm{b} & mathrm{d} ) are true
D. a, b, c & d are true
11
1350Mass of thin long metal rod is ( 2 mathrm{kg} ) and its moment of inertia about an axis
perpendicular to the length of rod and
passing through its one end is ( 0.5 k g m^{2} ) Its radius of gyration is:
( mathbf{A} cdot 20 mathrm{cm} )
B. ( 40 mathrm{cm} )
c. ( 50 mathrm{cm} )
D. ( 1 m )
11
1351Four particles each of mass ( m ) are lying symmetrically on the rim of a disc of mass ( M ) and radius ( R ). The moment of
inertia of this system about an axis passing through one of the particles and perpendicular to the plane of the disc is :
A ( cdot 16 m R^{2} )
в. ( quad(3 M+16 m) frac{R^{2}}{2} )
( mathrm{c} cdot_{(3 m+16 M)} frac{R^{2}}{2} )
D. Zero
11
1352A man is standing on a boat in still water. If he walks towards the shore, the boat will:
A. move away from the shore
B. remain stationary
c. move towards the shore
D. sink
11
1353If a car is moving forward, what is the
direction of the moment of the moment
caused by the rotation of the tires
A. It is heading inwards, i.e. the direction is towards inside of the car
B. It is heading outwards, i.e. the direction is towards outside of the car
c. It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
D. It is heading backward, i.e. the direction is towards back side of the motion of the car
11
1354When we jump out of a boat standing
in water it moves
A. to our sides
B. opposite to our direction
c. in our direction
D. does’t move at all
11
1355A rigid body of mass m rotates with angular velocity ( omega ) about an axis at a
distance a from the centre of mass ( C ).
The radius of gyration about ( C ) is ( K ) Then, kinetic energy of rotation of the body about new parallel axis is :
A ( cdot frac{1}{2} m K^{2} omega^{2} )
B ( cdot frac{1}{2} m a^{2} omega^{2} )
c. ( frac{1}{2} mleft(a+K^{2}right) omega^{2} )
D. ( frac{1}{2} mleft(a^{2}+K^{2}right) omega^{2} )
11
1356( m_{1} ) and diameter ( A O C ) has mass ( m_{2} )
Here, axis passes through mid-point of
diameter and the axis is perpendicular
to plane ( boldsymbol{A B C} )
Here, ( boldsymbol{A O}=boldsymbol{O C}=boldsymbol{R} ). The moment of
inertia of this composite system about
the axis is:
( mathbf{A} cdot frac{m_{1} R^{2}}{2}+frac{m_{2} R^{2}}{3} )
B. ( frac{m_{1} R^{2}}{2}+frac{m_{2} R^{2}}{6} )
( mathrm{c} cdot_{m_{1} R^{2}+} frac{m_{2} R^{2}}{3} )
D ( quad m_{1} R^{2}+frac{m_{2} R^{2}}{12} )
11
1357A quarter disc of radius ( R ) and mass ( m )
is rotating about the axis ( O O^{prime} )
(perpendicular to the plane of the disc)
as shown. Rotational kinetic energy of
the quarter disc is
( A )
в.
c. ( frac{1}{8} m R^{2} omega^{2} )
( D )
11
1358Which of the following statements is/are correct ?
a) The magnitude of the vector ( hat{mathbf{i}}+4 hat{mathbf{j}} ) is
5
b) Force ( (3 hat{mathrm{i}}+4 hat{mathrm{j}}) mathrm{N} ) acting on a particle causes a displacement 6jิm. The work done by the force is 30
c) If ( vec{A} ) and ( vec{B} ) represent two adjacent sides of a parallelogram, then ( |overrightarrow{mathbf{A}} times overrightarrow{mathbf{B}}| ) gives the perimeter of that parallelogram
d) A force has magnitude 20N. Its component in a direction making an angle ( 60^{0} ) with the force is ( 10 sqrt{3} mathrm{N} )
A . a & b are correct
B. a & c are correct
c. a ( & mathrm{d} ) are correct
D. all are wrong
11
1359Assume at ( x=x_{2}, u(x) ) is constant
Slope ( frac{-boldsymbol{d} boldsymbol{u}}{boldsymbol{d} boldsymbol{x}}=mathbf{0} . ) The particle is
displaced slightly from ( x=x_{2} ). Then:
A. particle will return back to ( x_{2} ) after oscillating.
B. particle will move further away from ( x_{2} )
c. particle will stay at ( x_{2} ).
D. particle will come to a point where ( frac{-d u}{d x} ) is maximum
or minimum
11
1360( K ) is the radius of gyration of a thin rod
when it is rotating about an axis perpendicular to the length of the rod and is passing through it’s centre. The length of that rod is :
A . ( 12 K )
в. ( 3 K )
c. ( 2 sqrt{3} K )
D. ( sqrt{3} K )
11
1361A vector ( vec{A} ) points vertically upward and ( vec{B} ) points towards north. The vector product ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}} ) is:
A. null vector
B. along west
c. along east
D. vertically downward
11
1362The torque of force ( overrightarrow{boldsymbol{F}}=mathbf{2} hat{mathbf{i}}-mathbf{3} hat{mathbf{j}}+mathbf{4} hat{boldsymbol{k}} )
newton acting at a point ( vec{r}=3 hat{i}+2 hat{j}+ ) ( 3 hat{k} ) metre about is:
A. ( 6 hat{i}-6 hat{j}+12 hat{k} N-m )
B . ( -6 hat{i}+6 hat{j}-12 hat{k} N-m )
c. ( 17 hat{i}-6 hat{j}-13 hat{k} N-m )
D. ( -17 hat{i}+6 hat{j}+13 hat{k} N-m )
11
1363A solid cylinder rolls without slipping on
an inclined plane inclined at an angle ( theta ) Find the linear acceleration of the
cylinder. Mass of the cylinder is ( M )
A ( cdot a=frac{1}{3} g sin theta )
B. ( a=frac{2}{3} g sin theta )
c. ( _{a=frac{1}{3}} g cos theta )
D. ( a=frac{2}{3} g cos theta )
11
1364The number of vectors of unit length perpendicular to vectors ( overline{boldsymbol{a}}=(mathbf{1}, mathbf{1}, mathbf{0}) & )
( bar{b}=(0,1,1) ) is:
( A )
B. 2
( c cdot 3 )
D. ( infty )
11
1365A uniform thin bar of mass ( 6 mathrm{m} ) and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of a hexagon is
A ( .20 m L^{2} )
( mathbf{B} cdot 6 m L^{2} )
c. ( frac{12}{5} m L^{2} )
D. ( 30 m L^{2} )
11
1366Match column I and column II11
1367A couple produces motion in a straight line.
A. True
B. False
11
1368and ( m_{3} ) are connected to the ends of a
mass-less rod of length ( L ) which lies at rest on a smooth horizontal plane. At
( t=0, ) an explosion occurs between ( m_{2} )
and ( m_{3}, ) and as a result, mass ( m_{3} ) is
detached from the rod, and moves with
a known velocity ( v ) at an angle of ( 30^{circ} )
with the y-axis. Assume that the
masses ( m_{2} ) and ( m_{3} ) are unchanged
during the explosion.

What is the velocity of the centre of
mass of the system consisting of three masses after the expulsion?
A ( cdot frac{v}{4}(hat{i}-3 hat{j}) )
B ( cdot frac{v}{4}(-hat{i}+sqrt{3} hat{j}) )
c. ( -v )
D. none of the above

11
1369A force of magnitude 6 in the direction of the vector ( vec{i}-2 vec{j}+2 vec{k} ) acts at the point whose position vector is ( vec{i}-vec{j} ). ( A )
second force acting at the point with position vector ( vec{j}-vec{k} ) forms a couple
with the first force. Find the vector
moment of the couple.
( mathbf{A} cdot-(2 vec{i}+vec{j}) )
B . ( -2(2 vec{i}+vec{j}) )
c. ( -4(2 vec{i}+vec{j}) )
D. ( -8(2 vec{i}+vec{j}) )
11
1370(i) On what factor does the position of the centre of gravity of a body depend?
(ii) What is the S.l.unit of the moment
of force?
11
1371Two discs of equal mass but different diameter are connected with an axle
system that allows them to roll down an
incline together. Both discs start and
finish at the same time. Find out which
of the following statement is true?
A. Their tangential velocity is the same
B. Their tangential acceleration is the same
c. Their angular velocity is the same
D. Their angular displacement is the same
E. Their angular acceleration is the same
11
1372All particles are situated at a distance
( R ) from the origin. The distance of centre
of mass of the body from the origin will
be
A. More than ( R )
B. Less than ( R )
c. Equal to ( R )
D. At the origin
11
1373Three rings each of mass ( m ) kg and
radius ( a ) are arranged as shown in the
figure. The moment of inertia of the arrangement about ( x-x^{prime} ) axis will be
A ( cdot frac{3}{2} m a^{2} )
B.
( c )
D. ( frac{2}{5} m a^{2} )
11
1374Three objects, A:(a solid sphere), B: (a thin circular disk) and ( mathrm{C} ) : ( (mathrm{a} ) circular
ring ( ), ) each have the same mass ( mathrm{M} ) and radius R. They all spin with the same angular speed ( omega ) about their own
symmetry axes. The amounts of work
(W) required to bring them to rest, would satisfy the relation.
A ( cdot W_{B}>W_{A}>W_{C} )
в. ( W_{C}>W_{B}>W_{A} )
c. ( w_{A}>W_{C}>W_{B} )
D. ( W_{A}>W_{B}>W_{C} )
11
1375A square plate of edge ( a / 2 ) is cut out
from a uniform square plate of edge ( ^{prime} a^{prime} ) as shown in figure. The mass of the
remaining portion is ( M . ) The moment of inertia of the shaded portion about an axis passing through’ ( O^{prime} ) (center of the square of side a) and perpendicular to
plane of the plate is:
( ^{A} cdot frac{9}{64} M a^{2} )
в. ( frac{3}{16} M a^{2} )
c. ( frac{5}{12} M a^{2} )
D. ( frac{M a^{2}}{6} )
11
1376When a spinning top slows down, it begins to wobble. This phenomenon can be explained by
A. gyroscopic precession
B. inertia of motion
c. force of gravity
D. more complicated types of motion are coming into play
11
1377Particles of masses ( boldsymbol{m}, boldsymbol{2 m}, boldsymbol{3} boldsymbol{m}, ldots(boldsymbol{n}) boldsymbol{m} )
grams are placed on the same line at distances ( l, 2 l, 3 l, dots(n) l ) cm from a fixed point. The distance of the centre of mass of the particles from the fixed
point in centimetres is:
A ( cdot frac{(2 n+1) l}{3} )
в. ( frac{l}{n+1} )
c. ( frac{nleft(n^{2}+1right) l}{2} )
D. ( frac{2 l}{nleft(n^{2}+1right)} )
11
1378If the length of the second’s hand in a stop-clock is ( 3 mathrm{cm} ) angular velocity linear velocity of the tip is:
A ( cdot 0.2047 r a d s^{-1}, 0.0314 m s^{-1} )
B. 0.2547 rads ( ^{-1}, 0.0314 mathrm{ms}^{-1} )
c. ( 0.10472 r a d s^{-1}, 0.06314 m s^{-1} )
D. 0.1047 rads ( ^{-1}, 0.00314 mathrm{ms}^{-1} )
11
1379On a stationary sail boat, air is blown at
the sails from a fan attached to the
boat. The boat will
A. remain at rest
B. spin round
c. move in the direction in which air is blown
D. move in a direction opposite to that in which air is blown
11
1380A common example of precession is
( A cdot a ) spinning top
B. a ball bearing
C. a ball rolling down an inclined plane
D. a ball sliding down an inclined plane
11
1381The moment o inertia of a circular disc
of radius ( 2 m ) and mass ( 1 k g ) about an
axis passing through the center of
mass but perpendicular to the plane of
the disc is ( 2 k g-m^{2} . ) Its moment of
inertia about an axis parallel to this
axis but passing through the edge of
the disc is (see the given figure.)
( mathbf{A} cdot 8 k g-m^{2} )
( mathbf{B} cdot 4 k g-m^{2} )
( mathbf{c} cdot 10 k g-m^{2} )
( mathbf{D} cdot 6 k g-m^{2} )
11
1382If is the angular momentum is ( L ) and ( I ) is the moment of inertia of a rotating body, then ( frac{L^{2}}{2 I} ) represents its
A. rotational PE
B. total energy
c. rotational KE
D. translation KE
11
1383A (trolley+child) of total mass ( 200 k g ) is moving at a uniform speed of ( 36 k m / h ) on a frictionless track. The child of
mass ( 20 k g ) starts running on the trolley from one end to the other ( (10 m ) away)
with a speed of ( 10 m s^{-1} ) relative to the
trolley in the direction of the trolley’s motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the
child begins to run and just before
jump?
11
1384A rigid body is a body in which
A. the distance between any two given points remains constant till an external forces exerted on it.
B. the distance between any two given points changes with time regardless of external forces exerted on it.
C. the distance between any two given points remains constant in time regardless of external forces exerted on it.
D. the distance between any two given points changes with time until external forces exerted on it.
11
1385In the figure shown, the spherical body
and block, each have a mass ( m ). The
moment of inertia of the spherical body
about centre of mass is ( 2 m R^{2} . ) The
spherical body rolls without slipping on the horizontal surface. The ratio of
kinetic energy of the spherical body to that of block is:
( A cdot frac{1}{3} )
B. ( frac{1}{2} )
( c cdot frac{2}{3} )
( D )
11
1386Which one of the following statements
İS wrong?
A. Direction of torque is parallel to axis of rotation
B. Direction of moment of couple is perpendicular to the plane of rotation of body
C. Torque vector is perpendicular to both position vector and force vector
D. The direction of force vector is always perpendicular to the directions of both position vector and torque vector
11
1387A wheel is rotating at 1800 rpm about its own axis. When the power is switched oft it comes to rest in 2 min.
Then, the angular retardation in rad ( s^{-1} )
is
( mathbf{A} cdot 2 pi )
в. ( pi )
c. ( pi / 2 )
D . ( pi / 4 )
E . ( pi / 6 )
11
1388Where should be the centre of gravity of a body?
A. It must lie within the body
B. It may be near but not essentially within the body
c. It changes its position from time to time
D. It must be outside the body
11
1389A vector ( bar{P}_{1} ) is along the positive ( x ) – axis.
If its cross product with another vector
( bar{P}_{2} ) is zero, then ( bar{P}_{2} ) could be:
( A cdot 4 hat{j} )
в. ( -4 hat{i} )
c. ( (hat{i}+hat{k}) )
D. ( -(hat{i}+hat{j}) )
11
1390A body A of mass M falling vertically downwards under gravity breaks into two part; a body ( B ) of mass ( frac{M}{3} ) and ( a ) body ( C ) of mass ( frac{2}{3} ) M. The COM of bodies B and ( C ) taken together shifts compared to that of body A towards:
A. depends on height of breaking
B. does not shift.
( c . ) body c.
D. body B
11
1391When disc B is brought in contact with
disc ( A, ) they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is:
A ( cdot frac{2 I omega}{3 t} )
B. ( frac{9 text { I }}{text { ? }} )
c. ( frac{9 mathrm{Ic}}{4 mathrm{t}} )
( D cdot frac{31}{2 t} )
11
1392Assertion
(A): When a solid Copper sphere and solid Wooden sphere, both having the same mass, are pinning about their own axis with same
angular velocity, then the wooden sphere has greater angular momentum.
Reason (R): Wood is less denser than
Copper. So radius of Wooden sphere is
more than that of Copper and so greater
moment of inertia.
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
c. ( A ) is true and ( R ) is false
D. A is false and R is true
11
1393Mr. Verma (50 ( K g ) ) and Mr. Mathur ( (60 K g) ) are sitting at the two extremes
of a ( 4 m ) long boat ( (40 K g) ) standing still in water. To discuss a mechanics
problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move in the water
during the process:
A ( .40 / 3 c m )
в. ( 20 / 3 ) ст
c. ( 10 / 3 c m )
D. ( 10 mathrm{cm} )
11
1394Consider a rectangular plate of
dimensions ( a times b ). If the plate is
considered to be made up of four rectangles of dimensions ( frac{a}{2} times frac{b}{2} ) and we
now remove one out of the four
rectangles, find the position where the
centre of mass of the remaining
system will be:
11
1395If two vectors are ( vec{A}=2 hat{i}+hat{j}-hat{k} ) and ( vec{B}=hat{j}-4 hat{k} cdot vec{A} times vec{B} ) is perpendicular to
This question has multiple correct options
A . ( vec{A} )
в. ( vec{B} )
c. ( vec{A}+vec{B} )
D . ( vec{A}-vec{B} )
11
1396A nucleus (mass no. 238) initially at rest decay into another nucleus (mass
no. 234 ) emitting an ( alpha ) particle (mass
no. 4 ) with the speed of ( 1.17 times ) ( 10^{7} m / )sec Find the recoil speed of the
remaining nucleus.
11
1397The area of a triangle formed with sides ( mathbf{5} hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}-hat{boldsymbol{k}} ) and ( mathbf{3} hat{mathbf{i}}+mathbf{2} hat{mathbf{j}}-hat{boldsymbol{k}} ) is:
A ( cdot sqrt{6} )
B. ( sqrt{3} )
( c cdot sqrt{frac{3}{2}} )
D. ( sqrt{frac{5}{2}} )
11
1398In figure the cylinder of mass ( 10 k g ) and
radius ( 10 mathrm{cm} ) has a tape wrapped round
¡t. The pulley weighs ( 100 N ) and has a
radius ( 5 c m . ) When the system is
released, the ( 5 k g ) mass comes down
and the cylinder rolls without slipping.
Calculate the acceleration and velocity of the mass as a function of time.
11
1399Four thin metal rods, each of mass ( M )
and length ( L, ) are welded to form a
square. The moment of inertia of the
composite structure about a line which bisects any two opposite rods is:
( ^{mathrm{A}} cdot frac{M L^{2}}{6} )
B. ( frac{M L^{2}}{3} )
c. ( frac{M L^{2}}{2} )
D. ( frac{2 M L^{2}}{3} )
11
1400Centre of gravity of the circular ring will
be:
A. At the periphery
B. At the center
c. outside it
D. None
11
1401( frac{w}{L} )11
1402Consider a ring performing pure rolling when on a fixed rough surface. There is
a point ‘A’ marked on the circumference of it. If velocity of centre of ring is uniform, then this point will move in cycloidal path as shown. Now, if the ring is performing pure rolling with uniform acceleration what will be the
path followed by this point?
A. increasing size of cycloid
B. decreasing size of cycloid
c. It will depend on direction of acceleration whether it is in the direction of velocity of centre or opposite.
D. No change in path will occur
11
1403ILLUSTRATION 9.24 A cylindrical drum, pushed along by a
board rolls forward on the ground. There is no slipping at any
contact. Find the distance moved by
the man who is pushing the board,
when axis of the cylinder covers a
distance L.
11
1404At which point is the centre of gravity
situated in: A circular lamina.
A. At the centre of radius
B. At the centre of semi circular lamina
c. At the centre of circular lamina
D. can not say
11
1405Four particles each of mass ‘ ( m^{prime} ) are
placed at the corners of a square of side
( L^{prime prime} . ) The radius of gyration of the system
about an axis normal to the square and
passing through its centre.
A ( cdot frac{L}{2} )
в. ( frac{L}{sqrt{2}} )
( c . L )
( D . sqrt{2} L )
11
1406A circular ring starts rolling down on an inclined plane from its top. Let ( boldsymbol{V} ) be velocity of its centre of mass on
reaching the bottom of inclined plane. If a block starts sliding down on an identical inclined plane but smooth, from its top, then the velocity of block
on reaching the bottom of
inclined plane is:
( mathbf{A} cdot frac{V}{2} )
B. ( 2 V )
c. ( frac{V}{sqrt{2}} )
D. ( sqrt{2} V )
11
1407A solid sphere is rolling down an
inclined plane without slipping. If the inclined plane has inclination ( theta ) with the
horizontal, then the coefficient of
friction ( mu ) between the sphere and the
inclined plane should be
A ( cdot mu geq 2 / 7 cot theta )
B. ( mu geq 2 / 7 tan theta )
c. ( mu geq 2 / 7 cos theta )
D. ( mu geq 4 / 7 sin theta )
11
1408Two planets have radii ( r_{1} ) and ( r_{2} ) and
their densities are ( rho_{1} ) and ( rho_{2} )
respectively. The ratio of acceleration due to gravity on them will be.
A ( cdot r_{1} rho_{1}: r_{2} rho_{2} )
B ( cdot r_{1} rho_{1}^{2}: r_{2} rho_{2}^{2} )
( mathbf{c} cdot r_{1}^{2} rho_{1}: r_{2}^{2} rho_{2} )
D ( cdot r_{1} rho_{2}: r_{2} rho_{1} )
11
1409In twenty minutes, the angular displacement of the minute hand of a
wrist watch is
A ( cdot frac{pi}{90} r a d )
в. ( frac{pi}{30} r a d )
D. ( frac{2 pi}{3} r a d )
11
1410Center of gravity of an object depends on its which of the following? This question has multiple correct options
A . Mass
c. shape
D. weight
11
1411Two discs of the same material and
thickness have radii ( 0.2 m ) and ( 0.6 m )
Their moments of inertia about their
axes will be in the ratio
A . 1: 81
B. 1: 27
( c cdot 1: 9 )
D. 1: 3
11
1412Assertion
Many great rivers flow towards the equator. The sediments that they carry
increase the time of rotation of the
Reason
The angular momentum of the earth about its rotation axis is conserved.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
1413A bullet of mass ( 10 g ) and speed
( 500 m / s ) is fired into a door and gets embedded exactly at the center of the door. The door is ( 1.0 m ) wide and weighs ( 12 k g . ) It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds
into it.
11
1414A cubical block of mass ( m ) and side ( L )
rests on a rough horizontal surface with
coefficient of friction ( mu . ) A horizontal
force ( boldsymbol{F} ) is applied on the block as shown in the figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is:
( A cdot frac{m g}{4} )
B. ( frac{m g}{8} )
( c cdot frac{m g}{2} )
D. ( m g(1-mu) )
11
1415A uniform sphere of radius ( boldsymbol{R} ) is placed on a smooth horizontal surface and a
horizontal force ( boldsymbol{F} ) is applied on it at a
distance ( h ) above the centre. The
acceleration of the centre of mass of the
sphere is
A. maximum when ( h=0 )
B. maximum when ( h= ) R
c. maximum when ( h=R / 2 )
D. independent of ( h )
11
1416A student is rotating on a stool at an
angular velocity ( ^{prime} omega^{prime} ) with their arms outstretched while holding a pair of
masses. The frictional effects of the
stool are negligible. Which of the following actions would
result in a change in angular momentum for the student?
A. A clockwise torque of ( 50 mathrm{Nm} ) and a counterclockwise torque of ( 25 mathrm{Nm} ) are both applied to the students arms by fellow students
B. The student brings the masses closer to their body
c. The student stretches the masses further away from their body
D. A second student steps onto the stool with the first student
E. A clockwise torque of ( 50 mathrm{Nm} ) and a counterclockwis torque of ( 50 mathrm{Nm} ) are both applied to the students arms
by fellow students
11
1417Assertion
The centre of mass of a body may lie where there is no mass
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
1418What is torque?11
1419A rod of mass ( m ) and length ( 2 R ) is fixed
along the diameter of a ring of same
mass ( m ) and radius ( R ) as shown in
figure.The combined body is rolling without slipping along ( x ) -axis. Find the
11
1420A thin uniform square lamina of side ( a )
is placed in the ( X Y ) plane with its sides
parallel to ( X ) and ( Y ) axes and with its
centre coinciding with the origin. Its moment of inertia about an axis
passing through a point on the ( Y ) axis at
a distance ( y=2 a ) and parallel to ( X )
axis is equal to its moment of inertia
about an axis passing through a point on the ( X ) axis at a distance ( x=d ) and
perpendicular to ( X Y ) plane. The value of
( boldsymbol{d} ) is:
A ( cdot frac{7}{3} a )
B. ( sqrt{frac{47}{12}} a )
c. ( frac{9}{5} a )
D. ( sqrt{frac{51}{12}} a )
11
1421The moment of a force about a given axis depends:
A. only on the magnitude of force
B. only on the perpendicular distance of force from the axis
c. neither on the force nor on the perpendicular distance of force from the axis
D. both on the force and its perpendicular distance from the axis
11
1422A fly wheel of moment of inertia lis rotating at n revolutions per sec. The work needed to double the frequency would be –
( mathbf{A} cdot 2 pi^{2} I n^{2} )
В. ( 4 pi^{2} I n^{2} )
( mathbf{c} cdot 6 pi^{2} I N^{2} )
D. ( 8 pi^{2} I n^{2} )
11
1423A solid cylinder ( C ) and a hollow pipe ( P ) of same diameter are in contact when they
are released from rest as shown in the
figure on a long incline plane. Cylinder ( C ) and pipe ( P ) roll without slipping. Determine the clear gap (in ( mathrm{m} ) ) between them after ( 2 sqrt{3} ) seconds.
11
1424A solid sphere of mass ( mathrm{M} & ) radius ( mathrm{R} ) is divided in two parts of masses ( frac{7 M}{8} & ) ( frac{M}{8}, ) and converted to a disc of radius ( 2 mathrm{R} )
& solid sphere of radius ‘r’ resp. Find ( frac{l_{1}}{l_{2}} )
if ( l_{1} & l_{2} ) are moment of inertia of disc
& solid sphere respectively.
A . 200
в. 140
( c cdot 120 )
D. 180
11
1425A solid sphere of mass ( M, ) radius ( R ) and
having moment of inertia about an axis passing through the centre of mass as
( I, ) is recast into a disc of thickness ( t )
whose moment of inertia about an axis
passing through its edge and perpendicular to its plane remains ( boldsymbol{I} ) Then, radius of the disc will be:
A ( cdot frac{2 mathrm{R}}{sqrt{15}} )
B ( cdot R sqrt{frac{2}{15}} )
c. ( frac{4 mathrm{R}}{sqrt{15}} )
D. ( sqrt{frac{2 R}{15}} )
11
1426A cracker at res