# Work, Energy And Power Questions

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

Question NoQuestionsClass
1A block of mass ( m ) is connected to a
spring of force constant ( k . ) Initially the block is at rest and the spring has natural length. A constant force ( boldsymbol{F} ) is applied horizontally towards right. The maximum speed of the block will be (there is no friction between block and
the surface)
A ( cdot frac{F}{sqrt{2 m k}} )
B. ( frac{F}{sqrt{m k}} )
c. ( frac{sqrt{2} F}{sqrt{m k}} )
D. ( frac{2 F}{sqrt{m k}} )
11
2A body rolling down a hill has:
A. K.E. only
B. P.E. only
C. neither K.E. nor P.E.
D. both K.E. and P.E
11
342. If the total mechanical energy of the particle is -40 J, then
it can be found in region
a. x 15
b. -10<x<-5 and 6 <x< 15
c. 10<x< 15
d. It is not possible.
11
412. A system consists of two identical cubes, each of mass
3 kg, linked together by a compressed weightless spring of
force constant 1000 Nm. The cubes are also connected
by a thread which is burnt at a certain moment. At what
minimum value of initial compression xo (in cm) of the
spring will the lower cube bounce up after the thread is
burnt through?
3 kg
&k=1000 Nm
3 kg
Fig. 8.306
11
5A bullet of mass ( 20 mathrm{g} ) travelling horizontally with a speed of ( 500 mathrm{m} / mathrm{s} )
passes through a wooden block of mass
10.0kg initially at rest on a surface. The bullet emerges with a speed of ( 100 mathrm{m} / mathrm{s} )
and the block slides ( 20 mathrm{cm} ) on the
surface before coming to rest, the coefficient of friction between the block
and the surface. ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
A . 0.16
B. 0.8
c. 0.32
D. 0.24
11
6Read the assertion and reason carefully to mark the correct option out of the
options given below:

Assertion: An astronaut in a satellite
feels weightlessness.
Reason: As observed by another
astronauts in the same satellite, force
of gravity and centrifugal force balance
each other.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
C. If assertion is true but reason is false
D. If assertion is false but reason is true

11
7A solid cylinder of mass 2 Kg and radius
( 0.2 mathrm{m} ) is rotating about its own
axis without friction with angular
velocity 3 rad/s. A particle of mass 0.5
Kg and moving with a velocity of ( 5 mathrm{m} / mathrm{s} ) strikes the cylinder and sticks to it as
shown in. The angular momentum of the
cylinder before collision will be
A. 0.12 Joule/s
B. 12 Joule/s
c. 1.2 Joule/s
D. 1.12 Joule/s
11
8The angular momentum of an electron in the hydrogen atom is ( frac{3 h}{2 pi} ). Here h is Planck’s constant. The kinetic energy of
this electron is:
A . 4.53 ev
B. 1.51 eV
c. 3.4 ev
D. 6.8 ev
11
9Illustration 8.59 An elevator of mass M with a per
mass m is moving upward with uniform velocity v. What is
the power delivered by the elevator?
Fig. 8.161
11
10When the bob of a simple pendulum swings, the work done by tension in the string is?
( mathbf{A} cdot>0 )
B . ( <0 )
c. zero
D. maximum
11
11Calculate the forces ( F(y) ) associated with the following one-dimensional
potential energies:
(a) ( U=-omega y )
(b) ( U=a y^{3}-b y^{2} )
( (c) U=U_{0} sin beta gamma )
11
12The block of mass ( M ) moving on the
frictionless horizontal surface collides
with the spring of spring constant ( boldsymbol{K} )
and compresses it by length ( L ). The maximum moment of the block after
collision is
A ( cdot sqrt{M K} L )
в. ( frac{K L^{2}}{2 M} )
c. zero
D. ( frac{M L^{2}}{K} )
11
13Force constants of two wires ( A ) and ( B ) of
the same material are ( K ) and ( 2 K )
respectively. If two wires are stretched equally, then the ratio of work done in stretching ( left(frac{W_{A}}{W_{B}}right) ) is:
A ( cdot frac{1}{2} )
B. ( frac{3}{2} )
( c cdot frac{1}{4} )
D.
11
14determine the total work done on the
block
A . 12.45
B . 24.9
c. 49.8
D. 99.6
11
15On a friction less surface, a ball of mass
( m ) moving at a speed ( v ) makes a headon collision with an identical ball at
rest. The kinetic energy of the balls after the collision is ( frac{3}{4} t h ) of the original. Find the coefficient of restitution?
A ( frac{1}{sqrt{2}} )
в. ( frac{1}{sqrt{3}} )
c. ( frac{3}{sqrt{2}} )
D. ( frac{1}{sqrt{5}} )
11
16A particle falls from a height ‘ ( h^{prime} ) upon a
fixed horizontal plane and rebounds. If
( e^{prime} ) is the coefficient of restitution, the
total distance travelled before it comes
to rest is
( ^{text {A }} ). ( hleft(frac{1+e^{2}}{1-e^{2}}right) )
c. ( frac{H}{2}left(frac{1-e^{2}}{1+e^{2}}right) )
D. ( frac{H}{2}left(frac{1+e^{2}}{1-e^{2}}right) )
11
17The displacement of ( m^{prime} ) on ( M ) is
A ( .0 .3 m )
в. ( 0.2 m )
c. ( 0.98 m )
D. ( 0.1 m )
11
18A ball collides with a smooth and fixed
inclined plane of inclination ( boldsymbol{theta} ) after falling vertically through a distance h. If it moves horizontally just after impact, the coefficient of restitution is
( mathbf{A} cdot tan ^{2} theta )
B ( cdot cot ^{2} theta )
( c . tan theta )
D. ( cot theta )
11
19Impulse of force is
A. Product of average force and time
B. Division of average force and time
C. Integration of average force and time
D. All of the above
11
20The potential energy of a rocket of mass ( 100 k g ) at height ( 10^{7} m ) from earth surface is ( 4 times 10^{9} ) Joule. The weight of
the rocket at height ( 10^{9} ) will be
( mathbf{A} cdot 4 times 10^{-2} N )
В . ( 4 times 10^{-3} N )
c. ( 8 times 10^{-2} N )
D. ( 8 times 10^{-3} N )
11
21Moon is a satellite of the Earth, but
weightlessness is not experienced at the surface of the Moon because
A. its distance from the Earth is more
B. it is a natural satellite
c. its size is big but density is very low.
D. its own mass is more
11
22A constant horizontal ( 4.0 N ) force acts
on a ( 300 g ) cart on a horizontal track as
the cart moves through a distance of ( 43.0 mathrm{cm} . ) The cart decelerates as a
result.
What was the work performed on the cart by the force?
в. ( -1.27 J )
c. ( 1.27 J )
D. ( 1.72 J )
E. None of the above
11
23Find the angle between ( vec{a}+vec{b}+vec{c} ) and ( vec{a}+vec{b}-vec{c} )
A ( cdot cos ^{-1}left(frac{8}{sqrt{57}}right) )
B. ( cos ^{-1}left(frac{9}{sqrt{75}}right) )
( ^{mathbf{C}} cdot cos ^{-1}left(frac{1}{sqrt{2}}right) )
D. ( cos ^{-1}left(frac{-7}{sqrt{85}}right) )
11
24Work done by the gravitational force on
a body of mass ( m ) moving on a smooth
horizontal surface through a distance
is: (Given acceleration due to gravity =
( boldsymbol{g}) )
A . ( m g s )
B. ( -m g s )
c. 0
D. ( 2 m g s )
11
25Two particles of mass ( m_{1} ) and ( m_{2} ) in projectile motion have velocities ( vec{v}_{1}< )
( vec{v}_{2} ) respectively at tine ( t=0 . ) They collide at time ( t_{0} . ) Their velocities become ( overrightarrow{v_{1}^{prime}} ) and ( vec{v}_{2}^{prime} ) at time ( 2 t_{0^{prime}} ) while still moving in
air. The value of
( left|left(m_{1} vec{v}_{1}^{prime}+m_{2} overrightarrow{v_{2}^{prime}}right)-left(m_{1} vec{v}_{1}+m_{2} vec{v}_{2}right)right| )
11
26A trolley is under the action of a
constant force ( F ). The sand contained by
it is poured out through a hole in the
floor at the rate of ( m ) per second.lf initial
mass of sand and trolley was ( M ) and
initial speed was ( u, ) the acceleration of
trolley at time ( t ) is given by
( A )
в.
c. ( frac{F}{M-m} )
D. ( frac{F}{M+m} )
11
27Identify the wrong statement.
A. ( A ) body can have momentum without energy
B. A body can have energy without momentum.
C. The momentum can conserved in an elastic collision.
D. Kinetic energy is not conserved in an inelastic collision
11
28What is the angle between two vector forces of equal magnitude such that their resultant is one-third of either of
the original forces?
( ^{mathbf{A}} cdot cos ^{-1}left(-frac{17}{18}right) )
B. ( cos ^{-1}left(-frac{1}{3}right) )
( c cdot 45^{circ} )
D. ( 120^{circ} )
11
29A car is being driven at a constant speed of ( 5 m / s ) by a force of ( 3 times 10^{8} N )
It takes 2 minutes to reach its
destination. What is the work done?
A ( .15 times 10^{8} J )
B . ( 18 times 10^{10} J )
c. ( 6 times 10^{10} J )
D . ( 10 times 10^{8} J )
11
3030. The system shown in Fig. 8.232 is released from rest with
mass 2 kg in contact with the ground, Pulley and spring
are massless, and friction is absent everywhere. The speed
of 5 kg block when 2 kg block leaves the contact with the
ground is (force constant of the spring k 40 Nm and
8 = 10 ms?)
5 kg
12 kg
a. 2 ms-
c. 2 ms!
Fig. 8.232
b. 2/2 ms.
d. 2 ms’
atende on weighing balance working
11
31It is well known that a raindrop or a small pebble falls under the influence of the downward gravitational force and the opposing resistive force. The resistive force is known to be
proportional to the speed of the drop. Consider a drop or small pebble of 1 g falling (from rest) from a diff of height ( 1.00 mathrm{km} . ) It hits the ground with a speed
of ( 50.0 mathrm{m} s^{-1} . ) What is the work done by
the unknown resistive force?
11
32A metal ball falls from a height 1 m on a
steel plate and jumps up to a height of
( 0.81 m . ) Find the coefficient of
restitution
11
33A block of mass ( m=0.1 mathrm{kg} ) is released from a height of ( 4 mathrm{m} ) on a curved smooth surface. On the horizontal surface, path
AB is smooth and path BC offers
coefficient of friction ( mu=0.1 . ) If the impact of block with the vertical wall at
C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be :
( left(operatorname{take} g=10 m / s^{2}right) )
A. ( 29 mathrm{m} )
B. 49 ( mathrm{m} )
c. ( 59 mathrm{m} )
D. ( 109 mathrm{m} )
11
34A sphere of mass ( m ) moving with constant velocity hits another sphere of
same mass at rest. If ( e ) is the coefficient
of restitution. The ratio of their
velocities after collision is :
( mathbf{A} cdot 1+e )
B. ( frac{1+e}{2} )
( c cdot frac{1+2 e}{1-2 e} )
D. ( frac{1-e}{1+e} )
11
35A uniform chain of length ( pi r ) lies inside
a smooth semicircular tube ( A B ) of
radius ( r . ) Assuming a slightly
disturbance to start the chain in
motion, the velocity with which it will
emerge from the end ( mathrm{B} ) of tube will be:
( sqrt[A cdot]{g rleft(1+frac{2}{pi}right)} )
B. ( sqrt{2 g rleft(frac{2}{pi}+frac{pi}{2}right)} )
c. ( sqrt{g r(pi+2)} )
D. ( sqrt{pi g r} )
11
36( mathbf{A} )
300 pound fullback carrying the football towards the goal line encounters a 150 pound defensive back
near the goal line. The two are moving at the same speed when they both leave their feet and collide head-on in mid-air.
The defensive back goes flying backward, and the fullback continues
forward, scoring a touchdown. As a result of the collision. How do the
player’s changes in momentum compare?
A. The amount of the defensive back’s momentum changes is twice as much as the fullback’s
B. The amount of the fullback’s momentum changes is twice as much as the back’s
c. The amount of the defensive back’s momentum changes is more than twice as much as the fullback’s
D. The amount of the fullback’s momentum change is more than twice as much as the fullback’s
E. The amount of momentum change for each player is the same
11
37Two balls shown in figure are identical Ball ( A ) is moving towards right with a
speed ( v ) and the second ball is at rest. Assume all collisions to be elastic.

Show that the speed of the balls remain unchanged after all the collisions have takes place (Assume frictionless surface)

11
38What is the gravitational potential energy of the mass ( m ? )
( ^{mathbf{A}} cdot frac{2}{sqrt{3}} frac{G M m}{l}(1-2 sqrt{3}) )
B. ( -frac{2}{sqrt{3}} frac{G M m}{l}(1+2 sqrt{3}) )
( ^{mathbf{c}}-frac{sqrt{3}}{2} frac{G M m}{l}(1-2 sqrt{3}) )
D. ( -frac{sqrt{3}}{2} frac{G M m}{l}(1+2 sqrt{3}) )
11
39If ( g ) is acceleration due to gravity on the
earth’s surface, the gain in the potential energy of an object of mass ( m ) raised from the surface of the earth to a height equal to the radius ( R ) of the earth is:
A. ( 2 m g R )
в. ( m g R )
c. ( frac{m g R}{4} )
D. ( frac{m g R}{2} )
11
40Energy stored in a stretched spring is gravitational potential energy.
A. True
B. False
c. Ambiguous
D. Data insufficient
11
41Assertion
In an elastic collision of two bodies, the momentum and energy of the system are conserved.
Reason
If two bodies stick to each other, after
colliding, the collision is said to be perfectly inelastic.
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
4217. The velocity-time graph of a particle moving in a straight
line is shown in Fig. 8.227. The mass of the particle is 2
kg. Work done by all the forces acting on the particle in
time interval between t=0 to t = 10 s is
v(ms)
10
10
Fig. 8.227
b. -300 J C. 400 J
a. 300 J
d. – 400 J
A
..
.
.1
11
43Assertion
Displacement ( (S) ) -time
(t) graph of a
particle moving in a straight line is
shown in figure. Work done by all the
forces is equal to change in kinetic
energy.
Reason
Work done by all the forces between
time interval ( t_{1} ) and ( t_{2} ) is definitely 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. Both Assertion and Reason are incorrect.
11
44A massive ball moving with speed ( mathbf{v} )
collides head-on with a tiny ball at rest having a very small mass as compared to the first ball. If the collision is elastic,
then immediately after the impact, the second ball will move with a speed approximately equal to
( A )
B. 2v
( c cdot v / 2 )
D. ( infty )
11
45Find total work done on the block as it
moves by ( 4 m ) as shown
11
46Illustration 8.19 A smooth block
of mass m moves up from bottom to
top of a wedge which is moving with
an acceleration ao. Find the work
done by the pseudo force measured
by the person sitting at the edge of
the wedge.
Fig. 8.42
11
47frictionless surface of an inclined plane,
as shown in the figure. The angle of the
incline suddenly changes from ( 60^{circ} ) and
( 30^{circ} ) at point ( B )
The block is initially at rest at ( boldsymbol{A} )
Assume that collisions between the
block and the incline are totally
inelastic. The speed of the block at point
( B ) immediately after it strikes the
second incline is
( mathbf{A} cdot sqrt{60} m / s )
B. ( sqrt{45} mathrm{m} / mathrm{s} )
( mathbf{c} cdot sqrt{30} m / s )
D. ( sqrt{15} mathrm{m} / mathrm{s} )
11
48A body is lifted over route I and then
route II such that force is always
tangent to the path. Coefficient of
friction is same for both the paths. Work
done
A. on both routes is same
B. on route lis more
c. on route II is more.
D. on both routes is zero
11
49A ball collides elastically with another ball of the same mass. The collision is
oblique and initially one of the ball was at rest. After the collision, the two balls
move with same speeds. What will be the angle between the velocity of the
balls after the collision?
A ( .30^{circ} )
B . 45
( c cdot 60 )
D. 90
11
50A bullet mass ( m ) is fired at a certain
angle q with the vertical. The bullet is returned to ground in time. The total change of momentum is equal to then :
( A cdot m g / 2 )
B. mgt
c. ( 2 mathrm{mgt} )
D. mg
11
51A particle moves along the ( x ) -axis from ( x=0 ) to ( x=5 m ) under the influence of
a force given by ( boldsymbol{F}=mathbf{7}-mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{x}^{2} boldsymbol{N} )
The work done in the process is
( mathbf{A} cdot 107 J )
B. ( 270 J )
c. ( 100 J )
D. ( 135 J )
11
52Work done by kinetic friction on a body
is never zero.
A. True
B. False
c. Ambiguous
D. Data insufficient
11
53Find the speed of A after all collisions
end.
A ( cdot frac{V}{8} )
B. ( frac{V}{4} )
c. ( frac{3 V}{8} )
D. ( 2 V )
11
54Illustration 8.10 A block of mass 5 kg is being raised
vertically upwards by the help of a string attached to it la
rises with an acceleration of 2 ms. Find the work done hu
the tension in the string if the block rises by 2.5 m. Also find
the work done by the gravity and the net work done.
11
55During one dimensional collision or
a) The bodies move along the line
joining their centre of mass before and after collision.
b) The bodies should move in opposite direction.
c) The bodies change their direction after collision.
d) The bodies move along the line joining their centre of mass before and after collision either in same direction
or in opposite direction.
A. Only a is correct
B. Only a & b are correct
( c . ) a, b ( & mathrm{c} ) are correct
D. Only a and d are correct
11
56A uniform cylinder of radius ( r ) and
length L and mass ( m ) is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is:
( ^{mathbf{A}} cdot_{m g}left[left(frac{L}{2}right)-rright] )
( ^{mathrm{B}}_{m g}left[left(frac{g}{2}right)-rright] )
c. ( m(g L-1) )
D. ( M g L r )
11
57An inelastic ball is dropped from a height of ( 100 mathrm{cm} . ) Due to collision with the earth ( 20 % ) of its energy is lost. To what height will the ball rise?
( mathbf{A} cdot 80 mathrm{cm} )
B. ( 40 mathrm{cm} )
c. ( 60 mathrm{cm} )
D. ( 20 mathrm{cm} )
11
58Two vectors of equal magnitude have a resultant equal to either of them. Then, the angle between them will be ( 2 pi / 3 )
radians. The angle in degrees is:
A ( .30^{circ} )
B. ( 120^{circ} )
( c cdot 60 )
D. ( 45^{circ} )
11
59A radioactive nucleus decays by ( boldsymbol{beta} )
emission. Both ( beta ) and neutrino move
mutually at right angle with momentum ( 6 times 10^{-21} k g m s^{-1} ) and ( 3 times )
( 10^{-21} k g m s^{-1} . ) The direction of recoil of
nucleus with respect to electron is :
A ( cdot tan ^{-1}left(frac{1}{2}right) )
B. ( tan ^{-1}(2) )
c. ( _{180-tan ^{-1}}left(frac{1}{2}right) )
D. ( 180-tan ^{-1}(2) )
11
60spring.
1500 Nm, k2 = 500 Nm’,m, = 2 kg, m,=
8. Given k, = 1500 Nm
1 kg. Find:
L00001
mi
Leelle
m2
Fig. 8.212
a. potential energy stored in the springs in
equilibrium, and
b. work done in slowly pulling down m, by 8
cm.
mis doned onto
11
61If a force of ( 4 N ) is applied on a body of
mass ( 20 k g ), then the work done in ( 3 r d )
second will be
A ( .1 .2 J )
в. ( 2 J )
c. 45
D. 16 ( J )
11
62Under the action of a force ( boldsymbol{F}=boldsymbol{C x} ), the
position of a body changes from 0 to ( x ) The work done is :
( ^{mathbf{A}} cdot frac{1}{2} C x^{2} )
в. ( C x^{2} )
( c cdot C x )
D. ( frac{1}{2} C x )
11
63A ball moving with a momentum of ( 5 k g m / s ) strikes against a wall at angle of
( 45^{circ} ) and is deflected at the same angle.
Calculate the change in momentum.
11
64A cyclist free-wheels from the top of a hill, gathers speed going down the hill, apply his brakes and eventually came to rest at the bottom of the hill. Which one
of the following energy changes take place?
A. Potential to kinetic to heat energy
B. Kinetic to potential to heat energy
c. Chemical to heat to potential energy
D. Kinetic to heat to chemical energy
11
65A bar of mass ( M ) and length ( L ) is in pure
translatory motion and its centre of
mass has velocity ( V ). It collides and sticks to a second identical bar which
is initially at rest. (Assume that it becomes one composite bar of length
( 2 L ) ). The angular velocity of the
composite bar after collision will be :
This question has multiple correct options
A ( cdot frac{3}{4} frac{V}{L} )
в. ( frac{4}{3} frac{V}{L} )
c. counterclockwise
D. Clockwise
11
66A ball after falling a distance of 5 meter
from rest hits floor of a lift and
rebounds. At the time of impact the lift was moving up with a velocity of 1 ( m / ) sec. The velocity with which the ball rebounds just after impact is- ( (g= ) ( mathbf{1 0} boldsymbol{m} / boldsymbol{s e c}^{2} )
A. ( 10 mathrm{m} / mathrm{sec} )
B. ( 11 mathrm{m} / mathrm{sec} )
c. ( 12 mathrm{m} / mathrm{sec} )
D. ( 13 mathrm{m} / mathrm{sec} )
11
67Three forces
( (hat{i}+3 hat{j}+hat{k}), frac{5}{7}(-2 hat{i}+9 hat{k}) ) and
( 11(2 hat{i}+hat{j}+6 hat{k}) ) are acting on a
particle. Calculate the work done in displacing the particle from point (4,-1,1) to point (11,6,8)
11
68A body of mass ( 0.1 mathrm{kg} ) is dropped from a
height of ( 10 mathrm{m} ) at a place wheres ( g= )
( 10 m s^{-2} . ) Its KE just before its strikes
the ground is:
A . 1
B. 1.04 J
c. 3.5
D. 10J
11
69A man weighing ( 60 mathrm{kg} ) lifts a body of mass 15 kg to the top of a building 10 m high in 3 minutes. His efficiency is
A . ( 20 % )
B. ( 10 % )
( c .30 % )
D. ( 40 % )
11
7019. A car drives along a straight level frictionless road by an
engine delivering constant power. Then velocity is directly
proportional to
a. t
b.
c. Se
d. None of these
11
71State and explain work energy principle. Mention any three examples for it.11
72Find the ratio ( m_{1}: m_{2} ? )
( A )
B. ( sqrt{2} )
c. ( 1 / sqrt{2} )
D. 2
11
73A ball is dropped from height hon the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is :
A ( cdot frac{h}{e^{2 n}} )
B. ( frac{e^{2 n}}{h} )
( c cdot h e^{2 n} )
D. ( h e^{n} )
11
7428. Work done by friction on the boy is
a. Equal to work done by boy
b. Equal to work done by the motor in running the
conveyor belt
c. Zero
d. None of above
11
75In which of the following cases is the work done positive or zero or negative?
a) Work done by the porter on a suitcase in lifting it from the platform on to his head.
b) Work done by the force of gravity on suitcase as the suitcase falls from
c) Work done by the porter standing on platform with suitcase on his head.
d) Work done by force of gravity on a ball thrown up vertically up into the sky.
e) Work done by force applied by hands of a man swimming in a pond.
11
76The potential energy of a particle of
mass ( 0.5 mathrm{kg} ) moving along ( mathrm{x} ) -axis is
given by ( U=left(x^{2}-4 xright) ) joule where ( x ) is
in metres. The time period of oscillation of the particle is?
11
77A bomb of ( 12 mathrm{kg} ) explodes into two pieces of masses 4 kg and 8 kg. The velocity of ( 8 mathrm{kg} ) mass is ( 6 mathrm{m} ) per second
.The kinetic energy of other mass is?
A. 48 joules
B. 32 joules
c. 24 joules
D. 288 joule
11
78A block of mass ( 5.0 mathrm{kg} ) slides down an incline of inclination ( 30^{0} ) and length 10
m. Find the work done by the force of gravity in joules?
A . 245
B. 300
( c .350 )
D. 400
11
79A box is put on a scale which is
empty. A stream of pebbles is then
poured into the box from a height ( h )
above its bottom at a rate of n pebbles
collide with the box such that they
immediately come to rest after collision, the scale reading at time ( t ) after the pebbles begin to fill the box is:
( mathbf{A} cdot m n{sqrt{(2 g h)}+g t} )
B. ( {sqrt{(2 g h)+g t}} )
c. ( {sqrt{(2 g h)-g t}} )
D ( cdot operatorname{mn}{(2 g h)-g t} )
11
80Which statement best represents the
principle of conservation of energy?
A. Energy cannot be used faster than it is created.
B. The supply of energy is limited, so energy must be conserved
C. The total energy in a closed system is constant
D. The total energy input to a system is equal to the useful energy output
11
81If ( |vec{A}|=|vec{B}|, ) then what is the angle between ( vec{A}+vec{B} ) and ( vec{A}-vec{B} )
A ( cdot 90^{circ} )
B. 60
( c .30 )
D. 0
11
82A bread gives a boy of mass ( 40 k g ) an
energy of ( 21 k J . ) If the efficiency is ( 28 % ) then the height can be climbed by him using this energy is
( mathbf{A} cdot 22 cdot 5 m )
в. ( 14.7 m )
( c .5 m )
D. ( 10 m )
11
83a) How are work, force and distance
related.
b) Find the work done by a pulley when
it lifts a block which is 5 m off the
ground with a ( 10 mathrm{N} ) force.
11
84A force ( boldsymbol{F}=-boldsymbol{K}(boldsymbol{y} hat{boldsymbol{i}}-boldsymbol{x} hat{boldsymbol{j}}), ) (where ( boldsymbol{K} ) is
a positive constant) acts on a particle moving in the ( X Y ) -plane. Starting from the origin, the particle is taken along the positive ( X ) -axis to the plane
( (a, 0) ) and then parallel to the ( Y ) -axis to the point ( (a, a) . ) The total work done by the force ( F ) on the particle is
A ( .-2 K a^{2} )
B ( .2 K a^{2} )
c. ( -K a^{2} )
D. ( K a^{2} )
11
85A particle is moved from (0,0) to ( (a, a) ) under a force ( F=3 i+4 j ) ) from two paths.
Path 1 is ( 0 P ) and path 2 is ( Q O P ). Let ( W_{1} )
and ( mathrm{W}_{2} ) be the work done by this force in two paths. Then:
A. ( w_{1}=w_{2} )
B. ( w_{1}=2 w_{2} )
( c cdot w_{2}=2 w_{1} )
( D cdot W_{1}=4 W_{2} )
11
86A particle is projected at time ( t=0 ) from a point ‘O’ with a speed ‘u’ at an angle ‘ ( theta )
to horizontal. Find the torque of a gravitational force on projectile about the origin at time ‘t’. (x, y plane is vertical plane)
11
87The coefficient of restitution of a
perfectly elastic collision is :
A .
B. 0
( c cdot infty )
D. –
11
88In a one-dimensional elastic collision,
the relative velocity of approach before collision is equal to:
A. sum of the velocities of the bodies
B. ( e ) times the relative velocity of separation after collision
c. ( 1 / e ) times the relative velocity of separation after collision
D. relative velocity of separation after collision
11
89The net work done by the tension in the
figure when the bigger block of mass ( M ) touches the ground is:
( mathbf{A} cdot+M g d )
в. ( -(M+m) g d )
( mathrm{c} .-m g d )
D. zer
11
90( mathbf{A} )
( 3 k g ) object has initial velocity ( (6 hat{i}- ) ( mathbf{2} hat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} . ) The total work done on the
object if its velocity changes to ( (8 hat{i}+ ) ( 4 hat{j}) m / s ) is :
A .2165
J 52665.53
в. ( 44 J )
c. ( 60 J )
D. ( 120 J )
11
91Illustration 8.7 A chain of length L and mass M is held on
a frictionless table with (1/n)th of its length hanging over the
edge (Fig. 8.9). Calculate the work done in pulling the chain
slowly on the table against gravity.
Fig. 8.9
11
92A ladder ( ^{prime} A B^{prime} ) of weight ( 300 N ) and length ( 5 m ) is lying on a horizontal surface. Its centre of gravity is at a distance of ( 2 m ) from end ( A . ) A weight of
( 80 N ) is attached at end ( B ). The work
done in raising the ladder to the vertical
position with end ( ^{prime} boldsymbol{A}^{prime} ) in contact with the ground is.
A. ( 500 J )
в. ( 1000 J )
c. ( 1150 J )
D. ( 1900 J )
11
93Which of the following devices convert light energy into electrical energy?
A. An electric bulb
B. A photocell
c. A microphone
D. A dynamo
11
94A block of mass ( 10 k g ) is released on a
fixed wedge inside a cart which is
moved with constant velocity ( 10 mathrm{ms}^{-1} )
towards right. There is no relative
motion between block and cart. Then
work done by normal reaction on block
in two seconds from ground frame will
be ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) )
A . ( 1320 J )
В. ( 960 J )
c. ( 1200 J )
D. ( 240 J )
11
95A body of mass 5 kg moving with a speed of ( 3 m s^{-1} ) collides head on with a
body of mass ( 3 mathrm{kg} ) moving in the
opposite direction at a speed of ( 2 m s^{-1} ) The first body stops after the collision. Find the final velocity of the second
body.
( mathbf{A} cdot 3 m s^{-1} )
B . ( 5 mathrm{ms}^{-1} )
( mathrm{c} cdot-9 mathrm{ms}^{-1} )
D. ( 30 m s^{-1} )
11
9658. In the above question, the maximum power delivered by
the agent in pulling up the rope is
a. I lgv
b.
a
ON
c. Mgv + v32
X
11
97Assertion
Work-energy theorem can be applied for
non-inertial frames also.
Reason
Earth is a non-inertial frame.
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
98If the potential energy between electron and proton at a distance ( r ) is given by ( U=-left(frac{k e^{2}}{3 r^{3}}right) . ) The force is :
A ( cdot_{F}=frac{k e^{2}}{r^{2}} )
B. ( _{F}=-frac{3}{4} frac{k e^{2}}{r^{4}} )
( ^{mathrm{c}} cdot_{F}=frac{k e^{2}}{r^{4}} )
D. ( _{F}=frac{k e^{2}}{r} )
11
99As per given figure to complete the
circular loop what should be the radius
if initial is ( 5 m )
A . ( 4 m )
B. 3 m
c. ( 2.5 m )
D. ( 2 m )
11
100A vector ( vec{A}=2 hat{i}+3 hat{j}+6 hat{k} ) makes an
angle of ( beta ) with positive direction of ( x- ) axis. ( beta ) is equal to:
A ( cdot tan ^{-1} frac{2}{7} )
B. ( sin ^{-1} frac{2}{7} )
( c cdot cos ^{-1} frac{2}{7} )
D. ( cos ^{-1} frac{4}{7} )
11
101A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a
ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:
( ^{A} cdotleft(frac{1-e}{1+e}right) )
в. ( left(frac{1+e}{1-e}right) )
c. ( left(frac{e+1}{e-1}right) )
D. ( left(frac{e-1}{e+1}right) )
11
102Given: ( overrightarrow{boldsymbol{A}}=boldsymbol{i}-mathbf{2} boldsymbol{j}, overrightarrow{boldsymbol{B}}=mathbf{2} hat{mathbf{i}}+ )
( mathbf{3} hat{boldsymbol{k}} boldsymbol{a} boldsymbol{n} boldsymbol{d} overrightarrow{boldsymbol{C}}=hat{boldsymbol{i}}+hat{boldsymbol{j}} )
Find component of vector ( overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}} ) along:
(i) x-axis
(ii) ( overrightarrow{boldsymbol{C}} )
A ( cdot 3 ; frac{1}{sqrt{2}} )
в. ( 2 ; frac{1}{sqrt{3}} )
c. ( _{3 ; frac{1}{sqrt{3}}} )
D. ( 2 ; frac{1}{sqrt{2}} )
11
103From a rifle of mass ( 4 k g, ) a bullet of
mass ( 50 g ) is fired with an initial
velocity of ( 35 m s^{-1} ). Calculate the initia
recoil velocity of the rifle.
11
104In a collinear collision, a particular with
an initial speed ( v_{0} ) strikes a stationary
particle of the same mass. If the final
total kinetic energy is ( 50 % ) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is?
( A cdot frac{v_{0}}{2} )
в. ( frac{v_{0}}{sqrt{2}} )
c. ( frac{v_{0}}{4} )
( D cdot sqrt{2} v_{0} )
11
1051. When the cord is burnt with a match releasing the spring.
the two masses fly apart with equal
a. Kinetic energy b. Speed
c. Momentum
d. Acceleration
WL: 1viro2
11
106A girl weighing 50 kg makes a high jump of ( 1.2 mathrm{m} . mathrm{What} ) is her kinetic energy at the highest point? ( left(boldsymbol{g}=mathbf{1 0 m s}^{-mathbf{2}}right) )
A. 6000
B. 600 J
c. 60 J
D. zero
11
107A point mass ( M ) moving with a certain velocity collides with a stationary point mass ( frac{M}{2} . ) The collision is elastic and
one dimension. Let the ratio of the final velocities of ( M ) and ( frac{M}{2} ) be ( x ). The value of ( x ) is :
( A cdot 2 )
B. 3
( c cdot frac{1}{2} )
D.
11
the figure. The coefficient of friction,
between the particle and the rough
track equals ( mu . ) The particle is released,
from rest, from the point ( boldsymbol{P} ) and it comes
to rest at a point ( R ). The energies, lost by
the ball, over the parts, ( P Q ) and ( Q R ), of
the track, are equal to each other, and
no energy is lost when particle changes
direction from ( P Q ) to ( Q R ) The values of
the coefficient of friction ( mu ) and the
distance ( x(=Q R), ) are respectively
close to.
A. 0.2 and 6.5 m
B. 0.2 and 3.5 m
c. 0.29 and ( 3.5 m )
D. 0.29 and 6.5
11
109A force ( boldsymbol{F}=(mathbf{1 0}+mathbf{0 . 5} boldsymbol{x}) boldsymbol{N} ) acts on a
particle in ( X ) direction, where ( x ) is in meters. Find the work done by this force during a displacement from ( boldsymbol{x}=mathbf{0} ) to
( boldsymbol{x}=mathbf{2} )
11
110A ball is dropped on the ground from the height of ( 1 m . ) The coefficient of restitution is ( 0.6 . ) The height to which the ball will rebound is (in ( m) )
A . 0.6
B. 0.4
( c .0 .36 )
D. 0.16
11
111If ( A+B=C ) and that ( C ) is
perpendicular to ( A ). What is the angle
between ( boldsymbol{A} ) and ( boldsymbol{B} ), if ( |boldsymbol{A}|=|boldsymbol{C}| ) ?
A ( cdot frac{pi}{4} r a d )
B. ( frac{pi}{2} r a d )
c. ( frac{3 pi}{4} r a d )
D. ( pi r a d )
11
112Two masses ( m_{1}=10 mathrm{kg} ) and ( m_{2}= )
( 5 k g ) are connected by an ideal string as
shown in the figure. The coefficient of
friction between ( m_{1} ) and the surface is
( mu=0.2 . ) Assuming that the system is
released from rest. The velocity of
blocks when ( m_{2} ) has descended by ( 4 m )
is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
A. ( 4 mathrm{m} / mathrm{s} )
в. ( 8 mathrm{m} / mathrm{s} )
c. ( 2 m / s )
D. ( 12 mathrm{m} / mathrm{s} )
11
113Two particles of equal mass go around a circle of radius ( R ) under the action of
their mutual gravitational attraction. The speech of each particle is
( ^{mathbf{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G M}right)} )
в. ( v=sqrt{left(frac{G M}{2 R}right)} )
( ^{mathrm{c}} cdot_{v}=frac{1}{2} sqrt{left(frac{G M}{R}right)} )
D. ( v=sqrt{left(frac{4 G M}{R}right)} )
11
114A body of mass ( m ) starts moving with
velocity ( V_{0} ) at point ( A ) on a frictionless
path as shown in the figure.

The speed of the body at point ( B ) will be:
A ( . ) zero
B. ( V_{0} )
c. ( frac{v_{0}}{2} )
D. ( 2 V_{0} )

11
115When two bodies collide, they
each other.
A. Push
B. Pull
c. Moves towards
D. All
11
116A tennis ball has a mass of ( 56.7 g m ) and
is served by a player with a speed of 180kmph. The work done in serving the ball is nearly:
begin{tabular}{l}
A. 7105 \
hline
end{tabular}
в. ( 71 J )
( mathrm{c} .918 mathrm{J} )
D. ( 91.8 J )
11
117A boy of mass ( M ) stands on a platform
of radius ( R ) capable to rotate freely
about its axis. The moment of inertia of
the platform is ( I . ) The system is at rest.
The friend of the boy throws a ball of mass ( m ) with a velocity ( v ) horizontally. The boy on the platform catches it. Find the angular velocity of the system in the
process.
A ( cdot frac{m v R}{(M+m) R^{2}} )
в. ( frac{m v}{I+M R^{2}} )
c. ( frac{m v R}{I+m R^{2}} )
D. ( frac{m v R}{I+(M+m) R^{2}} )
11
118A mass ( m_{1} ) moves with a great velocity.
It strikes another mass ( m_{2} ) at rest in a
head on collision and comes back along
its path with a low speed after collision. Then :
( mathbf{A} cdot m_{1}>m_{2} )
В. ( m_{1}=m_{2} )
( mathbf{c} cdot m_{1}<m_{2} )
D. there is relation between ( m_{1} ) and ( m_{2} )
11
119Illustration 8.62 A small body of mass m is located on a
horizontal plane at the point O. The body acquires a horizontal
velocity Vo. Find the mean power developed by the friction
force during the whole time of motion, if the frictional
coefficient u = 0.27, m= 1.0 kg and yo = 1.5 ms-1.
SO
11
120The mass of a bucket containing water is ( M_{0} . ) The bucket is pulled steadily up from a well of depth d. Due to a hole in the bucket the water is pouring out at a uniform rate and as a result the mass of
the bucket with water at the top of the
well reduces to M. Then the amount of
work done in pulling up the bucket is?
A ( cdotleft(M_{0}-Mright) g d )
в. ( frac{1}{2}left(M_{0}-Mright) g d )
c. ( left(M_{0}+Mright) g d )
D. ( frac{1}{2}left(M_{0}+Mright) g d )
11
121It is observed that for a ratio ( frac{boldsymbol{m}_{1}}{boldsymbol{m}_{2}}= )
( left(3-x^{2}+xright), ) maximum transfer of
momentum takes places from body 1 to body ( 2 . ) Then This question has multiple correct options
A ( . x=1 )
B. ( x=2 )
( c cdot x=3 )
D. x = –
11
122A sphere of mass ( m ) moving with velocity ( v ) hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in
terms of ( e ) )
A ( cdot frac{v_{1}}{v_{2}}=frac{1+e}{1-e} )
B. ( frac{v_{1}}{v_{2}}=frac{1-e}{1+e} )
c. ( frac{v_{1}}{v_{2}}=frac{1+e}{2} )
D. ( frac{v_{1}}{v_{2}}=frac{1-e}{2} )
11
123A particle of mass M is moving in a
horizontal circle of radius R with
uniform speed ( V ). when it moves from one point to a diametrically opposite point, its
A. kinetic energy changes by ( M V^{2} / 4 )
B. momentum does not change
c. momentum changes by 2 MV
D. kinetic energy changes by ( M V^{2} )
11
124Energy possessed by a body due to its motion is:
A. kinetic energy
B. nuclear energy
c. potential energy
D. thermal energy
11
125A bullet of mass 2.5 g moving with a velocity of ( 500 m s^{-1}, ) enters a wooden
block and comes out of it with a velocity of ( 100 m s^{-1} . ) Find the work done by the
bullet while passing through the wooden block.
A. 100 J
B. 300 J
c. ( 500 mathrm{J} )
D. 800 J
11
126A system absorbs ( 600 mathrm{J} ) of energy and does work equivalent to ( 400 mathrm{J} ) of energy. The internal energy change is
A . 1000
B. 200 J
c. ( 600 mathrm{J} )
D. 300 J
11
127Shape of graph between speed and kinetic energy of the body is:
A. Hyperbola
B. Straight line
c. Parabola
D. circle
11
128A particle of mass ( m_{1} ) is projected to
the right with a speed ( v_{1} ) onto a smooth
wedge of mass ( m_{2} ) which is
simultaneously projected due to the left
with a speed ( v_{2} ). Highest point on the wedge attained by the particle is ( frac{boldsymbol{m}_{2}left(boldsymbol{v}_{1}+boldsymbol{v}_{2}right)^{2}}{boldsymbol{x} boldsymbol{g}left(boldsymbol{m}_{1}+boldsymbol{m}_{2}right)} cdot ) Find ( boldsymbol{x} )
11
129The mass of the moon is ( 1 % ) of mass of
the earth.The ratio of gravitational pull of earth on moon to that of moon on
earth will be:
A . 1:
B. 1: 10
c. 1: 100
D. 2:1
11
130A smooth body is released from rest at a
point ( A ) at the top of a smooth curved track of vertical height ( 40 mathrm{cm} . ) What is
the speed of the body at the bottom of
the curved track? How far along the
adjoining smooth inclined plane will the
body go?
11
131toppr
graph correctly shows the momentum
of the blue object in each case. The red
graphs are all different.
Which graph best represents the
possible momentum of the red object before, during, and after the collision?
( A )
( B )
( c )
( D )
E
11
133A body of mass ( 20 mathrm{kg} ) is at rest. A force of ( 5 mathrm{N} ) applied on it. Calculate the work done in the first second11
134Find the component of ( vec{r} ) in the direction of ( vec{a}: )
A ( cdot frac{(vec{r} cdot vec{a}) vec{a}}{a^{2}} )
B. ( frac{(vec{r} cdot vec{a}) vec{a}}{a} )
c. ( frac{(vec{r} times vec{a}) vec{a}}{a^{2}} )
D. None of above
11
1351. Referring the graphs, which of the following is/are
correct?
1
1
2
3 U
Fig. 8.273
a. The particle has stable equilibrium at points 3 and b.
b. The particle is in neutral equilibrium at points b and
c. No power is delivered by the force on the particle at
points 1, 3, and b.
d. The particle has least kinetic energy at position 1.
11
136wul walking upoll a staircase.
20. A man of mass m is standing on a stationary flat car or mas
M. The car can move without friction along horizontal
rails. The man starts walking with velocity v relative to
the car. Work done by him
a. is greater than-mv2 if he walks along rails.
b. is less than-mv2 if he walks along rails.
c. is equal to
mv2 if he walks normal to rails.
d. can never be less than
11
137Assertion
The kinetic energy, with any reference,
must be positive.
Reason
In the expression for kinetic energy, the
velocity appears with power 2
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
138A particle of mass ( m ) is in UCM of
radius ( r ) and has momentum equal to
( P . ) Its ( mathrm{KE} ) is equal to:
( ^{mathrm{A}} cdot frac{P^{2}}{2 m} )
в. ( frac{P^{2}}{m} )
c. ( frac{P}{2 m} )
D. ( frac{P}{m} )
11
139( m_{2}=2 k g ) are connected by an ideal
spring, rest on a rough
horizontal surface. The spring is unstressed. The spring constant of
spring is ( boldsymbol{K}=mathbf{2} boldsymbol{N} / boldsymbol{m} . ) The coefficient
of friction between blocks and
horizontal surface is ( mu=frac{1}{2} . ) Now the
left block is imparted a velocity ( u )
towards right as shown. The largest
value of ( u(text { in } m / s) ) such that the block
of mass ( m_{2} ) never moves is (Take ( g= )
( left.10 m / s^{2}right) )
A . 10
B. 20
( c .5 )
D.
11
140If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{i}-4 hat{j}+alpha hat{k}, ) then value of
( boldsymbol{alpha} ) is:
A . -1
в. ( frac{1}{2} )
( c cdot-frac{1}{2} )
D. 1
11
141The angle between the vectors ( (hat{i}+hat{j}+ )
( hat{boldsymbol{k}}) ) and ( (hat{boldsymbol{i}}-hat{boldsymbol{j}}-hat{boldsymbol{k}}) ) is:
A ( cdot sin ^{-1} frac{sqrt{8}}{3} )
в. ( sin ^{-1} frac{1}{3} )
c. ( cos ^{-1} frac{sqrt{8}}{3} )
D. ( cos ^{-1} sqrt{frac{8}{3}} )
11
142Rahul is standing on the street and wants to throw an ( 8 k g ) book up to his
friend who is leaning out of a window
( 5 m ) above street level. With what
velocity Rahul must throw the book so
that it reaches his friend in the window?
A. ( 5 m / s )
в. ( 8 m / s )
c. ( 10 m / s )
D. ( 40 mathrm{m} / mathrm{s} )
E ( .50 mathrm{m} / mathrm{s} )
11
143A particle is moving in a potential region given by ( U=Kleft(x^{2}+y^{2}+z^{2}right) )
The force acting on the particle is given by:
A . ( -2 K(x hat{i}+y hat{j}+z hat{k}) )
B . ( K(x hat{i}+y hat{j}+z hat{k}) )
c. ( frac{K}{2}(x hat{i}+y hat{j}+z hat{k}) )
D. ( Kleft(x^{2} hat{imath}+y^{2} hat{jmath}+z^{2} hat{k}right) )
11
144A torch converts
energy to energy.
A. chemical, heat
B. electrical, chemical
c. chemical, light
D. light, electrical
11
145A cyclist wants to loop the loop inside the death globe of diameter 5 m. Find
the minimum velocity, that he should have at the lowest point and calculate the height from which he should start it.
( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
11
1469. The potential energy of the man
a. Increases by mg(i-h)
b. Increases by mg!
c. Increases by mgh
d. Increases by mg (21 – h)
11
1474 A ball of mass m moving with a velocity u rebounds from
a wall. The collision is assumed to be elastic and the force
of interaction between the ball and wall varies as shown
in Fig. 6.296. Then the value of F, is
AF
G

0.5 T T
Fig. 6.296
b. 2 mu/T c. 4 mu/T d. mu/2 T
a. mu/T
11
148A ball with momentum ( 0.5 k g m s^{-1} ) coming towards a batsman is hit by him such that it goes on the same path in opposite direction with momentum ( 0.3 k g m s^{-1} . ) If the time of contact of
the ball with the bat is ( 0.02 s ), find the
force on the ball by the bat.
A . ( 10 N )
в. ( 40 N )
( c .75 N )
D. 30 N
11
149Which of the following does not possess the ability to do work not because of motion?
A. A sparrow flying in the sky.
B. A sparrow moving slowly on the ground.
c. A sparrow in the nest on a tree
D. A squirrel going up a tree
11
150A spring ( left(k=100 N m^{-1}right) ) is suspended
in vertical position having one end fixed at top ( & ) other end joined with a ( 2 mathrm{kg} ) block. When the spring is in non deformed shape, the block is given initial velocity ( 2 mathrm{m} / mathrm{s} ) in downward direction. The maximum elongation of the spring is ( left(frac{sqrt{3}+1}{n}right) ) meter. Find ( n )
11
151When a stone is thrown upwards:
A. Kinetic energy increases and Potential energy decreases
B. both Kinetic energy and Potential energy increase
C. Kinetic energy decreases and Potential energy increases
D. both remain constant
11
152What are the limitations of the energy
obtained from oceans(any two)?
11
153A ( 90 mathrm{gm} ) ball moving at ( 100 mathrm{cm} / mathrm{s} ) collide head on with a stationary 10 gm ball. The coefficient of restitution is ( 0.5 . ) Their
respective velocities after collision are
A ( cdot 135 mathrm{cm} / mathrm{s}, 85 mathrm{cm} / mathrm{s} )
B. ( 85 mathrm{cm} / mathrm{s}, 135 mathrm{cm} / mathrm{s} )
( c .-85 mathrm{cm} / mathrm{s}, 135 mathrm{cm} / mathrm{s} )
D. ( 85 mathrm{cm} / mathrm{s},-135 mathrm{cm} / mathrm{s} )
11
154Given figure shows the vertical section
of a frictionless surface. A block of
mass ( 2 mathrm{kg} ) is released from the position
A, its kinetic energy as it reaches the position C is
A ( .180 mathrm{J} )
В. 140
c. ( 40 mathrm{J} )
D. 280
11
155For a particle projected in a transverse direction from a height h above earth’s surface, find the minimum initia
velocity so that it just grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth’s surface as perigee.
11
156The muscular energy required by our body is given to us by:
A. Air
B. water
c. oxygen
D. Food
11
157A body is acted upon by a force which is proportional to the distance covered. If distance covered is represented by ( s )
then work done by the force will be
proportional to.
( A )
B ( cdot s^{2} )
c. ( sqrt{s} )
D. None of the above
11
158A body is moving with a velocity 1 ms ( ^{-1} )
a force ( F ) is needed to stop it within a
distance ( x ). If the speed of the body is
( 3 m s^{-1}, ) the force needed to stop it with
in the same distance ( (x) ) will be:
A ( .9 F )
в. ( 6 F )
( c .3 F )
D. ( 1.5 F )
11
159The distance of the centre of mass of
the system from the centre of bigger sphere at the moment of collision is
4
3.27
( c cdot 3 r )
D. 47
11
160K. ( boldsymbol{E} ) of a body can be calculated by the amount of work done in stopping the moving body or by the amount of the work done in imparting the present
velocity to the body from the state of
rest
11
161( ln C H_{4} ) molecule, there are four ( C-H )
bonds. If two adjacent bonds are in ( hat{mathbf{i}}+ ) ( hat{boldsymbol{j}}+hat{boldsymbol{k}} ) and ( hat{boldsymbol{i}}-hat{boldsymbol{j}}-hat{boldsymbol{k}} ) direction, then find
the angle between these bonds.
A ( cdot sin ^{-1}left(frac{-1}{3}right) )
B. ( cos ^{-1}left(frac{1}{3}right) )
( ^{c} cdot sin ^{-1}left(frac{1}{3}right) )
D. ( cos ^{-1}left(frac{-1}{3}right) )
11
162What is the angle between ( (hat{mathbf{i}}+hat{boldsymbol{j}}+hat{boldsymbol{k}}) )
and ( hat{i} ? )
A ( cdot frac{pi}{6} )
в. ( frac{pi}{4} )
( c cdot frac{pi}{3} )
D. ( cos ^{-1}left(frac{1}{sqrt{3}}right) )
11
163A marble starts falling from rest on a
smooth inclined plane of inclination ( alpha )
After covering distance ( h ) the ball
rebounds off the plane. The distance
from the impact point where the ball rebounds for the second time is :
( A cdot 8 h cos alpha )
B. ( 8 h sin alpha )
( c cdot 2 h tan alpha )
D. ( 4 h sin alpha )
11
164In Fig. 8.246, the variation of potential energy of a particle
of mass m= 2 kg is represented w.r.t its x-coordinate. The
particle moves under the effect of the conservative force
along the x-axis. Which of the following statements is
1 UG)
20 —-
15
x(m)
ca
-15
Fig. 8.246
a. If it is released at the origin, it will move in negative
x-axis.
b. If it is released at x = 2 + A, where A → 0, then its
maximum speed will be 5 ms’ and it will perform
oscillatory motion.
c. If initially x = -10 and ū= v6i, then it will cross x
= 10.
d. x=-5 and x = +5 are unstable equilibrium positions
of the particle.
11
165A ( 10-k g ) block is pulled in the vertical
plane along a frictionless surface in the
form of an arc of a circle of radius ( 10 mathrm{m} )
The applied force is ( 200 N ) as shown in
the figure.If the block started from rest
at ( A, ) the velocity at ( B ) would be
A . ( 1.732 mathrm{m} / mathrm{s} )
B. ( 17.32 mathrm{m} / mathrm{s} )
c. ( 173.2 mathrm{m} / mathrm{s} )
D. none of these
11
166A ball of mass ( m ) moving with velocity ( v ) collides elastically with another ball of identical mass coming from opposite direction with velocity ( 2 v ). Their velocities after collision will be :
A. ( -v, 2 v )
В. ( -2 v, v )
c. ( v,-2 v )
D. ( 2 v,-v )
11
167A plane surface is inclined at an angle
of ( 60^{0} ) with the horizontal. A body of
mass ( 10 mathrm{kg} ) is uniformly accelerating, along the inclined plane surface. The
value of coefficient of friction ( mu_{k} )
between the body and the inclined
surface is ( 0.2, ) if the length of the
inclined plane is ( 10 mathrm{m} ), then the work
done to pull it to the top is ( Take ( boldsymbol{g}= )
( 10 m / s^{2} )
A . 666 J
B. 766 J
c. 866 J
D. 966 J
11
168A body of mass ( 1 k g ) is thrown upwards with a velocity ( 20 m / s . ) It momentarily comes to rest after attending a height of ( 18 m . ) How much energy is lot due to air friction (in J)
A . 10
B. 20
( c .30 )
D. 40
11
169A ball P moving with a speed of ( boldsymbol{v} boldsymbol{m} boldsymbol{s}^{-1} )
collides directly with another identical
ball Q moving with a speed ( 10 mathrm{ms}^{-1} ) in the opposite direction. P comes to rest after the collision. If the coefficient of
restitution is ( 0.6, ) the value of ( v ) is:
A ( cdot 30 m s^{-1} )
B. ( 40 mathrm{ms}^{-1} )
c. ( 50 m s^{-1} )
D. ( 60 m s^{-1} )
11
170Which of the following are correct?
This question has multiple correct options
( mathbf{A} cdot ) If ( R ) is the radius of a planet, ( g ) is the acceleration due to gravity, the mean density of the planet is ( 3 g / 4 pi G R )
B. Acceleration due to gravity is a universal constant.
C. The escape velocity of a body from earth is ( 11.2 mathrm{km} mathrm{s}^{-1} ) The escape velocity from a planet which has double the mass of earth and half its radius is ( 22.4 mathrm{km} mathrm{s}^{-1} )
D. The ratio of gravitational mass and inertial mass of a body at the surface of earth is 1
11
171The work done to pull them (the
molecules apart if they are at ( R_{0}, ) is:
A. ( U_{0} )
в. ( 2 U_{0} )
c. ( -2 U_{0} )
D. none
11
172If the vectors ( vec{A}=a hat{i}+hat{j}-2 hat{k} ) and ( hat{B}= )
( boldsymbol{a} hat{boldsymbol{i}}-boldsymbol{a} hat{boldsymbol{j}}+hat{boldsymbol{k}} ) are perpendicular to each
other then the positive value then the positive value of ‘a’ is
A. zero
в.
( c cdot-1 )
D. 3
11
173A retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance
travelled when same retarding force is applied is
A. The same
B. Doubled
c. Halved
D. Four times
11
174If ( a, b ) and ( c ) are three non-zero vectors
such that ( a cdot|b times c|=0 ) and ( b ) and ( c ) are
not parallel then ( a, b ) and ( c ) are
A. Collinear
B. Coplanar
c. May be both
D. None
11
175The relationship between force and
position is shown in the figure (in one
dimensional case). Work done by the
force in displacing a body from ( x=1 mathrm{cm} )
to ( x=5 c m ) is :
A. 700 erg
B. 70 erg
c. 60 erg
D. 20 erg
11
176Complete the following statement. The
work done on a system:
A. always changes the potential energy of the system
B. always changes the kinetic energy of the system
C. always changes the momentum of a system
D. can change either the potential energy or kinetic energy of the system
E. is not related to the energy of the system.
11
177If two balls each of mass ( 0.06 mathrm{kg} ) moving in opposite directions with speed of ( 4 m s^{-4} ) collide and rebound
with same speed, then the impulse imparted to each ball due to other is:
A ( .0 .48 mathrm{kg} mathrm{m} mathrm{s}^{-1} )
в. 0.53 kg ( m s^{-1} )
c. ( 0.8 mathrm{kg} mathrm{m} mathrm{s}^{-1} )
D. ( 0.92 mathrm{kg} mathrm{m} mathrm{s}^{-1} )
11
178A body of mass ( 2 k g ) is projected
vertically upwards with speed of ( 3 m / s ) The maximum gravitational potential energy of the body is (in J)
A . 18
в. 4.5
c. 9
D. 2.5
11
179From one corner A of a rectangular
billiard table ABCD placed on a
horizontal surface, a ball of mass and
negligible dimension is projected in the
direction making ( theta ) with side ( A B ) it strikes in other sides ( mathrm{BC}, mathrm{AD}, mathrm{DC} ) and ( mathrm{BC} )
the value of coefficient of restitution is:
( A )
в. ( sqrt{frac{a sin theta}{b cos theta+a sin theta}} )
c. ( sqrt{frac{a sin theta}{b sin theta-a cos theta}} )
D. ( sqrt{frac{a sin theta}{b sin theta+a cos theta}} )
11
18033. The ratio of the energy consumed by the camel during
uniform motion for the two cases when it moves with
speed 5 ms to the case when it moves with 10 ms
b. 19 a 10 a 20
a.
19
19
.
c. 10
10
11
181Due to a force of ( (6 hat{i}+2 hat{j}) mathrm{N} ) the displacement of a body is ( (3 hat{i}-hat{j}) m )
then the work done is?
A . 16
в. 12
( c .8 )
D. zero
11
182A ball tied at the end of a string and swinging back and forth, at what point in the swing would the ball have the highest potential energy?
A. At the bottom of the swing
B. Mid way between the bottom and the top of the swing
c. At the top of the swing
D. just past the bottom of the swing on the way up
E. Just past the top of the swing on the way back down
11
183* ULUULUULUU
13. A ring of mass m= 1 kg can slide over a smooth vertical
rod. A light string attached to the ring passing over a
smooth fixed pulley at a distance of L = 0.7 m from the
rod as shown in Fig. 8.217.
2
370
Fig. 8.217
At the other end of the string mass M= 5 kg is attached,
lying over a smooth fixed inclined plane of inclination
angle 37º. The ring is held in level with the pulley and
released. Determine the velocity of ring when the string
makes an angle (a=37°) with the horizontal. [sin 37° =
0.6]
11
184Which of the following is not an example of perfectly inelastic collision?
A. A bullet fired into a block, if bullet gets embedded into block
B. Capture of an electron by an atom
c. A man jumping onto a moving boat
D. A ball bearing striking another ball bearing
11
185The example given in the problem
represents collision.
A. elastic
B. partially inelastic
c. perfectly inelastic
D. none
11
186( N ) similar slabs of cubical shape of
edge ( b ) are lying on ground. Density of material of slab is ( rho . ) Work done to arrange them one over the other is
A ( cdotleft(N^{2}-1right) b^{3} rho g )
B. ( (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
187A body of mass ( 3 mathrm{kg} ) is under a constant force which causes a displacement s in
metres in it,given by the relation ( s= ) ( frac{1}{2} t^{2}, ) where ( t ) is in seconds. Work done
by the force in 2 seconds is:-
A ( cdot frac{5}{19} )
в. ( frac{3}{8} ) 」
( c cdot frac{8}{3} )
D. ( frac{19}{5} )
11
188Once a choice made regarding zero potential energy reference state, the change in potential energy is :
A . same
B. different
c. depend strictly on the choice of zero potential
D. become indetermine
11
1893. A bead is free to slide down on a smooth
wire rightly stretched between points A and
B on a vertical circle of radius 10 m. Find
the time taken by the bead to reach point
B, if the bead slides from rest from the
highest point A on the circle.
Fig. 5.209
11
190An object of mass ( m ) slides down a hil
of height ( h ) and of arbitrary shape and stop at the bottom because of friction.
The coefficient of friction may be different for different segments of the path. Find the work required to return the object to its initial position along the same path by by a tangential force
A ( . m g h )
в. 2 тун
c. ( -m g h )
D. It cant be calculated
11
1913. One of the forces acting on a particle is conservative,
then
a. Its work is zero when the particle moves exactly once
around any closed path.
b. Its work equals the change in the kinetic energy of the
particle.
c. It does not obey Newton’s second law.
d. Its work depends on the end points of the motion, not
on the path in between.
11
192When the displacement of a particle executing SHM is one – fourth of its amplitude, what fraction of the total
energy is the kinetic energy?
A ( cdot frac{16}{15} )
в. ( frac{15}{16} )
( c cdot frac{3}{4} )
D. ( frac{4}{3} )
11
193Choose the correct statement from the
following:
This question has multiple correct options
A. Kinetic energy of a body is quadrupled, when its velocity is doubled.
B. Kinetic energy is proportional to square of velocity.
C. Kinetic energy does not depend on mass of the body.
D. The change in kinetic energy of a particle is equal to the work done on it by the net force.
11
194Two identical 5 kg blocks are moving with same speed of ( 2 m / s ) towards each other along a friction-less horizontal
surface. The two blocks collide, stick
together and come to rest. Consider two
blocks as a system, the work done on
the system by the external forces will
be:
A . 20 Joule
B . -20 Joule
c. 0 Joule
D. None of these
11
195A particle of mass ( 0.1 mathrm{kg} ) moving with an initial speed v collides with another
particle of same mass kept at rest. If after collision the total energy becomes ( 0.2 mathrm{J}, ) then:
A. minimum value of v is ( 2 mathrm{m} / mathrm{s} )
B. maximum value v is 4 ( mathrm{m} / mathrm{s} )
c. minimum value v is 3 ( mathrm{m} / mathrm{s} )
D. maximum value of v is ( 6 mathrm{m} / mathrm{s} )
11
196A plastic ball is dropped from a height of ( 1 m ) and rebounds several times from
the floor. If 0.13 sec elapse from the moment it is dropped to the second impact with the floor, what is the
coefficient of restitution?
A . 0.85
B. 0.25
c. 0.39
D. 0.65
11
197A car of mass ( 1200 mathrm{kg} ) is moving with a speed of ( 81 mathrm{km} / mathrm{hr} ). Calculate its kinetic
energy.
11
198A body of mass ( m_{1} ) moving with an unknown velocity of ( v_{1} hat{i}, ) undergoes a collinear collision with a body of mass ( m_{2} ) moving with a velocity ( v_{2} hat{i} ). After
collision, ( m_{1} ) and ( m_{2} ) move with velocities of ( v_{3} hat{i} ) and ( v_{4} hat{i}, ) respectively. If
( m_{2}=0.5 m_{1} ) and ( v_{3}=0.5 v_{1}, ) then ( v_{1} ) is :
A ( cdot v_{4}-frac{v_{2}}{4} )
B. ( v_{4}-frac{v_{2}}{2} )
( mathbf{c} cdot v_{4}-v_{2} )
( mathbf{D} cdot v_{4}+v_{2} )
11
199A shown in figure there is a spring block
system. Block of mass ( 500 mathrm{g} ) is pressed against a horizontal spring fixed at one
end to compress the spring through 5.0
cm. The spring constant is ( 500 mathrm{N} / mathrm{m} ) When released, the block moves
horizontally till it leaves the spring Calculate the distance where it will hit
the ground 4 m below the spring?
( A cdot 6 m )
в. ( 4 m )
( c .8 m )
( D cdot sqrt{2} m )
11
200A Nall Ul mass U.c ng resus un diverica
post of height ( 5 mathrm{m} ). A bullet of mass 0.01
kg, traveling with a velocity ( V m / s ) in a
horizontal direction, hits the centre of
the ball. After the collision, the ball and
bullet travel independently. The ball hits
the ground at a distance of ( 20 m ) and
the bullet at a distance of ( 100 mathrm{m} ) from
the foot of the post. The initial velocity
( V ) of the bullet is
( A cdot 250 m / s )
B . ( 250 sqrt{2} mathrm{m} / mathrm{s} )
c. ( 400 mathrm{m} / mathrm{s} )
D. ( 500 mathrm{m} / mathrm{s} )
11
201If ( mathbf{W}_{1}, mathbf{W}_{2} ) and ( mathbf{W}_{3} ) represent the work
done in moving a particle from ( A ) to ( B ) along three different paths 1,2 and 3 respectively (as shown) in the
gravitational field of a point mass ( mathbf{m} )
find the correct relation between
( mathbf{W}_{1}, mathbf{W}_{2} ) and ( mathbf{W}_{3} )
A. ( mathrm{W}_{1}>mathrm{W}_{2}>mathrm{W}_{3} )
B. ( mathrm{W}_{1}=mathrm{W}_{2}=mathrm{W}_{3} )
c. ( mathrm{w}_{1}<mathrm{W}_{2}mathrm{W}_{1}>mathrm{W}_{3} )
11
202Two identical balls each of mass in are
moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :
A. 0
в. ( frac{1}{2} m v^{2} )
( mathrm{c} cdot m v^{2} )
( mathbf{D} cdot 2 m v^{2} )
11
20314. The maximum kinetic energy of the particle and the value
of x at which maximum kinetic energy occurs are
a. 29 J,0 m
b. 49 J, 0 m
c. 49 J, 2 m
d. 29 J, 2 m
11
20424. Which of the following statements is/are correcta
work?
a. In a certain reference frame,
W pseudo force + W conservative force
+ W non-conservative force + Wother forces = AK
b. Work done by friction is always negative.
c. Work done by a force is defined as the dot product
of the force and the displacement of the point of
application of force.
d. Work done by conservative force in moving a body
from A to B = potential energy of the body at A –
potential energy of the body at B.
.
.
cita nainen
11
205A uniform rod ( A B ) which is free to swing
in the vertical plane about a horizontal axis through ( A, ) is hanging freely. ( A ) particle of equal mass strikes the rod
with a velocity ( V_{0} ) and gets stuck to it.Find the angular velocity of the combination immediately after the
collision.
11
206Which of the following will lead to a change in kinetic energy of a body?
A. change in its mass
c. change in its velocity
D. all of the above
11
207A particle of mass ‘ ( m^{prime} ) and charge ( ^{prime} q^{prime} ) is accelerated through a potential
difference of ( ^{prime} V^{prime} ) volt. Its energy is…
A ( . q V )
в. ( m q V )
c. ( left(frac{q}{m}right) v )
D. ( frac{q}{m V} )
11
208Calculate the work done when a
2N force moves a body through a distance of ( 10 mathrm{m} )
A . 10
B. 2 J
c. 5 J
D. 20
11
209The value of ratio ( M / m ) is
4. 2: 3
B . 3: 2
( c cdot 4: 3 )
D. 3: 4
11
210Which of the following does not have potential energy?
A. An inflated balloon
B. Water in a flowing river
c. A fruit on the tree
D. A spinning top
11
211The work done by all the forces on a system equals the change in
A. total energy.
B. kinetic energy.
c. potential energy.
D. none of these
11
212A body is dropped from a certain height from the ground. When it is halfway down, it possess,
A. Only K.E.
B. Both K.E. and P.E.
c. only P.E.
D. zero energy
11
213Assertion (A): When a ball hits a floor
obliquely and gets reflected after inelastic collision, only the vertical component of its velocity gets changed. Reason (R): During collision the floor
exerts a force on the ball only along the normal but not parallel to the surface
A. Both Assertion
(A) and Reason (R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason (R) are correct but the reason does not give the correct explanation
c. A is true but R is false
D. A is false but R is true
11
214Quantities remaining constant in a collision are
A. Momentum, kinetic energy and temperature
B. Momentum but not kinetic energy and temperature
C. Kinetic energy and temperature but not momentum
D. None
11
215What is potential energy?
A. Energy of an abject due to its position or arrangement in a system
B. Energy of an abject due to its nature or arrangement in a system
C. Energy of an abject due to its shape or arrangement in a system
D. None
11
216If the initial speed of the cars is ( x mathrm{m} / mathrm{s} )
find ( 2 x )
11
217A boy a wagon along a horizontal surface for a distance of 10.0 meters.
The boy applies a force of 15 N straight along the handle while the wagon moves, and the handle makes an angle of 35 degrees with the horizontal.

How much work does the boy do on the wagon?
A. 150 Joules
B. 120 Joules
c. 86 Joules
D. 1.5 Joules
E. 0.67 Joules

11
218The potential energy of a particle of mass ( 5 mathrm{kg} ) moving in the ( mathrm{x} ) -y plane is given by the equation, ( U=-7 x+24 y )
Joule. Here ( x ) and ( y ) are in the meter at ( t=0, ) the particle is at the origin and moving with velocity ( (2 hat{i}+3 hat{j}) m / s . ) The
magnitude of acceleration of particle is
( mathbf{A} cdot 3 m / s^{2} )
B . ( 5 mathrm{m} / mathrm{s}^{2} )
D. ( 15 mathrm{m} / mathrm{s}^{2} )
11
219A particle is moving in a circular path of
radius a under the action of an attractive potential ( U=-frac{K}{2 r^{2}} . ) Its total
energy is
11
220A force acts on a body and displaces it
in it’s direction. The graph shows the
relation between the force and
displacement. The work done by the force is:
( mathbf{A} cdot 420 J )
B. ( 360 J )
c. ( 840 J )
D. ( 720 J )
11
221Two bodies of equal weight are kept at heights of h and 1.5 h respectively. The ratio of their P.E. will be:
A . 3: 2
B. 2: 3
c. 1:
D. none of these
11
222The resultant of ( vec{A} ) and ( vec{B} ) makes an angle ( alpha ) with ( vec{A} ) and an angle ( beta ) with ( vec{B} )
then :-
( mathbf{A} cdot alpha<beta )
B. ( alpha<beta ) if ( A<B )
c. ( alphaB )
D. ( alpha<beta ) if ( A=B )
11
223Sphere (1) moving with velocity ( 4 mathrm{m} / mathrm{s} )
collides another sphere (2) at rest. Find
final velocity of sphere (1) after collision collision perfectly elastic
( A cdot 2 hat{imath}+sqrt{3} hat{jmath} )
B . ( 2 hat{i}-sqrt{3} hat{j} )
( c cdot hat{i}+sqrt{3} hat{j} )
D. ( hat{i}-sqrt{3} hat{j} )
11
224A ball of mass ( 200 g ) falls from a height
of ( 5 m . ) What is its K.E. when it just
reaches the ground?
A . ( 9.8 J )
в. ( 98 J )
( mathrm{c} .980 mathrm{J} )
D. None of these
11
225A cannon of mass ( 10 times 10^{3} k g ) is
rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a ( 2.1 times 10^{3} k g ) shell
horizontally with an initial velocity of ( 550 m / s . ) Suppose the cannon is then
unbolted from the earth and no external force hinder its recoil. What would be the velocity (in ( boldsymbol{m} / boldsymbol{s} ) ) of a shell fired horizontally by the loose cannon? (Hint:
In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)
11
226A mass is at the center of a square, with
four masses at the corners as
shown. Rank the choices according to
the magnitude of the gravitational force
on the center mass.
( mathbf{A} cdot F_{A}=F_{B}F_{B}<F_{D}F_{C}=F_{D} )
D. None
11
227The potential energy of 1 kg particle free to move along the X-axis is given by ( boldsymbol{U}=left(frac{boldsymbol{x}^{4}}{boldsymbol{4}}-frac{boldsymbol{x}^{2}}{mathbf{2}}right) boldsymbol{J} )
The total mechanical energy of the particle is 2 J. Then Maximum speed of the particle is :
A ( cdot frac{3}{sqrt{2}} )
B. ( frac{1}{sqrt{2}} )
( c cdot sqrt{2} )
D. 2
11
228A car of mass ( m ) starts moving so that its velocity varies according to the law ( boldsymbol{v}=boldsymbol{beta} sqrt{boldsymbol{s}}, ) where ( boldsymbol{beta} ) is a constant, and ( boldsymbol{s} ) is
the distance covered. The total work
performed by all the forces which are acting on the car during the first ( t ) seconds after the beginning of motion is:
( mathbf{A} cdot m beta^{4} t^{2} / 8 )
B ( cdot m beta^{2} t^{4} / 8 )
( mathbf{c} cdot m beta^{4} t^{2} / 4 )
( mathbf{D} cdot m beta^{2} t^{4} / 4 )
11
229A person holds a bucket of weight ( 60 N )
He walks ( 7 m ) along the horizontal path
and then climbs up a vertical distance
of 5 m. The work done by the man is:
A . ( 300 J )
в. ( 420 J )
c. ( 720 J )
D. none of these
11
230When two bodies collide elastically then the quantity conserved is:
A. kinetic energy
B. mometum
c. both
D. none
11
231If two vectors ( 2 hat{i}+3 hat{j}+3 hat{k} ) and ( -4 hat{i}- ) ( 6 hat{j}+lambda hat{k} ) are parallel to each other then
value of ( lambda ) is
A . -6
B. –
( c .-3 )
D. -4
11
232Law of conservation of energy
states that :
A. energy cannot be destroyed but can be created and transformed from one form to another
B. enerry exists in only one form
C. energy exists in many forms but it cannot be transformed
D. energy can neither be created nor be destroyed but can be transformed from one form to another
11
233* *.162507,power transmite sebe sampel to load is
32. Maximum power transmitted by the camel to load is
a. 6250 Js-
b. 5000 JS-
c. 10 Js-1
d. 1250 JS-
11
234A block of mass ( m ) is pulled slowly by a
minimum constant force ( (boldsymbol{F}) ) on a
horizontal surface through a distance ( x )
The coefficient of kinetic friction is ( mu )
Find the work done by the force ( (boldsymbol{F}) )
11
235An ( 8 k g ) cat is dragged along a hardwood
floor such that her final velocity is
( 80 mathrm{cm} / mathrm{s} ) after being dragged through
( 2 m )
She is initially at rest. In this time interval, the work done on the cat by the normal force exerted by the floor is closest to:
A. zero
в. ( 1.88 J )
c. ( 2.56 J )
D . 78.48J
E . 156.965
11
236Data force ( , f=2 hat{i}+3 hat{j}-4 hat{k} )
displacement ( s=2 hat{i}+3 hat{j}-4 hat{k} ) find
work?
11
237A particle of mass ( m ) initially moving
with speed ( v . A ) force acts on the particle ( boldsymbol{f}=boldsymbol{k} boldsymbol{x} ) where ( boldsymbol{x} ) is the distance travelled
by the particle and ( k ) is constant. Find the speed of the particle when the work done by the force equals ( W )
A ( cdot sqrt{frac{k}{m}+v^{2}} )
B. ( sqrt{frac{2 W}{m}+v^{2}} )
c. ( sqrt{frac{2 W}{k}+v^{2}} )
D. ( sqrt{frac{W}{2 m}+v^{2}} )
11
238The particle executing simple harmonic motion has a kinetic energy ( K_{0} cos ^{2} omega t ) The maximum values of the potential energy and the total energy are respectively
A. ( K_{0} ) and ( K_{0} )
B. 0 and ( 2 K_{0} )
c. ( frac{K_{0}}{2} ) and ( K_{0} )
D. ( K_{0} ) and ( 2 K_{0} )
11
239In stretching a spring by ( 2 mathrm{cm} ) energy
stored is given by ( U, ) then stretching by
( 10 mathrm{cm} ) energy stored will be :
A. ( U )
B. ( 5 U )
c. ( frac{U}{25} )
D. 25U
11
240Two balls of mass ( m_{1} ) and ( m_{2} ) where
( m_{2}=0.5 m_{1}, ) undergo head on collision
as shown in figure.
If ( boldsymbol{v}_{3}=mathbf{0 . 5} boldsymbol{v}_{1} ) value of ( boldsymbol{v}_{4} ) is
fter collision
A ( cdot v_{4}=v_{1}+v_{2} )
B ( cdot v_{4}=v_{1}+2 v_{2} )
( mathbf{c} cdot v_{4}=2 v_{1}+v_{2} )
( mathbf{D} cdot v_{4}=2 v_{1}+3 v_{2} )
11
241The energy directly related to the speed of a moving body and its mass is:
A. Kinetic
B. Potential
c. solar
D. Electric
11
242Initially spring is relaxed. A person starts pulling the spring by applying a variable force ( F ). Where has the work
gone?
A. It is stored in the form of thermal energy in spring
B. It is stored in the form of potential energy in spring
C. It is stored in the form of kinetic energy in spring
D. Cannot be determined
11
243A frame of mass ( 200 g ) when suspended from a massless spring extends it by 10 ( c m . ) A lump of clay of mass ( 200 g ) is dropped from rest on to the frame from
a height of ( 30 mathrm{cm} ) as shown in figure.
What is the maximum distance
through which pan moves downwards?
11
244A machine, which is 75 percent efficient uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to
fall through that distance. What will its
velocity be at the end of its fall?
A ( cdot sqrt{32} mathrm{m} / mathrm{s} )
B. ( sqrt{24} m / s )
c. ( sqrt{18} mathrm{m} / mathrm{s} )
D. ( sqrt{9} m / s )
11
245Define kinetic energy.11
246A ball of mass ( M ) falls from a height ( h ) on a floor which the coefficient of
restitution is ( e . ) The height attained by the ball after two rebounds is:
( mathbf{A} cdot e^{2} h )
B ( cdot e h^{2} )
( mathbf{c} cdot e^{4} h )
D. ( frac{h}{e^{4}} )
11
247The slope of Kinetic Energy displacement curve of a particle in motion is:
A. equal to the acceleration of the particle
B. inversely proportional to the acceleration
c. directly proportional to the acceleration
D. none of these
11
248A lorry and a car moving with the same
K.E. are brought to rest by applying the same retarding force, then?
A. Lorry will come to rest in a shorter distance
B. Car will come to rest in a shorter distance
c. Both come to restin a same distance
D. None of the above
11
249A ( 250 g ) block slides on a rough horizontal table. Find the work done by
the frictional force in bringing the block to rest if it is initially moving at a speed of ( 40 mathrm{cm} / mathrm{s} ). If the friction coefficient between the table and the block is 0.1
how far does the block move before
coming to rest?
11
250A ball is dropped from a height ( 100 m ) on the ground. If the coefficient
of restitution is ( 0.2, ) the height to which the ball will go up after it rebounds for the IInd time
A . ( 15 m )
B. ( 1.6 mathrm{cm} )
( c .1 .6 m )
D. ( 40 mathrm{cm} )
11
251If the maximum angle rotated by the
rod after the collision is ( 60^{circ}-cos ^{-1} frac{z}{8} )
find the value of ( z )
11
( left(sigma_{1}>sigma_{2}right) ) are placed near each other
separated by distance ‘d. A small
change ‘ ( q ) ‘ is placed in between two
plates such that there is no effect on charge distribution on plates. Now this
charge is moved at an angle of ( 45^{circ} ) with the horizontal towards plate having
charge density ( sigma_{2} ) by distance ‘ ( a^{prime}(a< ) ( <boldsymbol{d}) . ) Find the work done by electric
field in the process.
A ( cdot frac{q aleft(sigma_{1}-sigma_{2}right)}{5 sqrt{2} epsilon_{0}} )
B. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{2 sqrt{2} epsilon_{0}} )
c. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{3 sqrt{2} epsilon_{0}} )
D. ( frac{q aleft(sigma_{1}-sigma_{2}right)}{4 sqrt{2} epsilon_{0}} )
11
253A bullet of mass ( m ) and charge ( q ) is fired
towards a solid uniformly charged
sphere of radius ( R ) and total charge ( +q ) If it strikes the surface of the sphere
with speed ( u ), find the minimum speed
( u ) so that it can penetrate through the sphere. (Neglect all resistance forces or
friction acting on bullet except electrostatic forces)
( A )
в.
[
frac{q}{sqrt{4 pi varepsilon_{0} m R}}
]
c. ( frac{q}{sqrt{8 pi varepsilon_{0} m R}} )
D.
11
254A uniform rod of length ( L ) rests on a
frictionless horizontal surface. The rodd
is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed ( v ) strikes the rod at its centre and becomes embedded in it.
The mass of the bullet is one-sixth the
mass of the rod. What is the final
angular velocity of the rod?
A ( cdot omega=frac{v}{9 L} )
B. ( omega=frac{2 v}{9 L} )
( c cdot omega=frac{3 v}{9 L} )
D. ( omega=frac{5 v}{9 L} )
11
255Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball
2. Initially, ball 1 moves with a speed ( v )
toward ball 2 which is at rest.
Immediately after collision, ball 1 travels at a speed of ( v / 3 ) in the same
direction. What type of collision has occured?
A. inelastic
B. elastic
c. completely inelastic
D. cannot be determined from the information giver
11
256If the work done in blowing a soap
bubble of volume ( ^{prime} V^{prime} ) is ( W ), then the
work done in blowing is soap bubble of
volume ( ^{prime} 2 V^{prime} ) is
A ( .4 W )
B. ( 8 W )
( mathbf{c} cdot 2^{1 / 3} W )
( mathbf{D} cdot 4^{1 / 3} W )
11
257A rubber ball drops from a height h. If the ball rises to h / 2 after rebounding three times coefficient of restitution ( e )
is
A ( cdot frac{1}{2} )
D.
11
258A body of mass ‘ ( m^{prime} ) starting from is
acted on by a force producing a velocity ( v=sqrt{k times s} ) where ( k ) is a constant and ( s )
is displacement.The work done by the
force in the first ( ^{prime} t^{prime} ) seconds is:
( mathbf{A} cdot m^{2} k^{2} t^{2} / 8 )
B ( cdot m k^{2} t^{2} / 4 )
( mathbf{c} cdot m k^{2} t^{2} / 8 )
D. ( m^{2} k^{2} t / 4 )
11
259A bullet of mass ( 0.01 mathrm{kg} ) is fired from a gun of mass ( 5 mathrm{kg} ) with velocity of ( 250 mathrm{m} / mathrm{s} ) calculate the speed with which the gun
recoils.
A. ( 0.50 mathrm{m} / mathrm{s} )
B. ( 0.25 mathrm{m} / mathrm{s} )
c. ( 0.05 mathrm{m} / mathrm{s} )
D. ( 0.025 mathrm{m} / mathrm{s} )
11
260A ball hits the ground and loses ( 20 % ) of
its momentum. Coefficient of
restitution is
A. 0.2
B. 0.4
( c cdot 0.6 )
D. 0.8
11
261A body of mass ( 2 mathrm{kg} ) makes an elastic collision with another body at rest and continues to move in the original direction at a speed equal to ( 1 / 3 ) of its original speed. The mass of the second body is
A. ( 2 k g )
в. ( 3 k g )
c. ( 1 k g )
D. ( 4 k g )
11
262State work energy theorem.11
263The force exerted by a weird, stretch
cord at given displacements is shown in
the above table. Experimentally the force is found to vary proportionally to
the square of the displacement, i.e.
( boldsymbol{F}(boldsymbol{x})=-boldsymbol{h} boldsymbol{x}^{2} ) where ( h ) is some
constant.
If the potential energy at ( x=0 m ) is
( U_{0}=0 J ) as shown above, determine
the potential energy at ( x=1.5 m )
begin{tabular}{|c|c|}
hline Displacement ( x ) & Force ( F ) \
hline ( 0 mathrm{m} ) & ( 0 mathrm{N} ) \
hline ( 1 mathrm{m} ) & ( -2 mathrm{N} ) \
hline ( 2 mathrm{m} ) & ( -8 mathrm{N} ) \
hline
end{tabular}
( mathbf{A} cdot 1.13 J )
B. ( 2.25 J )
c. ( 4.50 J )
D. ( 6.75 J )
E ( .7 .50 J )
11
264A body of mass ( 6 mathrm{kg} ) is under a force whic causes displacement in it which is given by ( s=frac{t^{2}}{4} mathrm{m}, ) where ( t ) is time. The work done
by the force in 2 s is
A . ( 12 J )
в. ( 9 J )
c. 6.5
D. 3
11
265A ball of mass m moves towards a
moving wall of infinite mass with a speed ‘v’ along the normal to the wall. The speed of the wall is ‘u’ toward the ball. The speed of the ball after elastic
collision with wall is
A. ( u+v ) away from the wall
B. ( 2 u+v ) away from the wall
c. ( |u-v| ) away from the wall
D. ( |v-2 u| ) away from the wall
11
266Find ( frac{boldsymbol{r}_{mathbf{1}}}{boldsymbol{r}_{2}} )
( mathbf{A} cdot 2^{1 / 6} )
B. ( frac{1}{2^{1 / 6}} )
( mathbf{C} cdot 2^{1 / 12} )
D. ( 2^{-1 / 12} )
11
267If
( M_{e} ) is the mass of earth and ( M_{m} ) is
the mass of moon ( left(M_{e}=81 M_{m}right) ). The
potential energy associated with object of mass ( m ) situated at a distance ( R )
from the centre of earth and ( r ) from
the centre of moon, will be :
( ^{mathbf{A}} cdot_{-G m M_{m}}left[frac{R}{81}+rright] frac{1}{R^{2}} )
в. ( -G m M_{m}left[frac{81}{r}+frac{1}{R}right] )
( ^{mathrm{c}} cdot_{-G m M_{m}}left[frac{81}{R}+frac{1}{r}right] )
D. ( -G m M_{m}left[frac{81}{R}-frac{1}{r}right. )
11
268A boy throws a ball of mass ( 0.5 mathrm{kg} ) upwards with an initial speed of ( 14 mathrm{m} / mathrm{s} ) The ball reaches a maximum height of
8m. The amount of energy dissipated by air drag acting on the ball during the ascent is
A . 4.9
B. 9.8
c. 0 J
D. 13.8 J
11
269One man takes 1 min to raise a box to a
height of 1 metre and another man takes ( 1 / 2 ) min. to do so. The potential energy in the two cases is
A. different
B. same
c. energy of the first is more
D. energy of the second is more
11
270A pump is used to lift ( 500 k g ) of water
from a depth of ( 80 m ) in ( 10 s ) (Take ( g=10 m s^{-2} ) ). Calculate the work
done by the pump.
A ( cdot 16 times 10^{5} J )
В. ( 4 times 10^{5} J )
c. ( 4 times 10^{8} J )
D. ( 2 times 10^{5} J )
11
271A body of mass ( 5 k g ) is taken from a
height of ( 5 m ) to ( 10 m . ) Find the increase
in its potential energy. Take ( boldsymbol{g}= ) ( 10 m s^{-2} )
A . ( 50 J )
в. ( 150 J )
( c .250 J )
D. ( 300 J )
11
27279. A rope ladder of length L is attached to a balloon of mass
M. As the man of mass m climbs the ladder into the balloon
basket, the balloon comes down by a vertical distance s.
Then the increase in potential energy of man divided by
the increase in potential energy of balloon is
Fig. 8.257
L-s
d. L-S
Sri
L-
s
e
11
273A ball is dropped from a height of ( 1 m ) The coefficient of restitution between the ground and the ball is ( 1 / 3 . ) The height to which the ball will rebound after two collisions with ground is :
A. ( 9 m )
в. ( 1 / 9 m )
c. ( 1 / 81 m )
D. ( 81 m )
11
274In a one-dimensional collision between
two particles, their relative velocity is ( bar{v}_{1} )
before the collision and ( bar{v}_{2} ) and the
collision.

This question has multiple correct options
A ( . overline{v_{1}}=overline{v_{2}} ) if the collision is elastic.
B. ( overline{v_{1}}=-overline{v_{2}} ) if the collision is elastic.
begin{tabular}{l|l}
c. ( |overline{v_{2}}|=left|v_{1}right| ) in all cases.
end{tabular}
D. ( v_{1}=-k bar{v}_{2} ) in all cases, where ( k geq 1 )

11
275A person bring a mass of ( 1 k g ) from
infinite to point ( A ). Initially the mass was at rest but is moves a speed of ( 2 m / s ) as it reaches to ( A ). The workdone
by the person on mass is ( -3 J ) the gravitational potential at ( boldsymbol{A} ) is
A. ( -3 J / k g )
в. ( -2 J / k g )
( mathbf{c} .-5 J / k g )
D. ( -7 J / k g )
11
276Assertion
When there is no external force on a
system, its kinetic energy must remain
constant
Reason
When there is no external force on a
system its linear momentum must
remain 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
27725. A block of 4 kg mass starts at rest and slides a distance
d down a friction less incline (angle 30°) where it runs
into a spring of negligible mass. The block slides an
additional 25 cm before it is brought to rest momentarily
by compressing the spring. The force constant of the spring
is 400 Nm. The value of d is (take g = 10 ms)
Lelille
) 30°
Fig. 8.229
a. 25 cm
c. 62.5 cm
b. 37.5 cm
d. None of the above
11
278( A B C ) is a frictionless circular track of
radius ( R ). A particle of mass ( m ) kg is
released from point ( boldsymbol{P}(boldsymbol{O P}=boldsymbol{R} / mathbf{2}) )
After collision with the track, particle moves along the track, then coefficient
of restitution is
A . 0.5
B. 0.3
( c .0 .2 )
D. non
11
279During “inelastic collision ”
a) There is a loss of kinetic energy.
b) Some of the kinetic energy is used to
deform the body.
c) Some of the kinetic energy is
liberated as heat.
d) There is a loss of mass energy.
A. Only a is true
B. Only b and c are true
( c cdot a, b & c ) are true
D. b, c & d are true
11
280The change in the P.E., when a body of mass ( m ) is displaced from Earth’s surface to a vertical height equal to radius of earth ( (mathrm{g}= ) acceleration due to gravity on earth surface) is:
A ( cdot frac{m g R}{2} )
в. ( frac{2 m g R}{3} )
c. ( frac{3 m g R}{4} )
D. ( frac{m g R}{3} )
11
281The water stored in an overhead tank
possesses energy
11
282A ball is dropped onto a floor from a height of ( 10 mathrm{m} ). If ( 20 % ) of its initial energy is lost, then the height of bounce is-
( A cdot 2 m )
B. ( 4 mathrm{m} )
( c cdot 8 m )
D. ( 6.4 mathrm{m} )
11
283An open knife edge of mass ( M ) is
dropped from a height ( h ) on a wooden
floor. If the blade penetrates distance in to the wood, the average resistance offered by the wood to the blade is
A. ( M g )
в. ( M gleft(1+frac{h}{s}right) )
c. ( operatorname{Mg}left(frac{1-h}{s}right) )
D. ( M gleft(frac{1+h}{s}right)^{ } )
11
284The correct relation relating the potential energy U and ( r ) between two atoms is
A ( cdot U_{(r)}=frac{A}{r^{12}}+frac{B}{r^{6}} )
B. ( U_{(r)}=frac{A}{r^{12}}-frac{B}{r^{6}} )
c. ( U_{(r)}=frac{A}{r^{6}}-frac{B}{r^{12}} )
D. ( -U_{(r)}=frac{K}{r^{2}} )
11
285A stone is dropped from a height equal to ( n R(R ) is the radius of the Earth)
from the surface of the Earth. The
velocity of the stone on reaching the surface of the Earth is :
A ( cdot sqrt{frac{2 g(n+1) R}{n}} )
в. ( sqrt{frac{2 g R}{n+1}} )
c. ( sqrt{frac{2 g n R}{n+1}} )
D. ( sqrt{2 g n R} )
11
286A ball of mass m collides head on with
another ball at rest. The KE of the
system left is ( 50 % ). Find the coefficient of restitution.
A ( cdot frac{1}{sqrt{2}} )
B. ( frac{sqrt{2}}{3} )
( c cdot frac{1}{2} )
D. zero
11
287Particle 1 experiences a perfectly elastic
collision with a stationary particle
2. Determine their mass ratio, if after a head-on collision the particles fly apart in the opposite directions with equal
velocities.
A ( cdot frac{2}{3} )
B. ( frac{3}{2} )
( c cdot frac{1}{3} )
D. 3
11
288A particle of mass ( m ) moving with a velocity ( (3 hat{hat{i}}+2 hat{j}) m s^{-1} ) collides with stationary body of mass ( M ) and finally moves with a velocity ( (-2 hat{i}+hat{j}) m s^{-1} ) If ( frac{M}{m}=frac{1}{13}, ) then:
A ( cdot ) the impuse received by ( M ) is ( m(5 hat{i}+hat{j}) )
B. The velocity of the ( M ) is ( frac{1}{13}(5 hat{i}+hat{j}) )
c. the coefficient of restitutions ( frac{11}{17} )
D. All of the above are correct
11
289A cosmic body ( A ) moves to the Sun with
velocity ( v_{0} ) (when far from the Sun) and
aiming parameter ( l ) the arm of the
vector ( vec{v}_{0} ) relative to the centre of the
Sun (figure shown above). Find the
minimum distance by which this body will get to the Sun.
11
290A body of mass ( 10 mathrm{kg} ) dropped from a height ( 20 mathrm{m}, ) acquires a velocity of 10 ( mathrm{m} / mathrm{s} ) after falling through a distance of 20 ( mathrm{m} ). What is the work done by the air resistance on the body?
A. 750 J
B. 1000
c. 1500
D. 2000 J
11
291A sphere of mass m moving with velocity u h its another stationary sphere of same mass. If e is the coefficient of restitution, what is the
ratio of velocities of two spheres after
the collision?
A ( .1: e )
в. ( frac{1-e}{1+e} )
c. ( frac{1+e}{1-e} )
D. ( 1: e^{2} )
11
292A bullet loses ( frac{1}{20} ) of its velocity after
penetrating a plank. How many planks are required to stop the bullet?
( mathbf{A} cdot mathbf{9} )
B. 11
( c cdot 7 )
D.
11
293A block of mass ( m ) is connected to
another block of mass ( M ) by a spring (massless) of spring constant ( k . ) The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force ( boldsymbol{F} ) starts acting on the
block of mass ( M ) to pull it. Find the
force on the block of mass ( m )
( A cdot frac{m F}{M} )
в. ( frac{(M+m) F}{m} )
c. ( frac{m F}{(m+M)} )
D. ( frac{M F}{(m+M)} )
11
294A body is constrained to move in the ( y ) direction. It is subjected to a force ( (-2 hat{i}+15 hat{j}+6 hat{k}) ) Newton. The work done by this force in moving the body through a distance of ( 10 mathrm{m} ) in positive ( y ) direction is:
A. 150
B. 60 J
( c ldots-20 J )
D . – 150 J
11
295How much work they do in just holding it ?
A. 250 J
B. 2500 J
c. 0 J
D. 625 J
11
296The angle between two vectors ( vec{A}= ) ( 4 hat{i}+3 hat{j}-2 hat{k} ) and ( vec{B}=-8 hat{i}-6 hat{j}+4 hat{k} ) is
( mathbf{A} cdot pi / 4 )
в. ( pi / 3 )
( c )
D. ( pi / 2 )
11
297If K.E. of a particle increases by ( 125 % ) then what is the ( % ) increase in its
momentum?
11
298Assuming that ( m ll M, ) find at what
distance ( x ) from the upper end of the rod
the bullet must strike for the
momentum of the system “bullet-rod” to remain constant during the impact.
A ( cdot x approx frac{1}{3} l )
в. ( x approx frac{4}{3} l )
c. ( _{x} approx frac{4}{5} l )
D. ( _{x} approx frac{2}{3} l )
11
299Calculate the change in the
gravitational potential energy of the
skier between ( A ) and ( B ) :
A ( cdot 1.8 times 10^{4} J )
B . ( 3.6 times 10^{2} J )
c. ( 3.6 times 10^{4} J )
D ( .1 .8 times 10^{2} J )
11
300A metal ball falls from a height of ( 1 mathrm{m} ) on to a steel plate and jumps upto a height of ( 81 mathrm{cm} . ) Find the coefficient of
restitution of the ball material.
A. 0.2
B. 9
( c cdot 0.9 )
D. 90
11
301The magnitude of scalar product of two
vectors is 8 and of vector product is ( 8 sqrt{3} . ) The angle between them is This question has multiple correct options
A. 30
B. ( 60^{circ} )
( c .120 )
D. 150
11
302The free-body diagram will be identical
to the one we drew in the example of the
frictionless plane, except we will have a vector for the force of friction in the
negative ( x ) direction. What is the work
done on the box by the force of kinetic
friction?
A ( . ) mumgh ( sin 30^{circ} )
B. ( mu ) mgh tan30 ( ^{text {0 }} )
c. ( mu m g h cot 30^{circ} )
D. ( mu ) mgh ( cos 30^{circ} )
11
having track,is ( mathrm{M}=1 mathrm{kg} ) and rests over a smooth horizontal floor.A cylinder of
radius ( r=10 mathrm{cm} ) and mass ( mathrm{m}=0.5 mathrm{kg} ) 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. ( (g=10 )
( left.boldsymbol{m} / boldsymbol{s}^{2}rightrangle )
11
304Illustration 8.34 A uniform rod of mass M and length Lis
held vertically upright on a horizontal surface as shown in
Fig. 8.72. Assuming zero potential energy at the base of the
rod, determine the potential energy of the rod.
MI
Fig. 8.72
11
30516. A block is suspended by an ideal spring of force constant
k. If the block is pulled down by applying a constant force
F and if maximum displacement of the block from its
initial position of rest is d, then
a. 7 / < 8 = 2
b. 8 = 2F
k
c. Work done by force F is equal to F8
d. Increase in energy stored in the spring is – ks?
2
11
306A particle of mass ( 5 mathrm{kg} ) is free to slide on a smooth ring of radius ( r=20 mathrm{cm} ) fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point 0 of the ring. Initially the particle is at rest at a point ( A ) of the ring such that ( angle O C A ) ( =60^{circ}, mathrm{C} ) being the centre of the ring.
The natural length of the spring is also equal to ( r=20 mathrm{cm} . ) After the particle is released, it slides down the ring, the contact force between the particle ( & ) the ring becomes zero when it reaches the lowest position B. Determine the force constant of the spring.
11
307If ( hat{i}, hat{j} ) and ( hat{k} ) represent unit vectors along the ( x, y ) and ( z ) -axes respectively, then the angle ( theta ) between the vectors ( (hat{i}+hat{j}+hat{k}) ) and ( (hat{mathbf{i}}+hat{mathbf{j}}) ) is equal to:
A ( cdot sin ^{-1}left(frac{1}{sqrt{3}}right) )
B. ( sin ^{-1}(sqrt{frac{2}{3}}) )
c. ( cos ^{-1}left(frac{1}{sqrt{3}}right) )
D. ( 90^{circ} )
11
308U. TINC UI Wese
67. A projectile is fired with some velocity making certain
angle with the horizontal. Which of the following graphs is
the best representation for the kinetic energy of a projectile
(KE) versus its horizontal displacement (x)?
KEA
DECKE
b.
ΚΕ
KE
11
309Two point mass ( m_{1} ) and ( m_{2} ) are placed
at point ( A ) and ( B ) respectively as shown in figure.Point A is the centre of hollow sphere of uniformly distributed total
mass ( m_{3} . ) Consider only gravitational
interaction between all masses and
neglect other gravitational forces.
Select the incorrect alternative.
A . Hollow sphere and point mass ( m_{1} ) moves with same acceleration
B. ( m_{1} ) and ( m_{2} ) moves with same acceleration
C. Net force on ( m_{1} ) is non-zero
D. Net force on hollow sphere and point mass ( m_{1} ) as a system is equal to force experienced by point mass ( m_{2} ) in magnitude
11
310A solid rectangular block of mass ( 200 k g ) has the dimensions ( l=2 m, b= )
( 1 m, h=0.5 m . ) It lies on a horizontal
floor on sides ( l ) and ( b ). The minimum
work needed to turn it so that it lies
on the sides ( b ) and ( h ) is:
A . zero
B. ( 1500 J )
c. ( 3000 J )
D. ( 2000 J )
11
311A cyclist comes to skidding stop in ( 10 mathrm{m} ) During this process, the force on the cycle due to the road is ( 200 mathrm{N} ) and is directly opposed to the motion.(a) how much work does the road do on the
cycle?
(b) How much work does the
A. -2000,,20000
B. – 2000 J,1000 J by each tyre
c. 0.2000
D . -2000 J,0 J
11
312The ( X ) and ( Y ) components of a
displacement vector are (15,7)( m ). Find the magnitude and direction of ( vec{A} )
11
313Choose the false statement
A. In a perfect elastic collision, the relative velocity of approach is equal to the relative velocity of separation
B. In an inelastic collision the relative velocity of approach is less than the relative velocity of separation
C. In an inelastic collision, the relative velocity of separation is less than the relative velocity of approach
D. In perfect inelastic collision relative velocity of separation is zero
11
314A ball of mass ( 0.20 mathrm{kg} ) falls freely from a certain height and rebounds elastically
with a speed of ( 40 mathrm{ms}^{-1} . ) The change in momentum of the ball is:
A ( cdot 4 k g m s^{-1} )
B. ( 8 mathrm{kg} mathrm{ms}^{-1} )
c. ( 16 k g m s^{-1} )
D. ( 40 mathrm{kg} mathrm{ms}^{-1} )
11
315Using dimensional anaysis,shown that the kinetic energy of a body of mass ( mathrm{m} )
moving with a velocity v varies as ( m v^{2} )
11
31644. A man places a chain (of mass m and length 1) on a table
slowly. Initially, the lower end of the chain just touches
the table. The man brings down the chain by length 1/2.
Work done by the man in this process is
a. -mg
b.
mg/
-3mgl
d. _ mg/
8
11
317Which of the following statements is
true for collisions-
A. Momentum is conserved in elastic collisions but not in inelastic collisions
B. Total kinetic energy is conserved in elastic collisions but momentum is not conserved
C. Total kinetic energy is not conserved in inelastic collisions but momentum is conserved
D. Total kinetic energy and momentum both are conserved in all types of collisions
11
318A certain simple harmonic vibrator of
mass ( 0.1 k g ) has a total energy of ( 10 J )
.Its displacement from the mean
position is ( 1 mathrm{cm} ) when it has equal
kinetic and potential energies. The amplitude ( A ) and frequency ( n ) of
vibration of the vibrator are
( ^{mathbf{A}} cdot A=sqrt{2} c m, n=frac{500}{pi} H z )
B. ( A=sqrt{2} c m, n=frac{1000}{pi} H z )
( ^{mathbf{C}} cdot A=frac{1}{sqrt{2}} c m, n=frac{500}{pi} H z )
D. ( A=frac{1}{sqrt{2}} c m, n=frac{1000}{pi} H z )
11
319Two vectors ( vec{A} ) and ( vec{B} ) such that ( (vec{A}+ )
( vec{B}) perp(vec{A}-vec{B}) . ) Then
( mathbf{A} cdot vec{A} | vec{B} )
B. ( vec{A} perp vec{B} )
C ( cdot|vec{A}|=|vec{B}| )
D ( cdot|vec{A}| neq|vec{B}| )
11
320A potential energy function for a twodimensional force is of the form ( U= )
( 3 x^{2} y-7 x . ) Find the force that acts at
the point ( (x, y) )
11
3219. A particle is released one by one from the top of two
inclined rough surfaces of height h each. The angles of
inclination of the two planes are 30 and 60°, respectively.
All other factors (e.g., coefficient of friction, mass of
block, etc.) are same in both the cases. Let K, and K2 be
the kinetic energies of the particle at the bottom of the
plane in the two cases. Then
a. K = K2
b. Ki > K2
c. Ki <K2
d. Data insufficient
11
322A shell of mass ( 200 g m ) is ejected from a gun of mass ( 4 k g ) by an explosion that
generates ( 1.05 k J ) of energy. The initial velocity of the shell is:
A ( cdot 40 mathrm{ms}^{-1} )
B . ( 120 mathrm{ms}^{-1} )
c. ( 100 mathrm{ms}^{-1} )
D. ( 80 mathrm{ms}^{-1} )
11
323The figure shown a ball striking the floor
at an angle ( alpha ) with speed ( u ) and
rebounds at an angle ( beta ) from the floor
with speed ( v . ) The value of co-efficient of restitution (e) is
A ( cdot frac{v}{u} )
в. ( frac{u}{v} )
c. ( frac{v sin beta}{u sin alpha} )
D. ( frac{v sin beta}{u cos alpha} )
11
324A particle of rest mass ( m_{0} ) moves with a
speed ( frac{C}{2} ) its total energy and kinetic
energy are:
( ^{mathrm{A}} cdot frac{sqrt{3}}{2} m_{0} C^{2} ; frac{sqrt{3}}{2} m_{0} C )
в. ( frac{2}{sqrt{3}} m_{0} C^{2} ; frac{0.25}{sqrt{3}} m_{0} C^{2} )
c. ( frac{2}{sqrt{3}} m_{0} C^{2} ; frac{0.27}{sqrt{3}} m_{0} C^{2} )
D. None of these
11
325A spring of spring constant k placed horizontally on a rough horizontal
surface is compressed against a block
of mass ( mathrm{m} ) placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between the
block and the surface is ( mu, ) the potential
energy stored in the spring is:
A ( cdot frac{mu^{2} m^{2} g^{2}}{k} )
B. ( frac{2 mu^{2} g^{2}}{k} )
( ^{mathrm{C}} cdot frac{mu^{2} m^{2} g^{2}}{2 k} )
D. ( frac{3 mu^{2} m g^{2}}{k} )
11
326The expression for kinetic energy is :
A ( cdot frac{1}{2} m v )
в. ( frac{1}{3} m v^{2} )
c. ( frac{1}{2 m} v^{2} )
D. ( frac{1}{2} m v^{2} )
11
327Consider the Earth to be a homogenous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The gravitation field measured by
A. A goes on decreasing and that by B goes on increasing
B. B goes a decreasing and that by A goes on increasing
c. each remains unchanged
D. each goes on decreasing
11
328A body of mass ( 15 mathrm{kg} ) is raised from certain depth. If the work done in
raising it by ( 10 mathrm{m} ) is ( 1620 mathrm{J} ), its velocity at this position is
( mathbf{A} cdot 2 m s^{-1} )
B. ( 4 m s^{-1} )
( mathrm{c} cdot 1 mathrm{ms}^{-1} )
D. ( 8 m s^{-1} )
11
329Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system is conserved.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement 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
330When the momentum of a body decreases by ( 10 % ), its ( mathrm{K.E.} ) decreases by
A . 20%
B. 40%
c. 36%
D. None of these
11
331A cannon, shell is fired to hit a target at
a horizontal distance ( boldsymbol{R} ). However, it
breaks into two equal parts at its highest point. One part (A) returns to the cannon. The other part:
This question has multiple correct options
A. will fall at a distance of ( R ) beyond the target
B. will fall at a distance of ( 3 R ) beyond the target
c. will hit the target
D. have nine times the kinetic energy of ( A )
11
332Two bodies of equal weight are kept at heights of ( h ) and ( 1.5 h ) respectively. The ratio of their P.E. is
( A cdot 3: 2 )
B. 2:3
( c cdot 1: 1 )
D. None of these
11
333A thin circular ring of mass ( M ) and
a constant angular velocity ( omega . ) Four
object each of mass ( m, ) are kept gently
to the opposite ends of two perpendicular diameters of the ring. The
angular velocity of the ring will be-
11
334The potential energy of an object of
mass ( m ) moving in ( x y ) plane in a
conservative field is given by ( boldsymbol{u}=boldsymbol{a} boldsymbol{x}+ )
( b y, ) where ( x ) and ( y ) are position
coordinates of the object. Find magnitude of its acceleration.
11
335Work done on body equals to change in its kinetic energy is known as
A. work done principle.
B. work-energy principle.
c. work-velocity principle.
D. speed-displacement principle
11
336A father holds his child on his shoulders
during a parade. The father does no work during the parade because:
A. No force acts on the child
B. The momentum of the child is constant
c. The potential energy of the child is varying
D. The child’s kinetic energy is constant
E. The child’s distance from the gro
11
337What is the magnitude of linear velocity
of the stick plus puck after the collision?
( mathbf{A} cdot v_{i} )
B. ( frac{v_{i}}{3} )
( c cdot frac{v_{i}}{2} )
D. ( frac{v_{i}}{sqrt{2}} )
11
338When the bob of a simple pendulum is displaced to one extreme position ( mathrm{P} ) and then released, it swings towards the centre position ( Q ) and then to the other extreme position R. At which position does the bob have maximum
kinetic energy?
A. Between P and Q
B.
( c cdot R )
D. Between Q and R
11
339Show that the total kinetic energy of a
sphere of mass ( m ) rolling along
horizontal plane with velocity ( boldsymbol{v} ) is
( 7 / 10 m v^{2} )
11
340A neutron moving with a speed ( v ) makes
a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place
is
A . ( 10.2 e V )
B. 20.4eV
c. ( 12.1 e V )
D. ( 16.8 e V )
11
341A body is acted upon by force which is inversely proportional to the distance covered. The work done will be
proportional to:
( A )
B ( cdot s^{2} )
c. ( sqrt{s} )
D. None of the above
11
342The sum of magnitudes of two forces
acting at a point is ( 16 N . ) If the
resultant force is ( 8 N ) and its direction
is perpendicular to smaller force, then the forces are:
A 6 Nand ( 10 N ) n
B. ( 8 N ) and ( 8 / N )
c. ( 4 N ) and ( 12 N )
D. ( 2 N ) and ( 14 N )
11
343In the figure shown, a block A moving with velocity ( 10 ~ m / s ) on a horizontal surface collides with another block B at
rest initially. The coefficient of restitution is ( frac{1}{2} . ) Neglect friction everywhere. The distance between the blocks at ( 5 s ) after the collision takes
place is ( 5 x(text { in } m) . ) Then ( x ) is
11
344Assertion
A particle is projected upwards with
speed ( v ) and it goes to a height ( h . ) If we double the speed then it will move to height ( 4 h )
Reason
In case of earth, acceleration due to gravity ( g ) varies as ( g propto frac{1}{r^{2}} r geq R )
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
345A block strikes the free end of a
horizontal spring with the other end fix, placed on a smooth surface with a
speed ( v . ) After compressing the spring by ( x, ) the speed of the block reduce to
half. Calculate the maximum
compression of the spring.
11
346If the vectors ( vec{P}=a tilde{i}+a hat{j}+ ) 3 ( hat{k} ) and ( vec{Q}=a hat{i}-2 hat{j}-hat{k} ) are
perpendicular to each other then the positive value of a is
A . zero
в.
( c cdot 2 )
D. 3
11
347Can you find at least one vector perpendicular to ( 3 hat{i}-4 hat{j}+7 hat{k} ? )
A ( cdot hat{i}+2 hat{j}+frac{6}{7} hat{k} )
B・ ( _{hat{i}+2 hat{j}}+frac{5}{7} hat{k} )
( mathbf{c} cdot hat{i}+3 hat{j}+frac{5}{7} hat{k} )
D・ ( hat{i}+2 hat{j}+frac{5}{6} hat{k} )
11
348A block of mass ( 100 g ) is moved with a speed of ( 5.0 m / s ) at the highest point in a closed circular tube of radius tube of
radius ( 10 mathrm{cm} ) kept in a vertical plane. The cross-section of the tube is such
that the block just fits in it. The block makes several oscillations inside the
tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.
A. ( -1.45 mathrm{J} )
в. +1.45 J
c. ( -2.9 J )
D. ( +2.9 J )
11
349A disc of radius ( 0.1 ~ m ) rolls without
sliding on a horizontal surface with a velocity of ( 6 m / s^{-1} ). Then, it ascends a
smooth continuous track as shown in
the figure. Given, ( g=10 m s^{-1}, ) the
height up to which it will ascend is
( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
A ( .2 .4 n )
в. 0.9 т
( c .2 .7 m )
D. ( 1.8 mathrm{m} )
11
350Tllustration 8.21 A bullet leaving the muzzle of a rifle barrel
with a velocity v penetrates a plank and loses one-fifth of its
velocity. It then strikes second plank, which it just penetrates
through. Find the ratio of the thickness of the planks,
supposing the average resistance to the penetration is same
in both the cases.
11
351Which of the following are correct?
This question has multiple correct options
A. An astronaut going from the earth to the Moon will experience weightlessness once.
B. When a thin uniform spherical shell gradually shrinks maintaining its shape, the gravitational potential at its centre decreases
C. In the case of a spherical shell, the plot of ( V ) versus ( r ) is continuous.
D. In the case of a spherical shell, the plot gravitational field intensity ( I ) versus ( r ) is continuous
11
352toppr
uniform area of cross-section is
attached with the particle. The other end of the band is suspended from a
rigid support. A force ( boldsymbol{K}left(boldsymbol{l}^{prime 2}-boldsymbol{l}^{2}right)^{1 / 2} ) is
required to stretch the band to a length
( l^{prime} . ) The particle is moved to a distance ( S )
(where ( S<<l ) ) and then released.
taking ( K=frac{M g}{S} ) and ( mu ) as the
coefficient of friction between the
particle and the groove, the velocity of
particle when passing through the
initial position is:
( ^{A} cdotleft(frac{g S}{3 l}(2 S-3 mu l)right)^{1 / 2} )
B. ( left[frac{g S}{3 l}(3 S-3 mu l)^{1 / 2}right] )
c. ( frac{g S}{l}(3 S-2 mu l)^{1 / 2} )
( ^{mathrm{D}}left[frac{g S}{2 l}(3 S-2 mu l)right]^{1 / 2} )
11
353If two balls each of mass ( 0.06 mathrm{Kg} )
moving in opposite directions with speed ( 4 mathrm{m} / mathrm{sec} ) collides and rebound
with the same speed,then coefficient of restitution for the collision will be:-
( A cdot frac{1}{4} )
B.
( c )
D.
11
354The maximum extension of the spring
( boldsymbol{x}_{boldsymbol{m}} ) is
( A cdot frac{m g}{K} )
в. ( frac{2 m g}{K} )
c. ( frac{3 m g}{K} )
D. ( frac{4 m g}{K} )
11
355A small body ( A ) starts sliding off the top
of a smooth sphere of radius ( R ). Find the
angle ( theta ) (shown in figure
above) corresponding to the point at which the body breaks off the sphere as
well as the break-off velocity of the body
A ( quad theta=arccos left(frac{1}{3}right) approx 52^{circ}, v=sqrt{frac{2 g R}{3}} )
B. ( theta=arccos left(frac{2}{3}right) approx 48^{circ}, v=sqrt{frac{2 g R}{3}} )
( ^{mathrm{c}} cdot_{theta}=arccos left(frac{2}{3}right) approx 48^{circ}, v=sqrt{frac{g R}{3}} )
D. ( _{theta}=arccos left(frac{1}{3}right) approx 52^{circ}, v=sqrt{frac{g R}{3}} )
11
35612. A block hangs freely from the end of a spring. A boy
then slowly pushes the block upwards so that the spring
becomes strain free. The gain in gravitational potential
energy of the block during this process is not equal to
a. The work done by the boy against the gravitational
force acting on the block
b. The loss of energy stored in the spring minus the work
done by the tension in the spring
c. The work done on the block by the boy plus the loss
of energy stored in the spring
d. The work done on the block by the boy minus the
work done by the tension in the spring plus the loss
of energy stored in the spring
e. The work done on the block by the boy minus the work
done by the tension in the spring
11
357A body of mass ( 1.5 mathrm{kg} ) is allowed to slide down along a quadrant of a circle from the horizontal position. In reaching to the bottom, Its velocity is ( 8 mathrm{m} / mathrm{s} ). The
work done in overcoming the friction is
12J. The radius of circle is
11
358A cord is used to lower vertically a block
of mass ( M ) by a distance ( d ) with constant downword acceleration ( frac{g}{2} ) work done by the cord on the block is
( ^{mathbf{A}} cdot frac{-M g d}{2} )
B. ( frac{M g d}{4} )
c. ( frac{-3 M g d}{4} )
D. ( M g d )
11
3593. Which of the following energies is conserved for the
system?
a. Kinetic energy b. Potential energy
c. Mechanical energy d. None of these
11
36019. A constant force F pushes the block m till the wedge M
starts sliding. If the stiffness of the light spring connecting
M and m is K, coefficient of friction between block and
wedge is y, and between the wedge and ground is My, find
the value of the force F
pornoon
м
|
Fig. 8.222
11
361A body moving towards a finite body at
rest collides with it. It is possible that:
This question has multiple correct options
A. both the bodies come to rest
B. both the bodies moves after collision
C. the moving body comes to rest and the stationary body starts moving
D. the stationary body remains stationary, the moving body changes its velocity
11
362A gun is mounted on a railroad car. The
mass of the car, the gun, the shells and
the operator is ( 50 mathrm{m} ) where ( mathrm{m} ) is the mass of the one shell. If the muzzle
velocity of shell is ( 200 mathrm{m} / mathrm{s} ), what is recoil speed of car after second shot?
A ( cdot frac{200}{49} mathrm{m} / mathrm{s} )
в. ( 200left(frac{1}{48}+frac{1}{48}right) mathrm{m} / mathrm{s} )
( ^{mathrm{c}} cdot_{200}left(frac{1}{48}+frac{1}{49}right) mathrm{m} / mathrm{s} )
D. ( 200left(frac{1}{48}+frac{1}{48 times 49}right) mathrm{m} / mathrm{s} )
11
363The two masses ( m_{1} ) and ( m_{2} ) are joined
by a spring as shown. The system is dropped to the ground from a height. The spring will be
A. neither compressed nor stretched regardless of the value of ( m_{1} ) and ( m_{2} )
B. neither compressed nor stretched only when ( m_{1}=m_{2} )
c. stretched when ( m_{2}>m_{1} )
D. compressed when ( m_{2}<m_{1} )
11
364Two elastic bodies ( P ) and ( Q ) having equal masses are moving along the same line with velocities of ( 16 mathrm{m} / mathrm{s} ) and ( 10 mathrm{m} / mathrm{s} )
respectively. Their velocities after the elastic collision will be in ( mathrm{m} / mathrm{s} )
A. 0 and 25
B. 5 and 20
c. 10 and 16
D. 20 and 5
11
365A block of mass ( m=0.1 mathrm{kg} ) is released
from a height of ( 4 mathrm{m} ) a curved smooth
surface. On the horizontal surface path
AB is smooth and path BC offers
coefficient of friction ( mu=0.1 . ) If the
impact of block with vertical wall at ( C ) be perfectly elastic, find the total
distance covered by the block on the horizontal surface before coming to
rest. (Take ( left.mathfrak{g}=10 frac{m}{s^{2}}right) )
11
36612. An engine pumps water continuously through a hole.
Speed with which water passes through the hole nozzle
is v, and k is the mass per unit length of the water jet as
it leaves the nozzle. Find the rate at which kinetic energy
is being imparted to the water.
a. I kv2 b. 1 kv? c. 2 d. v
2
2k 2k
anned by applying a catarina face when
11
367Two identical balls ( A & 13 ) of mass ( m )
each are placed on a fixed wedge as shown in figure Ball B is kept at rest and it is released just before two balls
collides. Bali A roll down without
slipping on inclined plane ( & ) collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is:
A ( cdot frac{m g h}{7} )
B. ( frac{m g h}{2} )
c. ( frac{2 m g h}{5} )
D. ( frac{7 m g h}{5} )
11
smooth pulley as shown in figure. If the system is released from rest, find the
work done by tension on both ( 1 mathrm{kg} ) and 2 kg blocks in 1 s. (Take ( g=10 m / s^{2} ) )
A ( cdot frac{200}{9} J,-frac{200}{9} J )
В. ( -frac{200}{9} J,+frac{200}{9} J )
c. ( +frac{200}{9} J,+frac{200}{9} J )
11
369A sphere of mass ( m_{1}=2 k g ) collides
with a sphere of mass ( m_{2}=3 k g ) which
is at rest. Mass ( m_{1} ) will move at right angle to the line joining centres at the
time of collision, if the coefficient of
restitution is
A ( cdot frac{4}{9} )
в. ( frac{1}{2} )
( c cdot frac{2}{3} )
D. ( sqrt{frac{2}{3}} )
11
370The K.E. of a body is increased most by doubling its :
A. mass
B. weigth
c. speed
D. P.E
11
371An automobile spring extends ( 0.2 mathrm{m} ) for
( 5000 mathrm{N} ) load. The ratio of potential energy stored in this spring when it has been compressed by ( 0.2 mathrm{m} ) to the potential energy stored in a ( 10 mathrm{F} ) capacitor at a potential difference of ( 10000 mathrm{V} ) will be:
A ( cdot 1 / 4 )
B.
( c cdot 1 / 2 )
( D cdot 2 )
11
372Two men, each of mass ( m ), stand on the
edge of a stationary car and jump off with a horizontal velocity u relative to
the car, first simultaneously and then one after the other. If friction be
negligible, in which case will they
impart greater speed to the car?
11
373Which of the following energy change involves frictional force?
A. Chemical energy to heat energy
B. Kinetic energy to heat energy
C. Potential energy to sound energy
D. chemical energy to kinetic energy
11
374State whether the given statement is
True or False :

A block of mass ( M ) is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force ( boldsymbol{F} ). The kinetic
energy of the block increases by ( 40 mathrm{J} ) in
1 ( s . ) The tension in the string is ( F )
A . True
B. False

11
375A small particle travelling with a
velocity v collides elastically with a
smooth spherical body of equal mass
and of radius ( r ) initially kept at rest. The
centre of this spherical body is located
a distance
8
11
376What is the least amount of
energy required by a man to lift an object weighing ( 1000 mathrm{N} ) to a height of ( 2 m ? )
A. 500 J
B. 2000 N
c. ( 500 mathrm{N} )
D. 2000 J
11
3779. A man M, of mass 80 kg runs up a staircase in 15 s.
Another man M, also of mass 80 kg runs up the same
staircase in 20 s. The ratio of the powers developed by
them will be
a. 1
d. none of these
11
378Two block ( A ) and ( B ) are connected to
each other as shown is fig. and spring
and pulley. The block ( B ) slides at a
horizontal top surface of stationary block ( C, ) and block ( A ) slides along
vertical slides of ( C ), both with same
uniform speed. The coefficient of friction between the block is ( 0.2(l) )
spring constant of spring is ( 1960 N / m )
f mass of block is ( 2 k g ). Find energy
stored in spring,
11
379Assertio
A block of mass ( m ) starts moving on a
rough horizontal surface with a velocity
( v . ) It stops due to friction between the
block and the surface after moving through a certain distance. The surface
is now tilted to an angle of ( 30^{circ} ) with the horizontal and the same block is made
to go up on the surface with the same
initial velocity ( v ). The decrease in the
mechanical energy in the second situation is smaller than that in the
first situation.
Reason
The coefficient of friction between the
block and the surface decreases with
the increase in the angle of inclination.
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
380Kinetic energy depends on:
A. Position
B. Velocity
c. shape
D. colour
11
381f a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k}, ) then the
value of ( alpha )
A . –
B. ( -frac{1}{2} )
( c cdot frac{1}{2} )
( D )
11
382Find the total acceleration of the sphere as a function of ( boldsymbol{theta}, ) the angle of deflection of the thread from the
vertical.
A. ( w=g sqrt{1+2 cos ^{2} theta} )
В. ( w=g sqrt{2+3 cos ^{2} theta} )
c. ( w=g sqrt{1+3 cos ^{2} theta} )
D. ( w=g sqrt{3+2 cos ^{2} theta} )
11
38324. A force F = 3î + 24 +ck N causes a displacement
r = ci +4j+ck m. The work done is 36 J. Find the
value(s) of c.
11
384A stationary body explodes into two
fragments of masses ( boldsymbol{m}_{1} ) and ( boldsymbol{m}_{2} . ) If momentum of one fragments ( mathrm{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)}{4 m_{1} m_{2}} )
D. ( frac{p^{2}}{2left(m_{1}-m_{2}right)} )
11
385Initially, the spheres ( A ) and ( B ) are the
potential ( V_{A} ) and ( V_{B} ) respectively. Now
sphere ( mathrm{B} ) is earthed by closing the switch. The potential of A will now
become ( _{–} )
( mathbf{A} cdot mathbf{0} )
B. ( V_{A} )
( mathbf{c} cdot V_{A}-V_{B} )
D. ( V_{B} )
11
386The work-energy theorem states that
the change in:
A. kinetic energy of a particle is equal to the work done on it by the net force
B. kinetic energy of a particle is equal to the work done by one of the forces acting on it
C. potential energy of a particle is equal to the work done on it by the net force
D. potential energy of a particle is equal to the work done by one of the forces acting on it
E. total energy if a particle is equal to the work done on it by the net force
11
387The electric current is produced by the stored water in dams,which possess:
A. Wind Energy
B. Potential Energy
C. Kinetic Energy
D. Solar Energy
11
388Imagine a light planet revolving around a very massive star in a circular orbit or
radius ( R ) with a speed of revolution ( T . ) If the gravitational force of attraction between the planet and the star is proportional to ( boldsymbol{R}^{-mathbf{5} / 2}, ) then
A ( cdot T^{2} ) is proportional to ( R^{2} )
B . ( T^{2} ) is proportional to ( R^{7 / 2} )
c. ( T^{2} ) is proportional to ( R^{3 / 2} / 2 ) proportional
D. ( T^{2} ) is proportional to ( R^{3.75} )
11
tative cu titteratur ac a mgin ( n_{1} )
above the floor of the elevator. After
making a collision with the floor of the
elevator it bounces to height ( h_{2} ). The
coefficient of restitution for collision is
e. For this situation, mark the correct
statement(s).
A . If elevator is moving down with constant velocity ( nu_{0} ) then ( h_{2}=e^{2} h_{1} )
B. If elevator is moving down with constant velocity ( nu_{0} ) then ( h_{2}=e^{2} h_{1}-frac{nu_{0}^{2}}{2 g} )
c. If elevator is moving with constant acceleration of ( g / 4 ) in upward direction, then impulse imparted by floor of the elevator to the ball is ( m(sqrt{2 g h_{2}})+sqrt{2 g h_{1}}+2 nu_{0} )
D. If elevator is moving with constant acceleration of ( g / 4 ) in upward direction, then it is not possible to determine a reaction between ( h_{1} ) and ( h_{2} ) from the given information.
11
390( A ) block ( A, ) whose weight is ( 200 N, ) is
pulled up a slope of length ( 5 m ) by
means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) )
as illustrated in the figure.The difference in work done by the force and the increase in potential energy of the block is :
A . ( 0 . )
в. ( 150 J )
( c .750 J )
D. ( 600 J )
11
391The amount of work has to be done in
assembling three charged particles at
the vertices of an equilateral triangle
A .434
в. 334
c. 234 」
D. 134 J
11
392The spring of the winding knob of a watch has
A. mechanical energy
B. only kinetic energy
c. only potential energy
D. kinetic or potential energy
11
393rest on a inclined plane and are separated by a distance of 6.0 m as
shown in figure. The coefficient of
friction between each of the blocks and
the inclined plane is ( 0.25 . ) The ( 2 k g ) block
is given a velocity of ( 10.0 mathrm{m} / mathrm{s} ) up the
inclined plane. It collides with ( boldsymbol{M} )
comes back and has a velocity of ( 1.0 m / s ) when it reaches its initial
position. The other block ( M ) after the
collision moves ( 0.5 m ) up comes to rest.
calculated the coefficient [Take ( sin theta= )
( left.tan theta=0.05 text { and } g=10 m / s^{2}right] )
( mathbf{A} cdot e=0.84, M=15 k g )
в. ( e=4, M=5 k g )
c. ( e=9, M=15 k g )
D. ( e=84, M=17 k g )
11
394A ball of mass M moving with a velocity V collides head on elastically with
another of same mass but moving with a velocity v in the opposite direction After collision,
A. the velocities are exchanged between the two balls
B. both the balls come to rest
c. both of them move at right angles to the original line of motion
D. one ball comes to rest and another ball travels back with velocity ( 2 v )
11
395Energy possessed by a body by virtue of its motion is :
A. Potential energy
B. Kinetic energy
c. Chemical energy
D. Electrical energy
11
396Calculate the work done to rise a body of ( 30 mathrm{kg} ) to a height of ( 50 mathrm{m}left(mathrm{g}=10 mathrm{m} mathrm{s}^{-2}right) )
(in kJ)
A . 100
B.
c. 15
D. 0.5
11
397The resultant of two vectors ( vec{P} ) and ( vec{Q} ) is
( vec{R} ) If ( vec{Q} ) is doubled then the new resultant vector is perpendicular to ( vec{P} ) Then magnitude of ( overrightarrow{boldsymbol{R}} ) is:
( ^{mathbf{A}} cdot frac{P^{2}-Q^{2}}{2 P Q} )
в. ( Q )
c. ( frac{P}{Q} )
D. ( frac{P+Q}{P-Q} )
11
398The potential energy of your body is
least when you are…
11
3997. Mark the correct statement(s).
a. Total work done by internal forces of a system on the
system is always zero.
b. Total work done by internal forces of a system on the
system is sometimes zero.
c. Total work done by internal forces acting between the
particles of a rigid body is always zero.
d. Total work done by internal forces acting between the
particles of a rigid body is sometimes zero.
par
o
n
e.meat antitance
11
400Example 8.9 A small bar A resting on a smooth horizontal
plane is attached by threads to a point P and by means of
weightless pulley, to a weight B possessing the same mass as
the bar itself. The bar is also attached to a point O by means of
a light non-deformed spring of length lo = 50 cm and stiffness
k=mgllo, where m is the mass of the bar. The thread PA having
been burned, the bar starts moving to the right. Find its velocity
at the moment when it is breaking off the plane.
Fig. 8.189
11
401A force ( overrightarrow{boldsymbol{F}}=(mathbf{5} hat{boldsymbol{i}}+boldsymbol{4} hat{boldsymbol{j}}) boldsymbol{N} ) acts on a body
and produced a displacement ( overrightarrow{boldsymbol{S}}= ) ( (6 hat{i}-5 hat{j}+3 hat{k}) m . ) The work done will be
A . ( 10 J )
в. 20 ( J )
( c .30 J )
D. ( 40 J )
11
402A force ( overrightarrow{boldsymbol{F}}=boldsymbol{x} hat{boldsymbol{i}}+boldsymbol{2} boldsymbol{y} hat{boldsymbol{j}} ) is applied on a
particle. Find out work done by ( boldsymbol{F} ) to
move the particle from point ( boldsymbol{A} ) to ( boldsymbol{B} )
A . ( -3.5 ~ J )
в. ( -2.5 mathrm{J} )
c. ( -4.5 J )
D. -45
11
40353. Net work done by the force F on the block is
a. 50J
b.

I
c. 75 J
d. None of these
11
404A body of mass ( m ) is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The
change in potential energy of body will
be
A. ( 3 m g R )
B. ( frac{1}{3} m g R )
c. ( 2 m g R )
D. ( frac{2}{3} m g R )
11
405By how much will the kinetic energy of a body increase if its speed is doubled?
A. 4 times
B. 2 times
c. 8 times
D. 16 times
11
406A ball is thrown vertically downwards with velocity ( sqrt{2 g h} ) from a height ( h ) After colliding with the ground it just reaches the starting point. Coefficient of restitution is :
A. ( 1 / sqrt{2} )
B. ( 1 / 2 )
c. 1
D. ( sqrt{2} )
11
40712. What is the mechanical energy of the system?
a. 35 J b. 64 J c. 86 J d. 49 J
11
408Two identical balls of equal masses ( A )
and ( mathrm{B} ) are lying on a smooth surface as shown in figure. Ball A hits the ball B
(which is at rest) with a velocity ( mathbf{v}=16 ) ( mathrm{m} / mathrm{s} . ) What should be the minimum
value of coefficient of restitution
between ( A ) and ( B ) so that ( B ) just reaches
the highest point of inclined plane:
( left(g=10 m / s^{2}right) )
( A cdot frac{2}{3} )
B. ( frac{1}{2} )
( c cdot frac{1}{3} )
D.
11
409What kind of energy transformation takes place at the thermal power
station?
11
410A body of mass ( m ) was slowly hauled up
the hill by a force ( F ) as shown in the figure, which at each point was directed
along a tangent to the trajectory. Find
the work performed by this force, if the
height of the hill is ( h, ) the length of its
base is ( l ) and the coefficient of friction
is ( mu . ) (Given acceleration due to gravity
( =g) )
A ( . W_{F}=m g h+mu m g l )
В. ( W_{F}=m g h-mu m g l )
c. ( W_{F}=mu m g l-m g h )
2.
11
411A body of mass ( 10 k g ) at rest is acted upon simultaneously by two forces ( 4 N )
and ( 3 N ) at right angles to each other.
The kinetic energy of the body at the end
of ( 10 s ) is
begin{tabular}{l}
A. ( 50 mathrm{J} ) \
hline
end{tabular}
в. ( 100 J )
c. ( 125 J )
D. ( 144 J )
11
412A block of mass ( m=0.1 mathrm{kg} ) is released
from a height of ( 4 mathrm{m} ) on a curved smooth
surface. On the horizontal surface, path
AB is smooth and path BC offers
coefficient of friction ( mu=0.1 . ) If the
impact of block with the vertical wall at ( mathrm{C} ) be perfectly elastic, the total distance covered by the block on the horizontal
surface before coming to rest will be :
( left.operatorname{take} g=10 m / s^{2}right) )
A ( .29 m )
в. ( 49 m )
( mathbf{c} .59 m )
( mathbf{D} cdot 109 m )
11
413Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic, the linear momenta of the system 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 and Reason correct
11
414Two bodies ( A ) and ( B ) of equal masses are
kept at height of h and ( 2 h ) respectively. ratio of their potential energy?
11
415In which of the following cases work is said to be done?
A. A man pushing a roller and displacing it
B. A boy sleeping
c. Girl writing in Examm
D. All of these
11
41615
32. A particle of mass m is projected at an angle a to the
horizontal with an initial velocity u. The work done by
gravity during the time it reaches its highest point is
a. u? sin’a
h mu costa
mu’sin’
a
d
mu sina
c.
11
417A boy held a book of ( 1 mathrm{kg} ) at a height of 1 metre for 60 seconds. Calculate the
work done.
A . 60 J
B. 30 J
c. 15 J
D.
11
418Find the velocity of the disc after the
collision.
A. ( v^{prime}=frac{4+eta}{4+eta} v )
B. ( v^{prime}=frac{4-eta}{4-eta} v )
( ^{mathrm{C}} cdot v^{prime}=frac{4-eta}{4+eta} v )
D. ( v^{prime}=frac{4+eta}{4-eta} v )
11
41917. The work done on a particle of mass m by a force
alatymitatio ja being the constant
K being the constant
of appropriate dimensions, when the particle is taken from
the point (a,0) to the point (0, a) along a circular path of
a 2Kx
Kx
Kr
2
d. o
11
420At what value of ( eta ) will the velocity of the
disc after the collision reverse its
direction?
A. ( eta4 )
( mathbf{c} cdot eta=4 )
D. ( eta=0 )
11
421A weight lifter jerks ( 220 k g ) vertically
through 1.5meters and holds still at
that height for two minutes. The work done by him in lifting and in holding it still are respectively (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s} )
):
A. ( 220 J, 330 J )
в. ( 3234 J, 0 )
c. ( 2334 J, 10 J )
D. ( 0,3234 J )
11
422c
The displacement-time graph of a body acted upon by some
es is shown in Fig. 8.291. For this situation match the
entries of Column I with the entries of Column II.
SA
Straight
Fig. 8.291
Column I
Column II
i. For OA, the total work done a. always positive
by all forces together is
ii. For OA, the work done by few b. can be positive
of the acting forces is
iii. For AB, the work done by few c. zero or can be
of the acting forces is
iv. For BC, the work done by all d. can be negative
forces together is
zero
11
423Two masses ( m_{1} ) and ( m_{2} ) are connected
by a spring of spring constant k and are placed on a smooth horizontal surface. Initially the spring is stretched through a distance ‘d’ when the system is
released from rest. Find the distance
moved by the two masses when spring is compressed by a distance ‘d’.
11
42424. If instead of moving up the plane, the man increases his
speed to the value v while moving down the inclined plane
through the same vertical distance h, then
a. W friction > 0
b. W friction = -mgh + mv2
c. Work done by the man can be positive, negative or
zero
2
d. Wfriction + W man = -mgh+ -mv2
11
425A ball is thrown horizontally from the top of a tower ( 40 mathrm{m} ) high. The ball strikes the ground at a point ( 80 mathrm{m} ) from the
bottom of the tower. Find the angle that
the velocity vector makes with the horizontal just before the ball hits the
ground.
( mathbf{A} cdot 45 m / s )
в. ( 90 mathrm{m} / mathrm{s} )
c. ( 37 m / s )
D. ( 53 m / s )
11
426Which of the following pairs of vectors
are parallel?
A ( . vec{A}=hat{i}-2 hat{j} ; vec{B}=hat{i}-5 hat{j} )
B . ( vec{A}=hat{i}-10 hat{j} ; vec{B}=2 hat{i}-5 hat{j} )
c. ( vec{A}=hat{i}-5 hat{j} ; vec{B}=hat{i}-10 hat{j} )
D. ( vec{A}=hat{i}-5 hat{j} ; vec{B}=2 hat{i}-10 hat{j} )
11
427The gravitational field is a conservative
field. The work done in this field by
moving an object from one point to
another
A. depends on the end-points only.
B. depends on the path along which the object is moved.
C. depends on the end-points as well as the path between the points.
D. is not zero when the object is brought back to its initial position.
11
428Two blocks of masses ( M_{1} ) and ( M_{2} ) are
connected by spring of constant ( boldsymbol{K} ). The spring is initially compressed and the system is released from rest at ( t=0 )
second. The work done by spring on the blocks ( M_{1} ) and ( M_{2} ) be ( W_{1} ) and ( W_{2} ) respectively by time t. The speeds of both the blocks at time t are non zero.
Then the value of ( frac{W_{1}}{W_{2}} ) equals to
A ( cdot frac{M_{1}}{M_{2}} )
в. ( frac{M_{2}}{M_{1}} )
( ^{mathrm{c}}left(frac{M_{1}}{M_{2}}right)^{2} )
( ^{mathrm{D}}left(frac{M_{2}}{M_{1}}right)^{2} )
11
429An electron moving in a electric
potential field ( V_{1} ) enters a higher
electric potential field ( V_{2} ) then the change in kinetic energy of the electron is proportional to
11
430A sphere of mass ( mathrm{m}, ) moving with a speed ( v, ) strikes a wall elastically at an angle of incidence ( theta ). If the speed of the sphere before and after collision is the same and the angle of incidence and
velocity normally towards the wall the angle of rebound is equal to the angle of incidence and velocity normally towards the wall is taken as negative then, the change in the momentum parallel to wall is :
A. mv ( cos theta )
B. 2 mv ( cos theta )
c. – 2 mv ( cos theta )
D. zero
11
431A ( 3.0 k g ) lump of clay is moving to the
left at ( 4.0 m / s . ) It collides in a perfectly inelastic collision with a ( 6.0 k g ) lump of
clay moving to the right at ( 2.0 m / s ) What is the total kinetic energy after
the collision?
( A cdot 62 J )
в. ( 36 J )
c. ( 25 J )
D. ( 12 . J )
E . ( 0 . J )
11
432Name the type of energy (kinetic energy
( K ) or potential energy ( U ) ) possessed in a compressed spring:
A. ( U )
в. ( K )
c. Both ( U ) and ( K )
D. None
11
433A vibrating body possesses:
A. electrical energy
B. nuclear energy
C . potential energy
D. sound energy
11
434A man of 60 kg gains 1000 cal of heat by eating 5 mangoes. His efficiency is ( 56 % ) To what height he canjump by using
this energy?
( mathbf{A} cdot 4 m )
в. ( 20 m )
( c .28 m )
D. ( 0.2 m )
11
435When a force retards the motion of a
body, the work done is :
A. zero
B. Negative
c. Positive
D. Positive or negative depending upon the magnitude of force and displacement
11
436State whether the given statement is
True or False :

The energy of an object that is due to the object’s motion is called kinetic
energy.
A. True
B. False

11
43745. Along which of the three paths is the work done
maximum?
а. ОА
b. OMA
c. OLA
d. Work done has the same value for all the three
paths.
11
438A man is climbing a staircase.
The energy he uses depends on:
This question has multiple correct options
A. The height of the staircase.
B. The weight of his body
c. The time taken to roach the top
D. The mass of his body.
11
439Two solid balls of rubber ( A ) and ( B ) whose
masses are ( 200 g m ) and ( 400 g m ) respectively, are moving in mutually opposite directions. if the velocity of bal ( A ) is ( 0.3 m / s ) and both the ball come to rest after collision, then the velocity of
ball ( B ) is :
A. ( 0.15 mathrm{m} / mathrm{s} )
в. ( -0.15 mathrm{m} / mathrm{s} )
c. ( 1.5 mathrm{m} / mathrm{s} )
D. None of these
11
440A ball of mass ( 0.2 k g ) is thrown against
the wall, the ball strikes the wall
normally with velocity of ( 30 m / s ) sand rebounds with velocity of ( 20 m / s ) Calculate the impulse of the force exerted by the ball on the wall
A . ( 2 N )
в. ( -10 N )
( c .20 N )
D. ( 40 N )
11
441toppr
height 1 m above the ground. The
particle is thrown from some point in
such a way that it strikes the ground
(perfectly inelastic) with velocity ( v_{0} ) at
an angle ( 37^{circ} ) with vertical just below ( O )
List
(P) Radius of curvature of particle just before striking the ground
(Q) Minimum value of ( v_{0} ) such that at highest point in vertical circle tension in the string ( T=0 )
(R) Negative of work done by gravity after it strikes the ground to the topmost point in frame moving with constant acceleration on ground is (assume that after collision the particle complete the vertical loop)
(S) Power delivered by the gravity at highest point is (assume that after
[
frac{5}{3} frac{v_{0}^{2}}{g}
]
collision the particle complete the vertical loop)
A. P- ( 2 ; Q-3 ; R-1 ; S-4 )
B. P- 3; Q- 2; R- 4; S-1
( mathrm{C} cdot cdot mathrm{Q}-1 ; mathrm{R}-2 ; mathrm{S}-3 )
D. P- 2; Q- 3; R-4; S-1
11
442A woman weighing ( 63 mathrm{kg} ) eats plum cake whose energy content is 9800 calories. If all this energy could be utilized by her, she can ascend a height of
A. ( 1 m )
B. ( 66 m )
( c cdot 100 m )
D. ( 42 m )
11
443Assertion
Work done by friction on a body sliding
down an inclined plane is negative
Reason
Work done is greater than zero, if angle between force and displacement is
acute or both are in same direction
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
444Give few examples where displacement of an object is in the direction opposite to the force acting on the object.11
445The balls, having linear momenta ( overrightarrow{mathbf{p}}_{1}= ) ( mathbf{p} hat{mathbf{i}} ) and ( overrightarrow{mathbf{p}}_{2}=-mathbf{p} hat{mathbf{i}}, ) undergo a collision in
free space. There is no extemal force
acting on the balls. Let ( overrightarrow{mathbf{p}}_{1} ) and ( overrightarrow{mathbf{p}}_{2} ) be
their final momenta. The following option(s) is (are) NOT ALLOWED for any
non-zero value of ( mathbf{p}, mathbf{a}_{1}, mathbf{a}_{2}, mathbf{b}_{1}, mathbf{b}_{2}, mathbf{c}_{1} )
and ( mathbf{c}_{2} )
This question has multiple correct options
( mathbf{A} cdot overrightarrow{mathbf{p}}_{1}=mathbf{a}_{1} hat{i}+mathbf{b}_{1} hat{mathbf{j}}+mathbf{c}_{1} hat{mathbf{k}} )
[
overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} mathrm{i}+mathrm{b}_{2}
]
B ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{c}_{1} hat{mathrm{k}} )
[
overrightarrow{mathrm{p}}_{2}=mathrm{c}_{2} hat{mathrm{k}}
]
C ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{a}_{1} mathrm{i}+mathrm{b}_{1} hat{mathrm{j}}+mathrm{c}_{1} hat{mathrm{k}} )
[
overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} hat{mathrm{i}}+mathrm{b}_{2} hat{mathrm{j}}-mathrm{c}_{1} hat{mathrm{k}}
]
D ( cdot overrightarrow{mathrm{p}}_{1}=mathrm{a}_{1} hat{mathrm{i}}+mathrm{b}_{1} hat{mathrm{j}} )
[
overrightarrow{mathrm{p}}_{2}=mathrm{a}_{2} mathrm{i}+mathrm{b}_{1} hat{mathrm{j}}
]
11
446A satellite is moving in a circular orbit
around earth with a speed ( V ), If its mass
is ( mathrm{m} ), then its total energy will be.
A ( cdot frac{3}{4} m v^{2} )
B. ( m v^{2} )
c. ( frac{1}{2} m v^{2} )
D. ( -frac{1}{2} m v^{2} )
11
447If vector ( vec{A}=hat{i}+c hat{j}+5 hat{k} ) and vector
( vec{B}=2 hat{i}+hat{j}-hat{k} ) are perpendicular,then
calculate the value of ( c )
11
44891. Figure 8.265 shows a plot of the potential energy as a
function of x for a particle moving along the x-axis. Which
of the following statement(s) is/are true?
UA
a
b
c
d
Fig. 8.265
a. a, c, and d are points of equilibrium
b. a is a point of stable equilibrium
c. b is a stable equilibrium point
d. All of the above
11
449retel NU I
Uuno muy ve Ullerent.
Tlustration 8.1 A constant force F =(3ỉ +2j+2) N acts
on a particle displacing it from a position 7; =(-î +-2) m
in a new position r = (i -j + 3k) m. Find the work done by
the force.
The displacement vector
=
11
450A wagon of mass 10 tons moving at a
speed of 12 kmph collides with another
wagon of mass 8 tons moving on the same track in the same direction at a
speed of ( 10 mathrm{kmph} ). If the speed of the first wagon decreases to 8 kmph. Find the speed of the other after collision
A. ( 18 mathrm{kmph} )
B. 25 kmph
c. ( 5 mathrm{kmph} )
D. ( 15 mathrm{kmph} )
11
451A particle experiences a positiondependent force given by
[
boldsymbol{F}(boldsymbol{x})=-boldsymbol{6} boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}+boldsymbol{3} / boldsymbol{x}^{2}
]
where ( x ) is in meters and ( F ) is in
Newtons (units have been abbreviated).
At ( x=1 m, ) what is the potential energy
of the particle relative to the potential energy at the origin?
A . ( +5 J )
в. ( +3 J )
( c .-3 J )
D. ( -5 . J )
E. Cannot be determined
11
45270. A force F = (3xy – 5z) ſ + 4 zł is applied on a particle.
The work done by the force when the particle moves from
point (0, 0, 0) to point (2, 4, 0) as shown in Fig. 8.250 is
(2, 4,0)
y= x2
(0,0,0)
Fig. 8.250
a. 280 units
c. 232 units
b. 140 units
d. 192 units
– units
11
453The spring shown in figure is
unstretched when a man starts pulling
the block. The mass of the block is ( M . ) If
the man exerts a constant force ( boldsymbol{F} )
The energy stored in the spring when the block passes through the
equilibrium position is
( ^{A} cdot frac{2 F^{2}}{k} )
B. ( frac{F^{2}}{k} )
( ^{mathbf{c}} cdot frac{F^{2}}{4 k} )
D. ( frac{F^{2}}{2 k} )
11
454A man of mass ( 50 k g ) climbs up a ladder
of height ( 10 m ). Calculate the increase in
his potential energy. ( left(boldsymbol{g}=mathbf{9 . 8 m} boldsymbol{s}^{-2}right) )
A . ( 490 J )
B . ( 2450 J )
c. ( 4900 J )
D. ( 0 . )
11
45519. The speed of the bob at the highest point on the circle is
a. 146 ms b. V26 ms?
c. 52 ms -1
d. 135 ms -1
11
456If the work done by the actor is ( y mathrm{kJ} ), find
( 2 y )
11
457Tllustration 8.2 Three constant forces F = 2-3j+2k,
És=i+j-k, and Ēz = 3 + j-2k in newtons displace a
particle from (1,-1, 2) to (-1,-1, 3) and then to (2,2,0)
(displacement being measured in metres). Find the total work
done by the forces.
11
458Thread is massless. On applying force ( F )
KE increases by ( 20 mathrm{J} ) in ( 1 mathrm{s} )
A. tension in the string is ( mathrm{Mg} )
B. the tension in the string is ( F )
c. work done by the tension in 1 s is 20 J
D. the work done by the force of gravity is 20 Jin
11
459Three vectors ( overrightarrow{boldsymbol{A}}=boldsymbol{a} overrightarrow{boldsymbol{i}}+overrightarrow{boldsymbol{j}}+overrightarrow{boldsymbol{k}}, overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{i}}+ )
( boldsymbol{b} overrightarrow{boldsymbol{j}}+overrightarrow{boldsymbol{k}}, overrightarrow{boldsymbol{C}}=overrightarrow{boldsymbol{i}}+overrightarrow{boldsymbol{j}}+boldsymbol{c} overrightarrow{boldsymbol{k}} ) are mutually
perpendicular ( (vec{i}, vec{j}, vec{k} ) are unit vectors along ( X, Y, Z ) axis respectively. The respective values of ( a, b ) and ( c ) are
( mathbf{A} cdot 0,0,0 )
B. ( -frac{1}{2},-frac{1}{2},-frac{1}{2} )
c. 1,-1,1
D. ( frac{1}{2}, frac{1}{2}, frac{1}{2} )
11
460Which of the following forms of energy
is released or absorbed in most
chemical reactions?
A. Light energy
B. Electrical energy
c. sound energy
D. Heat energy
11
461If the amount of heat given to a system is ( 35 J ) and the amount of work done on
the system is ( 15 J ), then the change in
internal energy of the system is
A. ( -50 J )
в. ( 20 J )
( c .30 J )
D. ( 50 J )
11
462A force ( (10 hat{i}-3 hat{j}+6 hat{k}) ) newton acts on a body of mass ( 100 g ) and displaces it from ( (6 hat{i}-5 hat{j}-3 hat{k}) ) metre to ( (10 hat{i}-2 hat{j}+7 hat{k}) m )
The work done is
( mathbf{A} cdot 21 J )
в. ( 361 J )
c. ( 121 J )
D. ( 1000 J )
11
463Illustration 8.30 A pendulum of mass m and length
suspended from the ceiling of a trolley which has a const
acceleration a in the maximum deflection of the pendula
from the vertical.
Om
Fig. 8.64
11
464A car weighing 1 ton is moving twice as fast as another car weighing 2 ton. The kinetic energy of the one-ton car is
A. less than that of the two-ton car is
B. some as that of the two-ton car is
c. more than that of the two-ton car is
D. impossible to compare with that of the two-ton car unless the height of each
11
465A completely inelastic is one in which the two colliding particles
A. split into small fragments flying in all directions
B. remain together after the collision.
c. are separated after the collision.
D. none of the above
11
466u. Directly proportional to t
66. A particle of mass m slides on a frictionless surface ABCD,
starting from rest as shown in Fig. 8.248. The part BCD is
a circular arc. If it looses contact at point P, the maximum
height attained by the particle from point C is
АО
2R/

IRIR
Fig. 8.248
– [2+xb]
– asztal
c. 3
d. None of these
11
467The gravitational potential energy of a body at a distance ( r ) from the centre of
earth is ( U . ) Its weight at a distance ( 2 r )
from the centre of earth is
A ( cdot frac{U}{r} )
в. ( frac{U}{2 r} )
c. ( frac{U}{4 r} )
D. ( frac{U}{sqrt{2} r} )
11
468A bullet of mass ( 5 g ) travels with a speed
of ( 500 m s^{-1} . ) if it penetrates a fixed target which offers a constant resistive
force of ( 1000 mathrm{N} ) to the motion of the
bullet, find :
(a) the initial kinetic energy of the bullet,
(b) the distance through which the bullet has penetrated.
( mathbf{A} cdot s=0.625 m )
B. ( s=0.725 mathrm{m} )
( mathbf{c} cdot s=0.225 m )
D. ( s=0.65 m )
11
469Two billiard balls of the same size and
mass are in contact on a billiard table.
third ball of the same size and mass
strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the
ball is:
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot 2 )
( overline{3} )
( D cdot 3 )
( bar{A} )
11
470Explain why water stored in a dam has potential energy.11
471A ball is let fall from a height ( h_{0} ). It makes ( n ) collisions with the earth. After
( n ) collisions it rebounds with a velocity
( v_{n} ) ‘ and the ball rises to a height ( h_{n} ) then coefficient of restitution is given
by:
( ^{mathbf{A}} cdot_{e}=left[frac{h_{n}}{h_{0}}right]^{1 / 2 n} )
( ^{mathrm{B}} e=left[frac{h_{0}}{h_{n}}right]^{1 / 2 n} )
c. ( _{e}=frac{1}{n} sqrt{frac{h_{n}}{h_{0}}} )
D. ( _{e}=frac{1}{n} sqrt{frac{h_{0}}{h_{n}}} )
11
472A sphere A moving with a speed u and rotating with an angular velocity ( omega ) makes a head-on elastic collision with
an identical stationary sphere B. There is no friction between the surface of ( A )
and B. Disregard gravity. Then which of the following statements is/are true? This question has multiple correct options
A. A will stop moving but continue to rotate with an angular velocity ( omega )
B. A will come to rest and stop rotating.
c. B will move with a speed u without rotating
D. B will move with a speed u and rotate with an angular velocity ( omega )
11
473Two bars of masses ( m_{1} ) and ( m_{2} )
connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between the bars
and the surface is equal to ( k ). The minimum constant force that has to be
applied in the horizontal direction to the
bar of mass ( m_{1} ) in order to shift the other bar is ( F_{min }=k gleft(m_{1}+frac{m_{2}}{x}right) )
Find ( x )
11
474Find the components of a vector ( overrightarrow{boldsymbol{A}}= ) ( 2 hat{i}+3 hat{j} ) along the directions of ( hat{i}+ ) ( hat{j} ) and ( hat{i}-hat{j} )
A ( cdot frac{5}{sqrt{2}}, frac{-1}{sqrt{2}} )
B. ( frac{-5}{sqrt{2}}, frac{-1}{sqrt{2}} )
c. ( frac{5}{sqrt{2}}, frac{1}{sqrt{2}} )
D. ( frac{-5}{sqrt{2}}, frac{1}{sqrt{2}} )
11
475A planet of radius ( boldsymbol{R}=frac{mathbf{1}}{mathbf{1 0}} times )
(radiusof Earth) has the same mass
density as Earth. Scientists dig a well of depth ( frac{R}{5} ) on it and lower a wire of the same length and of linear mass density ( 10^{-3} k g m^{-1} ) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth ( = )
( 6 times 10^{6} m ) and the acceleration due to
gravity of Earth is ( 10^{-2} ) )
( mathbf{A} cdot 96 N )
в. ( 108 N )
c. ( 120 N )
D. ( 150 N )
11
476Illustration 8.66 A pump is required to lift 1000 kg of water
per minute from a well 20 m deep and eject it at a rate of
20 ms-
a. How much work is done in lifting water?
b. How much work is done in giving it KE?
C. What HP (horsepower) engine is required for the purpose
of lifting water?
.
. DE
1
11
477If angular speed of the rod just after the impact is ( frac{1}{2} sqrt{frac{x g}{2 l}}, ) find the value of ( x )11
478A ( 20 mathrm{kg} ) object is being lifted through a
height of ( mathrm{m} ) when ( 484 mathrm{J} ) of
work is done on it.
11
479For what (finite) value of ( x operatorname{does} F(x)= )
( mathbf{0 ?} )
11
480A steel ball moving with a velocity ( bar{v} ) collides with an identical ball originally at rest. The velocity of the first ball after
the collision is :
A ( cdotleft(-frac{1}{2}right) bar{v} )
в. ( -bar{v} )
c. ( bar{v} )
D. zero
11
481A sphere ( A ) moving with speed ( u ) and
rotating with an angular velocity ( omega )
makes a head-on elastic collision with
an identical stationary sphere ( boldsymbol{B} ). There
is no friction between the surfaces of ( boldsymbol{A} )
and ( B . ) Choose the correct
This question has multiple correct options
A. ( A ) will stop moving but continue to rotate with an angular velocity ( omega )
B. ( A ) will come to rest and stop rotating
C. ( B ) will move with speed ( u ) without rotating
D. ( B ) will move with speed ( u ) and rotate with an angular velocity ( omega )
11
482What is the change in potential energy (in calories) of a ( 10 mathrm{kg} ) mass after ( 10 mathrm{m} ) fall?
A. 1000 call ( l )
в. ( 0.1 mathrm{kcal} )
c. 238.9 cal
D. 23.89 cal
11
483An engine can pump 40,000 liters of water to the vertical height of 35 meters in 5 minutes. Calculate the
gravitational potential energy of water at given height.
11
484The potential energy (in Sl units) of a particle of mass ( 2 k g ) in a conservative
field is ( U=6 x-8 y . ) If the initial velocity of the particle is ( vec{u}=-1.5 hat{i}+ ) ( 2 hat{j} ) then the total distance travelled by
the particle in first two seconds is:
A. ( 10 mathrm{m} )
B. 12m
( c .15 mathrm{m} )
D. 18m
11
485sides 2 a lies on a smooth horizontal
plane as shown in the figure. Three
point masses of mass m each strike the
block at ( A, B ) and ( C ) with speeds ( v ) as
shown. After the collision, the particles
come to rest. Then the angular velocity
acquired by the triangular block is (I is
the moment of inertia of the triangular
block about ( mathrm{G} ), perpendicular to the
plane of the block)
( A )
clockwise
B. ( frac{2 m v a}{l} ) clockwise
( frac{2 sqrt{3} m v a}{l} ) clockwise
D. None of these
11
48659. A particle A of mass 10/7 kg is moving in the positive
direction of x-axis. At initial position x = 0, its veloci
is 1 ms, then its velocity at x = 10 m is (use the graph
given)
Power (W)
10 (m)
Fig. 8.245
b. 2 ms-1
a. 4 ms-1
c. 312 ms -1
d. 100
3 ms1
11
4876. Mark the correct statement(s).
a. The work-energy theorem is valid only for particle
b. The work-energy theorem is an invariant law
physics.
c. The work-energy theorem is valid only in inertial
frames of reference.
d. The work-energy theorem can be applied in non-
inertial frames of reference too.
11
488A bomb at rest at the summit of a cliff
breaks into two equal fragments. One of
the fragments attains a horizontal velocity of ( 20 sqrt{3} m / s . ) The horizontal
distance between the two fragments, when their displacement vectors is inclined at ( 60^{0} ) relative to each other is
( (g=10), m / s^{wedge} 2 \$ \$ )
A ( cdot 40 sqrt{3} m )
B. ( 80 sqrt{3} m )
c. ( 120 sqrt{3} mathrm{m} )
.
D. ( 480 sqrt{3} mathrm{m} )
11
489A satellite of mass ( mathrm{m} ) is orbiting the earth in a circular orbit of radius r. It
starts losing energy due to small air
resistance at the rate of ( C J s^{-1} ). The
time taken for the satellite to reach the earth is: ( frac{G M m}{x C}left[frac{1}{R}-frac{1}{r}right] . ) Find the value of ( boldsymbol{x} )
11
490figure. The system is released from rest
and the block of mass 1 kg is found to
have a speed ( 0.3 m / s ) after it has
descended through a distance of 1 m.
The coefficient of kinetic friction
between the block and the table is (All
pulleys are massless and smooth and
strings are inextensible and light
acceleration due to gravity ( =10 m / s^{2} . ) ):
A . 0.12
B. 0.5
( c .0 . )
D. 0.15
11
491Sania, a high-board diver of mass ( 50 mathrm{kg} )
is diving from a height of ( 30 mathrm{m} ) into a pool (see figure given). What is the
potential energy of Sania at point ( A ) ?
( left(g=10 m s^{-2}right) )
A . ( 5000 J )
в. 10000 .
c. ( 15000 J )
D. 20000
11
492A bucket tied to a string is lowered at a constant acceleration of ( g / 4 ). If the mass of the bucket is ( m ) and is lowered
by a distance ( d ), the work done by the string on bucket will be:(assume the string to be massless, acceleration due
to gravity ( =g) )
A ( cdot frac{1}{4} m g d )
в. ( -frac{3}{4} m g d )
c. ( -frac{4}{3} m g d )
D. ( frac{4}{3} m g d )
11
493If under the action of fore ( boldsymbol{F}=-(boldsymbol{y} hat{boldsymbol{i}}+ )
( x hat{i} ) ) a particle moves form (0,0) to ( (a, 0) )
then to ( (a, a) ) then find work done by force
11
494Where will he have the highest potentia
energy?
A. In water
B. On land
( c . ) on
D. ons
11
495If a cricket ball hits you, it will hurt much more than a tennis ball would when moving with the same velocity because:
A. a cricket ball is bigger
B. a cricket ball has more mass
c. a cricket ball has less density
D. none of the above
11
49638. A particle of mass m moves with a variable velocity v,
which changes with distance covered x along a straight
line as v=k vx , where k is a positive constant. The work
done by all the forces acting on the particle, during the
first t seconds is
a. mk4
b. mk4,2
c. mk4 2
d. mk42
16
11
497Two,weights of ( 5 mathrm{kg} ) and ( 10 mathrm{kg} ) are placed on a horizontal table of height ( 1.5 mathrm{m} ) Which weight will have more potential energy?
( A cdot 5 mathrm{kg} )
в. ( 10 mathrm{kg} )
c. Both will have equal energy
D. None of the above
11
498Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system 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
499When a body of mass ( 1.0 mathrm{kg} ) is suspended from a certain light spring hanging vertically, its length increases by ( 5 mathrm{cm} . ) By suspending ( 2.0 mathrm{kg} ) block to the spring and if the block is pulled through ( 10 mathrm{cm} ) and released, the
maximum velocity in it in ( m / s ) is
A . 0.5
B. 1
c. 2
D. 4
11
500A mass of ( 3 mathrm{kg} ) is dropped from alower of ( 125 mathrm{m} ) high. After 3 s its ( mathrm{K} ). E. will be :
A . 1300 J
B. 1050 J
c. 750
D. 550
11
501Two identical buggies each of mass ( M ) moves one after due to inertia (without
friction) with the some velocity. A man
of mass ( m ) rides the rear buggy. At a certain moment, the manjumps into the front buggy with velocity relative to this buggy. Knowing that the mass of each buggy is equal to ( M ). Find the velocity with which the buggies will
move after that.
11
502A body of mass ( m ) is accelerated to
velocity ( v ) in time ( t^{prime} . ) The work done by the force as a function of time ( t ) will be
A ( cdot frac{m}{2} frac{v^{2} t^{2}}{t^{2}} )
B ( cdot frac{1}{2}left(frac{m v}{t^{prime}}right)^{2} t^{2} )
c. ( frac{m v}{2 t^{prime}} t^{2} )
D. ( frac{m v t^{2}}{2 t^{prime}} )
11
503A rifle bullet loses ( 1 / 20 ) th of its velocity
in passing through a plank. Assuming constant resistive force, the least
number of such planks required just to stop the bullet is:
A . 15
B. 10
( c cdot 11 )
D. 20
11
504A body starts from rest with uniform acceleration and acquires a velocity ( boldsymbol{v} )
in time ( T . ) The instantaneous kinetic
energy of the body at time ( t ) is
proportional to:
( mathbf{A} cdot(v / T) t )
B ( cdotleft(v^{2} / Tright) t^{2} )
C ( cdotleft(v^{2} / T^{2}right) t )
D. ( left(v^{2} / T^{2}right) t^{2} )
11
505Suppose that the acceleration of a free fall at the surface of a distant planet
was found to be equal to that at the surface of the earth. If the diameter of
the planet were twice the diameter of
the earth, then the ratio of mean density
of the planet to that of the earth would be:
A . 4: 1
B . 2: 1
c. 1: 1
D. 1: 2
11
506A moving body makes a perfectly inelastic collision with a second body of
equal mass at rest K.E lost during collision is of initial
K.E.
A ( cdot 1 / 4 )
B. 1/2
( c )
D.
11
507A single conservative force ( F(x) ) acts on a ( 1.0 k g ) particle that moves along the ( x- ) axis.The potential energy U(x) is given
by ( U(x)=20+(x-2)^{2} ) where ( x ) is in
meters.At ( x=5.0 m, ) the particle has a
kinetic energy of 20 J. What is the
mechanical energy of the system?
11
508Work done in lifting a body is
calculated by
A. Mass of the body ( times ) vertical distance moved
B. Force acting on a body ( times ) vertical distance moved
C. Weight acting on the body ( times ) vertical distance moved
D. None of the above
11
509A rubber develops a force ( boldsymbol{F}=(-2 x+ )
1) ( N, ) (Where ( x ) is the extension in its
natural length in ( m ) ). Work done by the force when rubber is stretched from
( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{1} boldsymbol{m} ) is :
A . ( 4 J )
B. ( 8 J )
c. ( Z ) ero
D. ( 10 J )
11
510The energy released in a modest size
atomic bomb (20 kiloton) is about ( 10^{14} )
J. On a monsoon day in Mumbai, there was a heavy rainfall of about 100 ( mathrm{cm} ) over an area of about ( 100 mathrm{km}^{2} ). The
energy released in the atmosphere on that day is roughly equivalent to that released in:
(Assume average height of clouds to be ( 2000 mathrm{m} )
A. 20 atomic bombs
B. 100 atomic bombs
c. Atomic bomb
D. Negligible compared to an atomic bomb
11
511Three vectors ( vec{A}, vec{B}, vec{C} ) satisfy the relation ( vec{A} cdot vec{B}=0 ) and ( vec{A} cdot vec{C}=0 . ) The
vector ( vec{A} ) is parallel to
A ( cdot vec{B} )
в. ( vec{c} )
c. ( vec{B} cdot vec{C} )
D . ( vec{B} times vec{C} )
11
512A ball is projected upwards. As it rises, there is increase in its:
A. Momentum
B. Retardation
c. Kinetic energy
D. Potential energy
11
513During inelastic collision between two bodies, which of the following quantities always remain conserved?
A. Total kinetic energy
B. Total mechanical energy
c. Total linear momentum.
D. speed of each body
11
514Three particles with masses 10,20 and 40 g are moving with velocities ( 10 hat{i}, 10 hat{j} ) and ( 10 hat{k} m / ) sec respectively. If due to some interaction the first particle comes to rest and the velocity of second becomes ( (3 hat{i}+4 hat{j} m / s e c) . ) Then
the velocity of third particle after their interaction is:
( mathbf{A} cdot hat{i}+hat{j}+5 hat{k} )
в. ( hat{j}+10 hat{k} )
c. ( hat{i}+hat{j}+10 hat{k} )
D. ( hat{i}+3 hat{j}+10 hat{k} )
11
515A body of mass ( M ) (figure shown above)
with a small disc of mass ( m ) placed on it rests on a smooth horizontal plane. The disc is set in motion in the
horizontal direction with velocity ( v . ) The
height (relative to the initial level) to
which the disc rise after breaking off
the body ( M ) is given as ( h= ) ( frac{M v^{2}}{x g(M+m)} . ) The friction is assumed to
be absent. Find ‘ ( x ) ‘.
11
516Given ( vec{A}=2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}+hat{j} . ) The
component of vector ( overrightarrow{boldsymbol{A}} ) along vector ( overrightarrow{boldsymbol{B}} ) is:
A ( cdot frac{1}{sqrt{2}} )
B. ( frac{3}{sqrt{2}} )
c. ( frac{5}{sqrt{2}} )
D. ( frac{7}{sqrt{2}} )
11
517Find the moment ( t_{0} ) at which the velocity vector forms an angle ( frac{pi}{4} ) with the acceleration vector.
A ( t_{0}=frac{1}{3 alpha} )
в. ( t_{0}=frac{2}{alpha} )
c. ( _{t_{0}}=frac{3}{alpha} )
D ( t_{0}=frac{1}{alpha} )
11
518The energy released on burning coal, oil, wood or gas is:
A. kinetic energy
B. heat energy
c. light energy
D. solar energy
11
519A cord is used to lower vertically a block
of mass ( M ) by a distance ( d ) with
constant downward acceleration ( boldsymbol{g} / mathbf{4} ) Work done by the cord on the block is:
A ( cdot_{M g} frac{d}{4} )
в. ( 3 M g frac{d}{4} )
c. ( _{-3 M g_{overline{4}}^{d}} )
D. ( M g d )
11
520A moving body weighing ( 400 N )
possesses ( 500 J ) of kinetic energy. Calculate the velocity with which the
body is moving. ( left(boldsymbol{g}=mathbf{1 0 m s}^{-1}right) )
11
521A man of 30 kg jumps up to a height of ( 2 mathrm{m} . ) What is his potential energy at the highest point?
A. 60 J
B. 50 J
c. 15 J
D. 600 J
11
522If the mass of the moving object is decreased ( 1 / 4 ) of its mass and its
velocity is increased to twice its previous velocity, what will be the kinetic energy of the object from the following?
A. ( 1 / 2 ) of the previous kinetic energy
B. 4 times of previous kinetic energy
c. Kinetic energy will remain constant
D. 2 times of the previous kinetic energy
11
523A tennis ball is released from height ( h ) above ground level. If the ball makes inelastic collision with the ground, to
what height will it rise after third
collision, e is the coefficient resitiution
between ball and ground?
A ( cdot h e^{6} )
B ( cdot e^{2} h )
( mathbf{c} cdot e^{3} h )
D. None of these
11
524The angle between ( overrightarrow{boldsymbol{R}}=mathbf{2} hat{mathbf{i}}+mathbf{3} hat{boldsymbol{j}}-mathbf{4} hat{boldsymbol{k}} )
and y-axis is
( ^{mathrm{A}} cdot cos ^{-1}left(frac{2}{sqrt{29}}right) )
в. ( cos ^{-1}left(frac{3}{sqrt{29}}right) )
( ^{mathrm{c}} cdot sin ^{-1}left(frac{3}{sqrt{29}}right) )
D ( cdot tan ^{-1}left(frac{3}{sqrt{29}}right) )
11
525A piece of stone placed on the roof
possesses
A. kinetic energy
B. potential energy
c. thermal energy
D. nuclear energy
11
526One of the rectangular components of a force of ( 50 N ) is ( 30 N . ) The other
rectangular component will be
A . ( 40 N )
в. ( 30 N )
( c .35 N )
D. ( 45 N )
11
527• 110 TO
15 Cous
48. Speed of the particle at A will be nearly
a. 4.0 ms-1 b. 2.8 ms- c. 3.6 ms-d. 5.6 ms-1
11
528та

Un
23. Which of the following options is correct regarding the
various work done?
a. Wgravity = -mgh
b. W friction > 0
c. Wman = mgh+ -mv2
d. Wfriction = 0
11
529A force of ( 10 mathrm{N} ) acts on a body of ( 2 mathrm{kg} ) mass for a distance of ( 1 mathrm{m} ). The kinetic
energy received by the body is:
A . 20
B. 10 J
c. 5 J
D. 2.5
11
530A coconut fruit hanging high in a palm tree has ………. owing to its location.
A. Free energy
B. Kinetic energy
c. Activation energy
D. Potential energy
11
531Two balls ( A ) and ( B ) having masses ( 1 k g )
and ( 2 k g, ) moving with speeds ( 21 m / s ) and ( 4 m / s ) respectively in opposite direction, collide head on. After collision ( A ) moves with a speed of ( 1 m / s ) in the same direction, the correct statements
is :
This question has multiple correct options
A. The velocity of ( B ) after collision is ( 6 m / s ) opposite to the direction of motion before collision
B. The coefficient of restitution is 0.2
c. The loss of kinetic energy due to collision is 200 J
D. The impulse of the force between the two balls is ( 40 mathrm{Ns} )
11
532A plot of velocity versus time is shown
in figure. A single force acts on the body.
The correct statement is?
A. In moving from ( C ) to ( D ), work done by the force on the body is positive
B. In moving from ( B ) to ( C ), work done by the force on the
body is positive
C. In moving from ( A ) to ( B ), the body does work on the
system
D. In moving from ( O ) to ( A ), work is done by the body and is negative
11
53325. A body of mass 1 kg is taken from infinity to a point
When the body reaches that point, it has a speed of 2 me1
The work done by the conservative force is – 5 J. Which
of the following is true (assuming non-conservative and
pseudo-forces to be absent).
a. Work done by the applied force is +7 J.
b. The total energy possessed by the body at Pis +7J.
c. The potential energy possessed by the body at Pis +5
d. Work done by all forces together is equal to the change
in kinetic energy.
11
534What is kinetic energy? Derive an
equation for the kinetic energy of a body of mass ‘ ( m ) ‘ moving at a speed ‘ ( v ) ‘
11
535The vector ( vec{c} ) is perpendicular to the vectors ( overrightarrow{boldsymbol{a}}=(mathbf{2},-mathbf{3}, mathbf{1}), overrightarrow{boldsymbol{b}}=(mathbf{1},-mathbf{2}, mathbf{3}) )
and satisfies the condition ( vec{c} .(hat{i}+2 hat{j}- ) ( mathbf{7} hat{k})=10 . ) Then the vector ( hat{c}= )
( A cdot(7,5,1) )
B. (-7,-5,-1)
( c cdot(1,1,-1) )
( c )
( D . ) none
11
536Illustration 8.63 A car of mass 500 kg moving with a speed
36 kmh in a straight road unidirectionally doubles its speed
in 1 min. Find the power delivered by the engine.
11
537The amount of work done in lifting a
mass ‘ ( m ) ‘ from the surface of the earth
to height ( 2 R ) is
A. ( 2 m g R )
в. ( 3 m g R )
c. ( frac{3}{2} m g R )
D. ( frac{2}{3} m g R )
11
538The mass of the particle is 2 kg. It is projected as shown in four different ways with same speed of ( 10 mathrm{m} / mathrm{s} / ). Find
out the work done by gravity by the
time the stone fails on ground.
A. 2000
B. 4000 J
c. 6000 J
D. 8000 J
11
539If ( g ) is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( mathrm{m} ) raised from the surface of the earth to a
height equal to the radius ( mathrm{R} ) of the earth, is:
( mathbf{A} cdot 2 mathrm{mgR} )
в. ( frac{1}{2} mathrm{mgR} )
c. ( frac{1}{4} mathrm{mgR} )
D. mgn
11
540Assertion
(A) : The value of coefficient
of restitution is independent of the masses and velocities of the colliding bodies but depends on their materials. Reason (R) : Coefficient of restitution is
the ratio of the relative velocity of separation or the relative velocity of approach
A. Both Assertion
(A) and Reason
(R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason
(R) are correct but the reason does not give the correct explanation
c. A is true but R is false
D. A is false but R is true
11
541A ball ( A ) is moving with velocity ( 5 m / s ) collides elastically with another identical ball ( B ) which is initially at rest
such that the velocity of ( B ) after the
collision makes an angle of ( 37^{circ} ) with the
initial velocity of ( A ). Then the
INCORRECT statement is :
A. speed of ( A ) after collision is ( 3 m / s )
B. Speed of ( B ) after collision is ( 4 m / s )
c. Balls ( A ) and ( B ) move at right angle after collision
D. Kinetic energy is not conserved as the collision is not head on
11
542A metallic wire of length ( L ) metre
extends by ( ell ) metre when stretched by suspending a weight ( M g ) from it. The mechanical energy stored in the wire is
( mathbf{A} cdot 2 M g ell )
в. ( M g ell )
c. ( frac{M g ell}{2} )
D. ( frac{M g ell}{4} )
11
543From a water fall, water is pouring down at the rate 100 kg per see on the blade of a turbine. If the height of the fall be 100 ( mathrm{m}, ) the power delivered to the turbine is approximately equal to
A. ( 100 mathrm{kW} )
B. 1 ( w )
( c cdot 1 k w )
D. 100 ( w )
11
544No work is said to have been done when
an object moves at an angle of with the direction of the
force.
A. 0
B. 90
( c cdot 180 )
D. Between 90 and 180
11
545( operatorname{Let} vec{A}=(hat{i}+hat{j}) ) and, ( vec{B}=(2 hat{i}-hat{j}) . ) The
magnitude of a coplanar vector ( overrightarrow{boldsymbol{C}} ) such that ( vec{A} cdot vec{C}=vec{B} cdot vec{C}=vec{A} cdot vec{B}, ) is given by:
A ( cdot sqrt{frac{10}{9}} )
B. ( sqrt{frac{5}{9}} )
c. ( sqrt{frac{-09}{2}^{9}} )
D. ( sqrt{frac{9}{12}} )
11
546A particle moves under the effect of a
force ( F=c x ) from ( x=0 ) to ( x=x_{1}, ) the
work done in the process is
A ( cdot c x_{1}^{2} )
B. ( frac{1}{2} c x_{1}^{2} )
( c cdot 2 c x_{1}^{2} )
D. zero
11
547A ball of mass ( 5 k g ) experience a force
( F=2 x^{2}+x . ) Work done in displacing
the ball by ( 2 mathrm{m} ) is then
A ( cdot frac{22}{3} J )
в. ( frac{44}{3} J )
c. ( frac{32}{3} J )
D. ( frac{16}{3} J )
11
548A block of mass 2 kg. is free to move
along the ( x ) -axis. It is at rest and from
( t=0 ) onwards it is subjected to a time-
dependent force ( F(t) ) in the ( x ) direction. The force ( F(t) ) varies with ( t ) as shown in the figure. The kinetic energy of the block after 4.5 second is :
11
549Identify the correct statement of Work-
Energy Theorem:
A. Work done by all the forces on a particle to displace it is equal to its change in kinetic energy.
B. Work done by all the forces on a particle is equal to its change in mechanical energy
C. Work done by all the forces acting on a particle is equal to change in its potential energy.
D. Work done by a force on a particle is equal to change in its kinetic energy.
11
550If ( vec{A} ) is perpendicular to ( vec{B}, ) then
( mathbf{A} cdot vec{A} times vec{B}=0 )
B . ( vec{A} cdot[vec{A}+vec{B}]=A^{2} )
c. ( vec{A} cdot vec{B}=A B )
D. ( vec{A} cdot[vec{A}+vec{B}]=A^{2}+A B )
11
551The velocity of a car increases from
( 54 k m / h ) to ( 72 k m / h . ) If the mass of the
car is ( 1500 k g, ) find the work done to increase the velocity.
A . ( 27000 J )
в. ( 131250 J )
c. ( 0 . )
D. ( 1500 J )
11
552A body is dropped from height 8 m. After
striking the surface it rises to ( 6 m )
what is the fractional loss in kinetic
energy during impact? Assuming the frictional resistance to be negligible.
A . ( 1 / 2 )
в. ( 1 / 4 )
c. ( 1 / 6 )
D. ( 1 / 8 )
11
553An engine draws water from a depth of ( 10 m ) with constant speed ( 2 m / s ) at the rate of ( 10 mathrm{Kg} ) per 10 second The power
of the engine is (in ( w a t t): ) (Take: ( g= ) ( 9.8 m / s^{2} )
A. 102
B. 98
( c .100 )
D. 200
11
554A block of mass m is released from rest onto a spring A
ving stiffness ka = mg/2h as shown in Fig. 8.219. If
the block compresses spring B through a distance h, find
the:
m
m
В
llllledagoon
Fig. 8.219
a. stiffness of the string B
b. equilibrium position of the block
c. maximum velocity of the block
d. maximum acceleration of the block
11
555( boldsymbol{x}>2 boldsymbol{R} )
( mathbf{A} cdot frac{2 G M m^{prime}}{(x-r)^{2}}+frac{G m m^{prime}}{(x+r)^{2}} )
( mathbf{B} cdot frac{G M m^{prime}}{2(x-R)^{2}}+frac{2 G m m^{prime}}{(x-r)^{2}} )
( mathbf{C} cdot frac{G M m^{prime}}{(x+R)^{2}}+frac{G m m^{prime}}{(x+r)^{2}} )
D. ( frac{G M m^{prime}}{(x-R)^{2}}+frac{G m m^{prime}}{(x-r)^{2}} )
11
556A small ball is suspended from a fixed
point ( boldsymbol{O} ) by means of a light and inextensible string of length ( l ). The bal is first taken aside such that string becomes horizontal and then released
from rest. At the bottom it collides with
a fixed obstacle. The coefficient of
restitution is ( e . ) Find the maximum
angular deflection of the string after ( n ) th collision
11
55716. Power supplied to a particle of mass 2 kg varies with
time as P = 37/2 W. Here t is in second. If the velocity
of particle at t=0 is v= 0, the velocity of particle at time
t = 2 s will be
a. 1 ms-1 b. 4 ms-1 c. 2 ms- d. 272 ms-
11
558What is the magnitude of angular
velocity of the stick plus puck after the collision?
A ( cdot frac{6 v_{i}}{5 l} )
в. ( frac{5 v_{i}}{6 l} )
c. ( frac{v_{i}}{l} )
D. ( frac{v_{i}}{sqrt{2} i} )
11
559A steel ball is dropped from a height ( h_{0} ) The collision of the ball with the floor is
inelastic with coefficient of restitution
e. Then, the height up to which the ball will rise after second collision is :
( mathbf{A} cdot e^{4} h_{0} )
B. 2eh
( c cdot e^{2} h_{0} )
D. ( e^{-2} h_{0} )
11
560q.1 A block is released from rest from a height ( h=5 ) m. After traveling through the smooth curved surface it moves on
the rough horizontal surface through
length ( I=8 mathrm{m} ) and climb onto the other
smooth curved surface through a height
h. If ( mu=0.5, ) find ( h )
( A cdot 2 m )
в. 3
( c cdot 1 m )
D. zero
11
561A bob of mass ( m ), suspended by a string
of length ( l_{1} ) is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it
collides elastically with another bob of mass ( m ) suspended by a string of length
( l_{1}, ) which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical
plane, the ratio ( l_{1} / l_{2} ) is
( mathbf{A} cdot mathbf{1} )
B. 3
( c .5 )
D. ( 1 / 5 )
11
and that ofmars is ( 3200 mathrm{km} ). The mass
of the earth is 10 times the mass of
mars. An object weight ( 200 mathrm{N} ) on the surface of earth. Its weight on the
surface of mars will be.
A. 80 N
B. 40 N
( c . ) 20
( D cdot 8 N )
11
563A small block of superdene material
has mass ( 2 times 10^{24} ) kg. It isn’t at a
height ( h<<R ). It falls towards earth.
Find its speed when it is at a height ( h / 2 )
A ( cdot sqrt{frac{2 g h}{3}} )
в. ( sqrt{frac{3 g h}{4}} )
c. ( sqrt{frac{2 g h}{5}} )
D. ( sqrt{frac{g h}{2}} )
11
564A block of mass ( m ) moving with speed ( v )
collides with another block of mass ( 2 m )
at rest. The lighter block comes to rest after collision. What is the value of
coefficient of restitution?
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{3}{4} )
D. ( frac{1}{4} )
11
565A ball is thrown vertically downwards from a height of ( 20 mathrm{m} ) with an initial
velocity ( v_{0} . ) It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same
height. The initial velocity ( v_{0} ) is (Take
( boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2} mathbf{)} )
A ( cdot 10 m s^{-1} )
B. ( 14 mathrm{ms}^{-1} )
( mathrm{c} cdot 20 mathrm{ms}^{-1} )
D. ( 28 m s^{-1} )
11
566A box of mass ( 50 k g ) is pulled along on
an inclined plane of ( 12 m ) length and ( 2 m )
height by a constant force of ( 100 N ) from rest. It acquires a velocity of ( 2 m / s ) when
it reaches the top of the plane. The work done against friction in joules is
A . 50
B. 100
( c cdot 150 )
D. 200
11
567A heavy steel ball of mass greater than ( 1 mathrm{kg} ) moving with a speed of ( 2 mathrm{m} / mathrm{s} ) collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision
the ping pong ball moves approximately
with a speed
A. ( 2 m / s )
в. ( 4 m / s )
c. ( 2 times 10^{4} m / s )
D. ( 2 times 10^{3} mathrm{m} / mathrm{s} )
11
568A bullet of mass ( m ) is fired with a
velocity ( v ) into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is
A ( cdot frac{m v}{2 s^{2}} )
в. ( frac{m v^{2}}{2 s} )
c. ( frac{2 s}{m v^{2}} )
D. ( frac{m s^{2}}{2 v} )
11
569A bullet of mass ( A ) and velocity ( B ) is fired into a block of wood of mass ( C . ) If loss of
any mass and friction be neglected, then velocity of the system must be
( ^{text {A }} cdot frac{A B}{A+C} )
в. ( frac{A+C}{B+C} )
c. ( frac{A C}{B+C} )
D. ( frac{A+B}{A C} )
11
570In the figure ( m_{1} ) and ( m_{2}left(m_{1}<m_{2}right) ) are
joined together by a pulley. When the mass ( m_{1} ) is released from the height ( h )
above the floor, it strikes the floor with
speed (Given: Acceleration due to gravity ( =g ) )
A ( cdot sqrt{2 g hleft(frac{m_{1}-m_{2}}{m_{1}+m_{2}}right)} )
в. ( sqrt{2 g h} )
c. ( sqrt{frac{2 m_{2} g h}{m_{1}+m_{2}}} )
D. ( sqrt{frac{2 m_{1} g h}{m_{1}+m_{2}}} )
11
571A mass of ( 10 mathrm{kg} ) is at a point ( mathrm{A} ) on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your
11
572Two particles of masses ( m_{1}, m_{2} ) movie
with initial velocities ( u_{1} ) and ( u_{2} . ) On
collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be
( v_{1} ) and ( v_{2} ) then we must have :
A ( cdot frac{1}{2} m_{1} u_{1}^{2}+frac{1}{2} m_{2} u_{2}^{2}=frac{1}{2} m_{1} v_{1}^{2}+frac{1}{2} m_{2} v_{2}^{2}-varepsilon )
B. ( frac{1}{2} m_{1} u_{1}^{2}+frac{1}{2} m_{2} u_{2}^{2}+varepsilon=frac{1}{2} m_{1} v_{1}^{2}+frac{1}{2} m_{2} v_{2}^{2} )
c. ( frac{1}{2} m_{1}^{2} u_{1}^{2}+frac{1}{2} m_{2}^{2} u_{2}^{2}-varepsilon=frac{1}{2} m_{1}^{2} v_{1}^{2}+frac{1}{2} m_{2}^{2} v_{2}^{2} )
D. ( m_{1}^{2} u_{1}+m_{2}^{2} u_{2}-varepsilon=m_{1}^{2} v_{1}+m_{2}^{2} v_{2} )
11
573A ball is dropped from a height ( h ) on a
floor of coefficient of restitution ( e ). The
total distance covered by the ball just before the second hit is
( mathbf{A} cdot hleft(1-2 e^{2}right) )
B. ( hleft(1+2 e^{2}right) )
c. ( hleft(1-e^{2}right) )
( D cdot h e^{2} )
11
574A sphere of mass ( m_{1} ) in motion hits
directly another sphere of mass ( m_{2} ) at
rest and sticks to it, the total kinetic
energy after collision is ( 2 / 3 ) of their total
K.E before the collision. Find the ratio
( boldsymbol{m}_{1}: boldsymbol{m}_{2} )
11
575Which of the following statements is/are correct about work?
This question has multiple correct options
( mathbf{A} cdot operatorname{In} ) a certain reference frame, ( W_{text {pseudo force}}+ )
( W_{text {conservattive force}}+W_{text {non-conservattive force}}+ )
( W_{text {other forces}}=Delta K )
B. Work done by friction is always negative.
C. Work done by a force is defined as the dot product of the force and the displacement of the point of application of force.
D. Work done by conservative force in moving a body from ( A ) to ( B= ) potential energy of the body at ( A ) potential energy of the body at B
11
576A block ( A ), whose weight is ( 200 N ), is
pulled up a slope of length ( 5 m ) by
means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) )
as illuminated in figure. By how much has the potential energy of the block ( boldsymbol{A} )
increased?
( A cdot 0 J )
В. ( 750 J )
( c .600 J )
D. ( 450 J )
11
577Suppose a vertical tunnel is dug along
the diameter of the earth, assumed to
be a sphere of uniform mass density ( rho )
If a body of mass ( m ) is thrown in this
tunnel, its acceleration at a distance ( y )
from the centre is given by:
A.
[
frac{4 pi}{3} G rho y m
]
B.
[
frac{3}{4} pi rho y
]
( c )
[
frac{4}{3} pi rho y
]
( D )
[
frac{4}{3} pi G rho y
]
11
578A man of mass ( mathrm{m} ) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
( W_{text {gravity}}= ) work done by gravity on the
man
( W_{text {friction}}= ) work done by gravity on the
man
( W_{text {man }}= ) work done by man Which of the following options is correct regarding the various work done? This question has multiple correct options
( mathbf{A} cdot W_{g r a v i t y}=-m g h )
B. ( W_{f r i t t i o n}>0 )
( mathbf{c} cdot W_{m a n}=m g h+frac{1}{2} m v^{2} )
D. ( W_{f r i t i o n}=0 )
11
579Why does the grinding wheels have length mass and moderate diameter?11
58010. The potential energy of the balloon
a. Decreases by mgh b. Increases by mgh
c. Increases by mg(l – h) d. Increases by mgl
11
581Two vectors ( vec{A} ) and ( vec{B} ) have magnitudes ( A=3.00 ) and ( B=3.00 . ) Their vector product is ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}=-mathbf{5 . 0 0 hat { k }}+mathbf{2 . 0 0 hat { mathbf { i } }} )
What is the angle between ( vec{A} ) and ( vec{B} ) ?
( ^{mathrm{A}} cdot sin ^{-1}left[frac{sqrt{29}}{9}right] )
( ^{mathrm{B}} cdot_{cos ^{-1}}left[frac{sqrt{29}}{9}right] )
( ^{mathrm{c}} cdot sin ^{-1}left[frac{sqrt{29}}{10}right] )
D. ( sin ^{-1}left[frac{sqrt{29}}{19}right] )
11
58237. During the first half of the motion, applied force transfers
more energy to the
a. Kinetic energy
b. Potential energy
c. Equal to both
d. Depends upon mass of the block
11
583A ball collides with a smooth fixed wall
with a velocity ( 10 mathrm{m} / mathrm{s} ) and returns with
a velocity 6 m/s. Considering oblique
collision, the coefficient of restitution ( e )
can not be:
A . 0.8
B. 0.6
c. 0.5
D. 0.4
11
584A man has a strange ability to jump
from any height to another with ease
The manjumps to P then to Q, R, S, T
and then into water. For which jump will he require the. highest energy?
A. Land to
B. s to
( c cdot Q ) to ( R )
D. R to
11
585A boy carrying a box on his head is walking on a level road from one place to another on a straight road is doing no work against gravity.
A. True
B. False
11
586A smooth rubber cord of length ( l ) whose
coefficient of elasticity is ( k ) is
suspended by one end from the point ( boldsymbol{O} ) (figure shown above). The other end is fitted with a catch ( B . ) A small sleeve ( A )
of mass ( m ) starts falling from the point
O. Neglecting the masses of the thread and the catch, find the
maximum elongation of the cord.
11
587A ball is dropped from a height h. If the coefficient of restitution be e, then to
what height will it rise after jumping
twice from the ground?
( A cdot e h / 2 )
B. 2 en
( c cdot e h )
D. ( e^{4} h )
11
588A sphere of mass ( m ) moving with a
constant velocity ( boldsymbol{v} ) hits another
stationary sphere of the same mass. If ( e )
is the coefficient of restitution, then the
ratio of the velocities of the first sphere
to the second spheres after the collision
will be :
A ( cdotleft(frac{1+e}{1-e}right) )
B ( cdotleft(frac{e-1}{e+1}right) )
c. ( left(frac{1-e}{e+1}right) )
D. ( left(frac{1+e}{e-1}right) )
11
589A body of mass 5 kg at rest is under the action of a force which gives it a
velocity given by ( v=3 t mathrm{m} / mathrm{s}, ) here ( t ) is
time in seconds. The work done by the force in two seconds will be:
( mathbf{A} cdot 90 J )
B. ( 45 J )
( c .180 J )
D. ( 30 J )
11
590( K ) is the force constant of a spring. The
work done in increasing its extension
from ( l_{1} ) to ( l_{2} ) will be:
( mathbf{A} cdot Kleft(l_{2}-l_{1}right) )
в. ( frac{K}{2}left(l_{2}+l_{1}right) )
( mathbf{c} cdot Kleft(l_{2}^{2}-l_{1}^{2}right) )
D. ( frac{K}{2}left(l_{2}^{2}-l_{1}^{2}right) )
11
591A particle is projected at ( 60^{circ} ) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is?
( A cdot K )
B. zero
c. ( K / 4 )
D. ( K / 2 )
11
592Two particles of masses ( m_{1} ) and ( m_{2} ) in
projectile motion have velocities ( v_{1} ) and
( v_{2} ) respectively at time ( t=0 . ) They
collide at time ( t_{0} . ) Their velocities
become ( v_{1}^{prime} ) and ( v^{prime}_{2} ) at time ( 2 t_{0} ) while
still moving in air. The value of
( left[left(boldsymbol{m}_{1} boldsymbol{v}_{1}^{prime}+boldsymbol{m}_{2} boldsymbol{v}_{2}^{prime}right)-left(boldsymbol{m}_{1} boldsymbol{v}_{1}+boldsymbol{m}_{2} boldsymbol{v}_{2}right)right] )
A . zero
в. ( left(m_{1}+m_{2}right) g t_{0} )
c. ( 2left(m_{1}+m_{2}right) g t_{0} )
D. ( frac{1}{2}left(m_{1}+m_{2}right) g t_{0} )
11
593Block A is hanging from a vertical spring and is at rest. Block B strikes the block A with velocity v and sticks to it. Then the value of ( v ) for which the spring just attains natural length is :
( A )
[
sqrt{frac{60 m g^{2}}{k}}
]
в.
[
sqrt{frac{6 m g^{2}}{k}}
]
c. ( sqrt{frac{10 m g^{2}}{k}} )
D. none of these
11
594Find the angular velocity of the rod after the collision.
A ( cdot omega=frac{3 v}{(4+eta) l} )
B. ( omega=frac{12 v}{(4+eta) l} )
c. ( omega=frac{3 v}{(4-eta) l} )
D. ( _{omega}=frac{12 v}{(4-eta) l} )
11
595A cubical vessel of height ( 2 mathrm{m} ) is full of water. The work done in pumping the water out of the vessel is?
A . ( 72.3 mathrm{kJ} )
B. ( 78.4 mathrm{kJ} )
c. ( 64.5 mathrm{kJ} )
D. ( 57.9 mathrm{kJ} )
11
596( x )
a small block is projected along it’s
length with velocity ( v ) towards front.
Coefficient of restitution for each
collision is ( e . ) The cart rests on a smooth
ground and can move freely. The time
taken by block to come to rest w.r.t. cart
is :
A ( cdot frac{e d}{(1-e) v} )
B. ( frac{e d}{(1+e) v} )
( c cdot d )
( bar{e} )
D. infinite
11
597Kinetic energy of a body depends on its:
A. Position
B. Velocity
c. shape
D. colour
11
598A uniform flexible chain of mass ( mathrm{m} ) and
length ( 2 ell ) hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain slips over the pin. The speed of
chain when it leaves pin is
в. ( sqrt{g ell} )
c. ( sqrt{4 g ell} )
D. ( sqrt{3 g ell} )
11
599The change in the value of ( g ) at a height
( h ) above the surface of earth is the same
as at a depth ( d ) below the earth. When
both ( d ) and ( h ) are much smaller than the
radius of earth, then which one of the
following is correct?
( ^{A} cdot_{d}=frac{h}{2} )
B. ( d=frac{3 h}{2} )
c. ( d=2 h )
( mathbf{D} cdot d=h )
11
600The weight of a person on a planet ( A ) is about half that on the Earth. He
can jump upto ( 0.4 mathrm{m} ) height on the surface of the Earth. How high he can jump on the planet ( A ) ?
( mathbf{A} cdot 0.4 mathrm{m} )
B. ( 0.2 mathrm{m} )
c. ( 0.8 mathrm{m} )
D. ( 1.6 mathrm{m} )
11
601A uniform chain has a mass ( m ) and
length ( l ). It is held on a frictionless table
with two third of its length hanging over the edge. Find the work done injust
pulling the hanging part back on the
table.
11
602A heavier body moving with certain velocity collides head on elastically with
a lighter body at rest. Then
A. smaller body continues to be in the same state of rest
B. smaller body starts to move in the same direction with same velocity as that of bigger body
c. the smaller body starts to move with twice the velocity of the bigger body in the same direction
D. the bigger body comes to rest
11
603A ball is dropped from a height of ( 10 mathrm{m} ) If the energy of the ball reduces by ( 40 % ) after striking the ground, how high can
the ball bounce back? ( left(g=10 m s^{-2}right) )
( A cdot 6 m )
B. 10 ( m )
( c cdot 3 m )
D. 12
11
6045. A block of mass m is released from rest at point
A. The compression in spring (force constant k)
when the speed of block is maximum is found to
he nmg cos e
2. What should be the value of n?
4k
u=0
Fig. 8.300
11
605(a) ( A ) ball of mass ( m ) is thrown vertically upward from the ground with an initial speed ( v, ) its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall
downward and attains the speed again before striking the ground. It implies that the magnitude of initial and final momentum of the ball are same. Yet, it
is not an example of conservation of momentum. Explain why?
(b) A bullet of mass 20 g is horizontally
fired with a velocity ( 150 m s^{1} ) from a pistol of mass 2 kg. What is the recoil velocity of the pistol?
11
606Two particles of equal mass m have respective initial velocties ( u hat{i} ) and ( uleft(frac{hat{i}+hat{j}}{2}right) . ) They collide completely inelastically. The energy lost in the
process is?
A ( cdot frac{1}{3} m u^{2} )
B. ( sqrt{frac{2}{3}} m u^{2} )
c. ( frac{3}{4} m u^{2} )
D. ( frac{1}{8} m u^{2} )
11
6073. n balls each of mass m impinge elastically each second on
a surface with velocity u. The average force experienced
by the surface will be
a. mnub . 2 mnu c. 4 mnu d. mnu/2
11
608State the energy conversion taking place in a solar cell.11
609Underline the correct alternative:
(a) When a conservative force does
positive work on a body, the potential energy of the body increases decreases / remains unaltered.
(b) Work done by a body against friction always results in a loss of its kinetic / potential energy.
(c) The rate of change of total momentum of a many-particle system is proportional to the external force / sum of the internal forces on the system.
(d) In an inelastic collision of two
bodies, the quantities which do not change after the collision are the total kinetic energy / total linear momentum
/ total energy of the system of two bodies.
11
610When an apple falls from a tree what happens to its gravitational potential energyjust as it reaches the ground?11
611Describe the energy transformation taking place in an oscillating pendulum.11
61271. The potential energy of a particle is determined by the
expression U = a (x + y), where a is a positive constant.
The particle begins to move from a point with coordinates
(3, 3), only under the action of potential field force. Then
its kinetic energy T at the instant when the particle is at a
point with the coordinates (1,1) is
a. 8 a b. 24a c. 160. d. Zero
T
1
11
613A book of mass ( 5 mathrm{kg} ) is placed on a table and it is pressed by ( 10 mathrm{N} ) force then normal force exerted by the table on the book is
A . 10 N
в. 70 N
( c . ) 59 ( mathrm{N} )
D. 50 N
11
614Two bodies of masses ‘ ( m ) ‘ and ‘2m’ are
thrown upwards with a velocity of ‘ ( u^{prime} )
and ‘3 ( u ) ‘ from the surface respectively.
What is the ratio of their potential energies at the highest point?
A . 1: 9
в. 3: 1
( mathbf{c} cdot 1: 18 )
D. 4: 1
11
615Define the following terms:
Kinetic energy.
11
616An object is displaced from position
vector ( r_{1}=(2 i+3 j) m ) to ( r_{2}=(4 i+6 j) m ) under
the action of a force ( F=left(3 x^{2} i+2 y jright) N . ) Finf the work done by this force.
11
617A car is moving along a straight level road with constant speed. Then
A. The work done on the car is infinite
B. The work done on the car is zero
c. The work done on the car is a measure of the gravitational potential energy
D. The work done on the car cannot be found
11
618Force acting on a particles moving in a
straight line varies with the velocity ( v ) of
the particles as ( boldsymbol{F}=boldsymbol{K} ) where ( boldsymbol{K} ) is a
constant. The work done by this force in time ( t ) is
A ( cdot frac{K}{v^{2}} t )
в. ( 2 K t )
c. all the above
D. None of these
11
619Two object collides elastically mass ( 2 m )
is moving with velocity ( U ) and mass ( m ) is initially at rest. After the collision, the
objects move away with velocities ( u )
and ( v, ) as shown in above figure.
Find the relation between ( u ) and ( v ? )
A ( cdot 2 u cos 30^{circ}=v cos 60^{circ} )
B ( cdot u cos 30^{circ}=2 v cos 60^{circ} )
c. ( 2 u sin 30^{circ}=v sin 60^{circ} )
D. ( u sin 30^{circ}=2 v sin 60^{circ} )
E ( cdot u sin 30^{circ}=v cos 60^{circ} )
11
620Fig. shows a bead of mass ( m ) moving
with uniform speed ( v ) through a ( U- )
shaped smooth wire the wire has a semicircular bending between ( A ) and
B. Calculate the average force exerted
by the bead on the part ( A B ) of the wire.
11
621A projectile is fired with the a speed ( u )
at an angle ( theta ) above the horizontal field. The coefficient of restitution be tween
the projectile and filed is e. Find the position from the starting point when the projectile will land at its second
collision
A ( cdot frac{e^{2} u^{2} sin 2 theta}{g} )
B. ( frac{left(1+e^{2}right) u^{2} sin 2 theta}{g} )
( ^{mathbf{C}} cdot frac{left(1+e^{2}right) u^{2} sin theta cos theta}{g} )
D. ( frac{(1+e) u^{2} sin 2 theta}{g} )
11
622In the game of cricket, the stumps falls when the ball strikes them. This is an
example of
A. contact force
B. Non contact force
c. Displacement force
D. None
11
623A ( 10 k g ) ball is dropped from a height of 10 ( m ). Find (a) the initial potential
energy of the ball,
(b) the kinetic energy just before it reaches the ground, and
(c) the speed just before it reaches the ground.
11
6242. A body is moved along a straight line by a machine deliv-
ering constant power. The distance moved by the body in
time t is proportional to
(IIT JEE, 1984)
2 1/2 b. 3/4 c. 812 d. p.
11
625Rakesh lifts a heavy book from the floor
of the room and puts it in the book shelf
of height ( 2 m . ) In this process, he takes 5 seconds. On which of the following does the work done by him depend?
A. Mass of the book and the time taken to do work
B. Weight of the book and the height of the book shelf
c. Height of the book shelf and the time taken to do work
D. Mass of the book, height of the book shelf and the time taken to do work
11
626A hollow smooth uniform sphere ( boldsymbol{A} ) of
mass ( m ) rolls without sliding on a
smooth horizontal surface. It collides
stationary smooth hollow sphere ( boldsymbol{B} ) of
the same mass mm and same radius.
The ratio of the kinetic energy of ( boldsymbol{B} ) to that of ( A ) just after the collision is
A . 1: 1
B. 2: 3
( c cdot 3: 2 )
D. None
11
627A body explodes in mid-air. Does its momentum remain conserved?11
62817. A vehicle of mass m starts moving along a horizontal
circle of radius R such that its speed varies with distances
covered by the vehicle as c= KVs, where K is a constant.
Calculate:
a. Tangential and normal force on vehicle as function of
b. Distance s in terms of time t.
c. Work done by the resultant force in first t seconds after
the beginning of motion.
11
629A diver stands at the top of a platform
that is 15 meters high.After diving, she challenges herself from a cliff that is 30
meters high.since she is twice as far
from the surface of the earth when she
is on the cliff as compared with the diving board, how does her weight on the cliff compare with her weight on the
diving board?
A. Her weight on the cliff is half as much
B. Her weight on the cliff is one-fourth as much
C. Her weight on the cliff is about the same
D. Her weight on the cliff is twice as much
E. Her weight on the cliff is four times as much
11
630The work done in turning a magnet of
magnetic moment ( M ) by an angle of ( 90^{circ} )
from the meridian is ( n ) times the
corresponding work done to turn it
through an angle of ( 60^{circ} . ) Where ( n ) is
given by
A ( cdot 1 / 2 )
B. 2
c. ( 1 / 4 )
D.
11
631Write an expression for the magnitude
of the resultant vector ‘R’ of two vectors
( vec{A} ) and ( vec{B} ) acting at a point. When will this resultant vector ‘R’ be maximum?
11
632A ball is allowed to fall from a height of
( 10 mathrm{m} . ) If there is ( 40 % ) loss of energy due to impact, then after one impact ball will go upto:
A. ( 10 m )
B. ( 8 m )
( c .4 m )
D. ( 6 m )
11
6338. A man slowly pulls a bucket of water from a well of depth
h = 20 m. The mass of the uniform rope and bucket full
of water are m= 200 g and M 19.9 kg, respectively. Find
the work done (in kJ) by the man.
11
634Water stored in a dam possesses:
A. no energy
B. electrical energy
c. kinetic energy
D. potential energy
11
635Calculate energy needed for moving a mass of ( 4 k g ) from the centre of the earth
to its surface (in joule). If radius of the
earth is ( 6400 mathrm{km} ) and acceleration due
to gravity at the surface of the earth is
( boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s e c ^ { 2 }} )
A ( cdot 1.28 times 10^{8} J )
в. ( 1.28 times 10^{6} J )
c. ( 2.56 times 10^{8} J )
D. ( 2.56 times 10^{1} 0 J )
11
636If ( |vec{A}+vec{B}|=|vec{A}|=|vec{B}| ) the angle
between ( A ) and ( B ) will be :-
A ( cdot 90^{circ} )
B . ( 120^{circ} )
( c cdot 0^{c} )
D. ( 60^{circ} )
11
637A force ( F=-6 x^{3} ) is acting on a block
moving along x-axis. Work done by this
force is:
This question has multiple correct options
A. Positive in displacing the block from ( x=3 ) to ( x=1 )
B. Positive in displacing the block from ( x=-3 ) to ( x=-1 )
c. Negative in displacing the block from ( x=0 ) to ( x=4 )
D. zero in displacing the block from ( x=-2 ) to ( x=+2 )
11
638A bullet of mass 20 g moving with a velocity of ( 500 mathrm{m} / mathrm{s} ), strikes a tree and goes out from the other side with a velocity of ( 400 mathrm{m} / mathrm{s} ). Calculate the work done by the bullet (injoules) in passing through the tree.
( mathbf{A} cdot 900 J )
B. ( 800 J )
c. ( 950 J )
D. ( 500 J )
11
639A solid sphere rolls without slipping on
a rough horizontal floor, moving with a
speed ( boldsymbol{v} . ) It makes an elastic collision
with a smooth vertical wall. After
impact,

This question has multiple correct options
A. it will move with a speed ( v ) initially.
B. its motion will be rolling without slipping
C. its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.
D. its motion will be rolling without slipping only after some time.

11
640is said to be done only when the force applied on a body makes the body
to move.
A. work
B. Momentum
c. Retardation
D. None of these
11
641An overhead tank having some water
possesses ( ldots ) mergy.
A. Kinetic
B. Potential
c. Thermal
D. Electrical
11
642A wire suspended vertically from one of its ends is stretched by attaching a weight of ( 200 mathrm{N} ) to the lower end. The weight stretches the wire by 1 mm. Then the energy stored in the wire is
A . 0.1
B. 0.2
c. 10
D. 20
11
643A system is provided 50 joule of heat and work done no the system is 10 J. The change in in iternal energy during the process is
A . ( 40 mathrm{J} )
B. 60 J
c. 80
D. 50 J
11
64416. The blocks A and B shown in Fig. 8.238 have masses MA
= 5 kg and MB = 4 kg. The system is released from rest.
The speed of B after A has travelled a distance 1 m along
the incline is
5 m
37°
Fig. 8.238
11
64568. Two constant forces É 2 act on a body of mass 8 kg.
These forces displace the body from point P (1, 2, 3) to Q
(2,3,7) in 2 s starting from rest. Force F, is of magnitude
9 N and is acting along vector (2î – 2j + k). Work done
by the force F2 is
a. 80J b. -80 J C. -180 J d. 180 J
11
646toppr ( t )
Which of the diagrams shown In
( (overline{4}) )
figure correctly shows the change in kinetic and potential energy of the drop
during its fall up to the ground?
( A )
B.
( c )
( D )
11
647The coefficient of restitution (e) for a
perfectly elastic collision is
A . -1
B.
( c cdot alpha )
( D )
11
648In a shotput event, an athlete throws the
shotput of mass ( 10 k g ) with an initial
speed of ( 1 m s^{1} ) at ( 45^{circ} ) from a height
( 1.5 m ) above ground. Assuming air resistance to be negligible and
acceleration due to gravity to be ( 10 m s^{2} )
the kinetic energy of the shotput when it just reaches the ground will be:
A . 2.5 .5
в. ( 5.0 J )
c. ( 52.5 J )
D. ( 155.0 J )
11
649A spring of force constant ( mathrm{k}=300 mathrm{N} / mathrm{m} ) connects two blocks having masses 2 kg and 3 kg, lying on a smooth horizontal plane. If the spring block system is released from a stretched position, find the number of complete oscillations in 1 minute. Take ( pi=sqrt{10} )
A .44
B. 150
( c cdot 34 )
D. 55
11
650Kinetic energy of the liquid per unit mass is
( mathbf{A} cdot frac{1}{2} m v^{2} )
B ( cdot frac{1}{2} v^{2} )
C ( cdot frac{1}{2} m^{2} v )
D. ( m v^{2} )
11
651A 5 kg mass moving at a speed of ( 13 m s^{-1} ) collides head on with a body of
mass ( 1 mathrm{kg} ) at rest, if they move with a common velocity after collision in the same direction, find the velocity?
A ( cdot 103 mathrm{ms}^{-1} )
B . ( 10.83 mathrm{ms}^{-1} )
c. ( 1.03 mathrm{ms}^{-1} )
D. ( 20 mathrm{ms}^{-1} )
11
652Which one of the following statements
does hold good when two balls of
masses ( m_{1} ) and ( m_{2} ) undergo elastic
collision?
A. When ( m_{1}m_{2} ) and ( m_{2} ) at rest, after collision the ball of mass ( m_{2} ) moves with four times the velocity of ( m_{1} )
c. When ( m_{1}=m_{2} ) and ( m_{2} ) at rest, there will be maximum
transfer of K.E
D. When collision is oblique and ( m_{2} ) at rest with ( m_{1}=m_{2} ) after collision the ball moves in opposite direction
11
653Statement A : A neutron travelling with a velocity collides head on an atom of
atomic mass number ( A ) at rest. The
fraction of the total energy retained by neutron is ( left(frac{A-1}{A+1}right)^{2} )
Statement B : The kinetic energy
conserves during an elastic collision
( A cdot A ) and ( B ) are true
B. A is true but B is false
c. A is false but B is true
D. A and B are false
11
65427. Work done by gravity to w.r.t. the conveyor belt is
a. -mgh
b. -= mgh
2
mgh
d. None of above
11
655The angle between the diagonals of a cube with edges of length 1 is:
( A cdot sin ^{-1}(1 / sqrt{3}) )
B . ( cos ^{-1}(1 / sqrt{3}) )
c. ( tan ^{-1}(1 / sqrt{3}) )
D. ( cot ^{-1}(1 / sqrt{3}) )
11
656The work done in dragging a stone of mass 100 kg up an inclined plane 1 in 100 through a distance of ( 10 mathrm{m} ) is:
A . 100 J
B. 980 J
c. 9800
D. 98 J
11
657A ball of mass ( 100 g ) is thrown with a
speed of ( 15 mathrm{m} / mathrm{s} ). Calculate its kinetic
energy.
11
658A neutron moving with a certain kinetic energy collides head on with an atom of mass number A. The fractional kinetic
energy retained by it is
A ( frac{A-1}{A+1} )
( ^{mathrm{B}}left(frac{A+1}{A-1}right)^{2} )
c. ( frac{A+1}{A-1} )
( ^{D cdot}left(frac{A-1}{A+1}right)^{2} )
11
659Potential energy function describing the interaction between two atoms of a
diatomic molecule is ( U(r)=frac{a}{r^{12}}-frac{b}{r^{6}} )
Force acting between them will be zero
when the distance between them would
be
A
( left(frac{a}{b}right)^{frac{1}{6}} )
11
660Student A and student B sit in identical
office chairs facing each other, as
shown in figure. Student A is heavier
than student B. Student A suddenly pushes with his feet. Which of the following statements related to
momentum is correct?
A. Momentum of A is greater than momentum of
B. Momentum of A and B are equal but opposite in direction
9 mentum of of B is greater than momentum of
D
direction
11
661A constant force acting on a body of mass ( 3.0 mathrm{kg} ) changes its speed from ( 2.0 mathrm{ms}^{-1} ) to ( 3.5 mathrm{ms}^{-1} ) in ( 25 mathrm{s} ). The
direction of the motion of the body
remains unchanged. What is the magnitude of the force (in newton)?
A . 0.18
в. 0.36
c. 0.72
D. 0.24
11
662toppr
following graph best represents the relation between the force exerted by
the table on the chain with time?
(Assume that the fallen part
immediately comes to rest after
collision with table and does not form a
heap)
( A )
3
( c )
D
11
663Car ( X ) of mass 200 kg moving at ( 5 mathrm{m} / mathrm{s} ) collides with car Y of mass ( 300 mathrm{kg} ) moving in the same direction at ( 3 mathrm{m} / mathrm{s} ) After the collision they move off together. What is their common velocity just after the collision?
A. ( 4.2 mathrm{m} / mathrm{s} )
B. ( 5.6 mathrm{m} / mathrm{s} )
( c cdot 3.8 m / s )
D. ( 7.8 mathrm{m} / mathrm{s} )
11
664Calculate the work done in moving the
object from ( x=2 ) to ( x=3 mathrm{m} ) from the
given graph.
11
665A marble going at a speed of ( 12 m s^{-1} ) hits another marble of equal mass at rest. If the collision is perfectly elastic. Find the velocity of the first after collision.
A . 4
B.
c. 2
D. 3
11
666A particle of mass ( 0.5 k g ) travels in a straight line with velocity ( boldsymbol{v}=boldsymbol{a} boldsymbol{x}^{3 / 2} )
where ( a=5 m^{-1 / 2} s^{-1} . ) What is the work
done by the net force during its displacement from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{2 m} ? )
11
667A ball is dropped from a height ( 8 mathrm{m} ) on a smooth horizontal surface. If height attained by the ball after the second
collision is ( 2 mathrm{m} ), then the coefficient of
restitution is :
A ( cdot frac{1}{4} )
B. ( frac{1}{2} )
c. 1
D. ( frac{1}{sqrt{2}} )
11
668A particle moves in ( x y ) plane. The position vector at any time ( t ) is ( vec{r}= ) ( left{(2 t) hat{i}+left(2 t^{2}right) hat{j}right} m . ) The rate of change of ( theta ) at time ( t=2 ) second (where ( theta ) is an
angle which its velocity vector makes
with positive ( x-a x i s) ) is:
A ( cdot frac{2}{17} operatorname{rad} / s )
в. ( frac{1}{14} r a d / s )
c. ( frac{4}{7} ) rad ( / ) s
D. ( frac{6}{5} ) rad ( / ) s
11
669A light and a heavy body have equal kinetic energies. The light body has greater momentum.
A. True
B. False
11
670In a one-dimensional collision between
two identical particles ( boldsymbol{A} ) and ( boldsymbol{B} . boldsymbol{B} ) is
stationary and ( A ) has momentum ( p )
before impact. During impact, ( B ) gives
an impulse ( J ) to ( A ). Find the coefficient
of restitution between ( A ) and ( B ? )
11
671The potential energy between two atoms in a molecule is given by, ( U_{(x)}=frac{a}{x^{12}}- ) ( frac{B}{X^{6}}, ) where a and b are positive
constants and ( x ) is the distance
between the atoms. The system is in stable equilibrium when –
( mathbf{A} cdot x=0 )
B ( cdot x=frac{a}{2 b} )
c. ( x=left(frac{2 a}{b}right)^{1 / 6} )
D. ( x=left(frac{11 a}{5 b}right) )
11
672A uniform rod is resting freely over a
smooth horizontal plane. A particle
moving horizontally strikes at one end
of the rod normally and gets stuck. Then
This question has multiple correct options
A. the momentum of the particle is shared between the particle and the rod and remains conserved
B. the angular momentum about the mid-point of the rod before and after the collision is equal
C. the angular momentum about the centre of mass of the combination before and after the collision is equal
D. the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle
11
673Consider the following statements ( A ) and ( mathrm{B} ) and identify the correct answer:
( A: ln ) an elastic collision, if a body
suffers a head on collision with another
of same mass at rest, the first body
comes to rest while the other starts
moving with the velocity of the first one.
( B: ) Two bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities.
A. A and B are true
B. A and B are false
c. A is true but B is false
D. A is false but B is true
11
674A block of mass ( 20 mathrm{kg} ) is slowly slid up on a smooth incline of inclination53 ( ^{o} ) by
a person. Calculate the work done by the person in moving the block through a distance ( 4 mathrm{m}, ) if the driving force is ( (mathrm{a}) ) parallel to the incline and (b) in the
horizontal direction. ( left[boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right] )
11
67521. The kinetic energy K of a particle moving along a circle
of radius R depends upon the distance s as K = as?. The
force acting on the particle is
7112
82
a. 2a \$
b. 2as 1+
asli
c. 2as
d. 2a
11
676A man, of mass ( m ), standing at the bottom of the staircase, of height ( boldsymbol{L} )
climbs it and stands at its top.
This question has multiple correct options
A. Work done by all forces on man is equal to the rise in potential energy mgL
B. Work done by all forces on man is zero
c. work done by the gravitational force on man is mgL
D. The reaction force from a step does not do work because the point of application of the force does not move while the force exists
11
67728. A massless platform is kept on a light elastic spring as
shown in Fig. 8.231. When a particle of mass 0.1 kg is
dropped on the pan from a height of 0.24 m, the particle
strikes the pan, and the spring is compressed by 0.01 m.
From what height should the particle be dropped to cause
a compression of 0.04 m?
0.1 kg
Fig. 8.231
b. 2.96 m c. 3.96 m
a. 0.96 m
d. 0.48 m
11
678Kinetic energy is proportional to
This question has multiple correct options
A. velocity
B. mass
C . square of velocity
D. acceleration
11
679Two bodies of equal weight are kept at heights of ( h ) and ( 1.5 h ) respectively. The
ratio of their P.E. is:
( A cdot 3: 2 )
B. 2: 3
c. 1: 1
D. None of these
11
680A rocket is moving in a gravity free space with a constant acceleration of
( 2 m s^{-2}, ) along ( +x ) direction (see figure) The length of a chamber inside the
rocket is ( 4 mathrm{m} ). A ball is thrown from the
left end of the chamber in ( +x ) direction with a speed of ( 0.3 m s^{-1} ) relative to the rocket. At the same time, another ball
is thrown in – ( x ) direction with a speed of
( 0.2 m s^{-1} ) from its right end relative to the rocket. The time in seconds when
the two balls hit each other is
( A )
( B .3 )
( c )
( D )
11
681A ball of mass ( 0.2 mathrm{kg} ) is thrown vertically upwards by applying a force by hand. If the hand moves ( 0.2 mathrm{m} ) while applying
the force and the ball goes up to 2 in height further, find the magnitude of
the force. Consider ( g=10 m / s^{2} )
( A cdot 16 N )
B. 20 N
c. 22
D. ( 180 mathrm{N} )
11
682State work energy theorem. Plot spring
force ( F ) versus ( x ) and obtain the
expression for elastic potential energy of spring.
11
683A body moves through a distance of ( ^{prime} boldsymbol{m}^{prime} )
in the following different ways. In which case is the maximum work done?
A. when pushed over an inclined plane
B. when lifted vertically upward
c. when pushed over smooth rollers
D. when pushed on a plane horizontal surface
11
684A glass ball collides with a smooth horizontal surface with a velocity ( a hat{i}- )
b ( hat{j} ). If the coefficient of restitution of
collision be ( e, ) find the velocity of the ball just after the collision.
11
685If the potential energy of two molecules is give by, ( U=frac{A}{r^{12}}-frac{B}{r^{6}} ) then at
equilibrium position, its potential energy is equal to?
A ( cdot frac{A^{2}}{4 B} )
B. ( -frac{B^{2}}{4 A} )
c. ( left(frac{2 A}{B}right)^{frac{1}{6}} )
D. 3A
11
686A block of mass ( m ) is moving with a
constant acceleration ( a ) on a rough
horizontal plane. If the coefficient of friction between the block and ground is
( mu, ) the power delivered by the external
agent in a time interval ( t ) from the
beginning is equal to:
A ( cdot m a^{2} t )
в. ( mu ) mgat
( mathbf{c} cdot mu m(a+mu g) g t )
D. ( m(a+mu g) a t )
11
6876. In Fig. 8.301, shown all the surfaces are frictionless,
and mass of the block is m = 100 g. The block and the
wedge are held initially at rest. Now the wedge is given a
horizontal acceleration of 10 ms? by applying a force on
the wedge, so that the block does not slip on the wedge.
Then find the work done in joules by the normal force in
ground frame on the block in 1 s.
10 ms 2
Fig. 8.301
11
688A body of mass ( 6 mathrm{kg} ) is under a force of 6 N which causes displacement in it given by ( S=frac{t^{2}}{4} ) at where ‘t’ is time. The
work done by the force in 2 s is:
A . 12
B. 9 J
c. 6 J
D. 3 J
11
689( vec{A} ) and ( vec{B} ) are two vectors ( operatorname{given} vec{A}= ) ( 2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}+hat{j} . ) The magnitude of the component ( vec{A} ) along ( vec{B} ) is11
690Which is incorrect?
( mathbf{A} cdot K cdot E cdot propto(operatorname{moment} u m)^{2} )
B. ( K . E . propto(text {velocity})^{2} )
C. ( K . E . propto(operatorname{mas} s)^{2} )
D. ( K . E . propto ) mass
11
691Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.11
692A metal bullet moving at ( 400 mathrm{ms}^{-1} ) strikes on a tree trunk and get
embedded inside it. Assuming total kinetic energy is converted to heat and ( 50 % ) of heat is absorbed by the bullet,
find the increase in its temperature. (specific heat capacity of metal ( = ) ( 200 J k g^{-1} K^{-1} ) and bullet not melts
11
693A vertical spring with force constant ( k )
is fixed on a table. A ball of mass ( mathrm{m} ) at a
height h above the free upper end of the
spring falls vertically on the spring so that the spring is compressed by a
distance d. The net work done in
the process is
( ^{mathbf{A}} cdot m g(h+d)-frac{1}{2} k d^{2} )
B . ( m g(h-d)-frac{1}{2} k d^{2} )
c. ( m g(h-d)+frac{1}{2} k d^{2} )
D ( m g(h+d)+frac{1}{2} k d^{2} )
11
694On a smooth surface there are five
identical equally spaced balls ( A, B, C, D ) and E present with initial velocities ( 10 mathrm{m} / mathrm{s},-5 mathrm{m} / mathrm{s}, 2 mathrm{m} / mathrm{s},-3 mathrm{m} / mathrm{s} )
( 3 mathrm{m} / mathrm{s} ) respectively, Collision between any two ball assumed to be elasitc.
Then after all possible collision which pair of balls will have same speed as of initial
( A cdot A & D )
B. B &
( c cdot c & D )
( D cdot A & C )
11
695One end of a spring of natural length
( ell_{0}=0.1 mathrm{m} ) and spring constant ( mathrm{k}=80 )
N/m is fixed to the ground and other
end is fitted with a smooth ring of mass ( mathbf{m}=2 mathrm{gm}, ) which is allowed to slide on a
horizontal rod fixed at a height ( h= ) ( 0.1 mathrm{m} . ) Initially, the spring makes an
angle of ( 37^{circ} ) with vertical when the
system is released from rest.

When the spring becomes vertical,
speed of ring is ‘ ( v^{prime} mathrm{m} / mathrm{s}, ) find ‘ ( v ) ‘. ( left(cos 37^{circ}=frac{4}{5}right) )

11
696A ball falls on the ground from a height of ( 2.0 m ) and rebounds up to a height of 1.5 ( m . ) Find the coefficient of restitution11
697A particle of mass ( M, ) moving with a
velocity ( u ) makes a head on collision
with a particle of ( m ) initially at rest so that the final velocities are along the
same line. If the collision is elastic and ( frac{M}{m}=k, ) then the final velocity of the second particle of mass ( boldsymbol{m} ) is :
A ( frac{2 u}{1+k} )
В ( frac{2 k u}{1+k} )
c. ( frac{2 u}{1-k} )
D. ( frac{k M u^{2}}{2(1-k)} )
11
698Two particles of mass ( m ), constrained to move along the circumference of a smooth circular hoop of equal mass ( m )
are initially located at opposite ends of
a diameter and given equal velocities ( v_{0} )
shown in the figure. The entire
arrangement is located in gravity free space. Their velocityjust before collision is?
( A )
в. ( frac{sqrt{3}}{2} v_{0} )
c. ( frac{2}{sqrt{3}} v )
D. ( frac{sqrt{7}}{3} v_{0} )
11
699What is the speed of the proton when it is ( 8 A ) away from the nucleus?
A ( cdot 1.85 times 10^{5} mathrm{ms}^{-1} )
В. ( 1.85 times 10^{4} m s^{-1} )
c. ( 1.85 times 10^{3} m s^{-1} )
D. ( 1.85 times 10^{2} mathrm{ms}^{-1} )
11
Suppose two particles 1 and 2 are projected in vertical plane
simultaneously.
Their angles of projection are ( 30^{circ} ) and ( theta )
respectively, with the horizontal. Let
they collide after a time ( t ) in air. Then
This question has multiple correct options
A ( cdot theta=sin ^{-1}(4 / 5) ) and they will have same speed just
before the collision
B . ( theta=sin ^{-1}(4 / 5) ) and they will have different speed just
before the collision
C . ( x<1280 sqrt{3}-960 m )
D. It is possible that the particles collide when both of them are at their highest point.
11
701A body of mass 2 kg starts with an initial velocity ( 5 mathrm{m} / mathrm{s} ). If the body
is acted upon by a time dependent force
(F) as shown in the figure, then work
done on the body in 20 s is
11
702Work-energy theorem is valid in the
presence of
A. External forces only
B. Internal forces onlhy
c. conservative forces only
D. All type of forces
11
703The speed of the disc ( M ) is
( A cdot 0 )
B. ( frac{v_{0}}{2} )
( c cdot frac{200}{sqrt{5}} )
( D cdot v_{0} )
11
704An object of mass ( m ) is tied to a string
of length ( l ) and a variable force ( F ) is
applied on it which brings the string
gradually at an angle ( theta ) with the vertical
Find the work done by the force ( F )
A. ( m g l(1-cos theta) )
в. ( m g l(2-cos theta) )
c. ( _{m g l}left(1-frac{cos theta}{2}right) )
D ( cdot operatorname{mgl}left(2-frac{cos theta}{2}right) )
11
705U. 4VEA
50. Two identical blocks A and B are placed on two inclined
planes as shown in Fig. 8.241. Neglect resistance and other
friction.
Fixed
1
Fixed
h
21
– KM
Fig. 8.241
Read the following statements and choose options.
Statement I: The kinetic energy of A on sliding to I will
be greater than the kinetic energy of B on sliding to 0.
Statement II: The acceleration of A will be greater than
acceleration of B when both are released on the inclined
plane.
Statement III: The work done by external agent to move
the block slowly from position B to O is negative.
a. Only statement I is true
b. Only statement II is true
c. Only I and III are true
d. Only II and III are true
11
7064. The power exerted on the body at 2 s is
a. 50 W b. 100 W c. 150 W d. 200 W
11
707An object ( A ) of mass ( 1 k g ) is projected vertically upward with a speed of ( 20 m / s . ) At the same moment another object ( B ) of mass ( 3 k g, ) which is initially
above the object ( A ), is dropped from a
height ( h=20 m . ) The two point like
objects ( (A text { and } B) ) collide and stick to
each other. The kinetic energy is ( boldsymbol{K} ) (in ( boldsymbol{J} )
of the combined mass just after collision, find the value of ( boldsymbol{K} / mathbf{2 5} )
11
708Find the angle between ( overrightarrow{boldsymbol{A}}=mathbf{4} hat{mathbf{i}}+hat{mathbf{j}}+ )
( mathbf{3} hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}+mathbf{3} hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}} )
11
709The work done in bringing three
particles each of mass ( 10 g m ) from large distances to the vertices of an
equilateral triangle of side ( 10 mathrm{cm} ) is
A ( cdot 10^{-13} J )
( J )
В. ( 2 times 10^{-13} mathrm{J} )
c. ( 4 times 10^{-11} J )
D. ( 10^{-11} J )
11
710P5
13. A 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.
a. p and E are conserved if both X and Y are free to
move.
b. (a) is true only if X and Y have 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
711An elevator platform is going up at a
speed ( 20 mathrm{ms}^{-1} ) and during its upward motion a small ball of 50 g mass falling
in downward direction strikes the
platform elastically at a speed ( 5 mathrm{ms}^{-1} ) Find the speed (in ( mathrm{ms}^{-1} ) ) with which the
ball rebounds:
11
712A cricket ball and a ping-pong ball are dropped from the same height in a vacuum chamber. When they have
fallen half way down, they have the
same:
A. velocity
B. potential energy
c. kinetic energy
D. rest energy
11
713A particle of mass ( mathrm{m} ) is attached to one
end of a massless spring of force
constant ( mathrm{k}, ) lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time ( t=0 ) with
an initial velocity ( u_{0} . ) When the speed of
the particle is ( 0.5 u_{0} . ) It collides elastically with a rigid wall. After this collision.
This question has multiple correct options
A. The speed of the particle when it returns to its equilibrium position is ( u_{0} )
B. The time at which the particle passes through the equilibrium position for the first time is ( t=pi sqrt{frac{m}{k}} )
c. The time at which the maximum compression of the spring occurs is ( t=frac{4 pi}{3} sqrt{frac{m}{k}} )
D. The time at which the particle passes through the equilibrium position for the second time is ( t= ) ( frac{5 pi}{3} sqrt{frac{m}{k}} )
11
714Two particles ( A ) and ( B ) are moving with
constant velocities ( v_{1} ) and ( v_{2} cdot A t t=0, v_{1} )
makes an angle ( theta_{1} ) with the line joining
( A ) and ( B ) and ( v_{2} ) makes an angle ( theta_{2} ) with
the line joining ( A ) and ( B ). Find their
velocity of approach
11
71534. A person of mass 70 kg jumps from a stationary helicopter
with the parachute open. As he falls through 50 m height,
he gains a speed of 20 ms. The work done by the viscous
air drag is
a. 21000 J
b. -21000 J
c. -14000 J
d. 14000 J
Abortiol, looted in
one dimensional notential field hoe
11
716A boy held a book of ( 1 mathrm{kg} ) at a height of 1 metre for 60 seconds. Calculate the
work done :
A . 60 J
B. 30 J
c. 15 J
D.
11
717A body of mass ( 300 mathrm{kg} ) is moved
through ( 10 m ) along a smooth inclined
plane of an angle ( 30^{circ} . ) The work done in moving the mass in joules is:
( left(g=9.8 m s^{-2}right) )
A. 9800
B. 14700
( c .3450 )
D. 4900
11
718A rigid massless rod of length ( boldsymbol{L}=mathbf{1} boldsymbol{m} )
joins two particles each of mass ( m= )
1 kg. The rod lies on a frictionless table,
and is struck by a particle of equal
mass ( m=1 k g ) and velocity ( v_{0}=7 sqrt{2} )
moving as shown in the figure. After the collision the partcle moves straight back. Calculate the angular velocity of mass after collision, assuming that collision is perfectly elastic.
11
719A machine raises a load of ( mathbf{7 5 0} boldsymbol{N} )
through a height of ( 16 m ) in ( 5 s . ) Calculate
energy spent by machine:
A. ( 12000 k J )
в. ( 12 k J )
c. ( 1200 J )
D. ( 120 k J )
11
720A block of mass ( 0.5 k g ) is moving with a speed of ( 2.0 m / s ) on smooth surface. It
strikes another mass of ( 1.0 k g ) and then they move together as a single body. The energy loss during collision is (in J)
A . 0.16
B. 0.67
c. 1.0
D. 6.7
11
721A neutron moving with velocity u collides with a stationary ( boldsymbol{alpha}- ) particle
The velocity of the neutron after collision is
A. ( -frac{30}{5} )
в. ( frac{30}{5} )
c. ( frac{20}{5} )
D. ( -frac{2 U}{5} )
11
722A body freely falls from a certain height
on to the ground in a time ( t . ) During the
first one third of the time interval it
gains a kinetic energy ( Delta k_{1} ) and during the last one-third of the interval, it gains
a kinetic energy ( Delta k_{2} ). The ratio ( Delta k_{1} )
( boldsymbol{Delta} boldsymbol{k}_{2} ) is:
A . 1: 1
B. 1: 3
c. 1: 4
D. 1: 5
11
723A particle ( (boldsymbol{m}=mathbf{1} boldsymbol{k} boldsymbol{g}) ) slides down a
frictionless rack (AOC) starting from
rest at a point ( A ) (height ( 2 m ) ). After
reaching ( C, ) the particle continuous to
move freely in air as a projectile. When
it reaching its highest point ( boldsymbol{P} ) (height
1 ( m ) ), the kinetic energy of the particle
(in J) is : (Figure drawn is schematic and not to scale; take ( g=10 m s^{-2} )
11
724How far from the midpoint of the stick
is the center of mass of the stick-puck
combination after the collision?
A. ( l ) ( overline{2} )
B. ( frac{l}{3} )
c. ( frac{l}{4} )
D. None of these
11
725A sphere of mass m moving with a constant velocity hits another
stationary sphere of the same mass. If ( e ) is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be:
A ( cdot frac{(1-e)}{(1+e)} )
в. ( frac{(1+e)}{(1-e)} )
c. ( frac{(e-1)}{(e-1)} )
D. ( frac{(e+1)}{(e-1)} )
11
726The speed of an object of mass ( 2 k g ) increases from ( 2 m / s ) to ( 4 m / s ) in ( 3 s )
Find out the total work done on the
object during this time interval?
A . ( 4 J )
B. 6.5
c. ( 12 J )
D. 24J
ह. ( 36 J )
11
727If object having total energy ( boldsymbol{E}_{1} ) is
having the same ( P E ) curve as shown in
the figure, then
( mathbf{A} cdot r_{0} ) is the maximum distance of the object from the
earth’s centre
B. the object and the earth system is bounded one
C. the ( K E ) of the object is zero when ( r=r_{0} )
D. all the above
11
through distance of ( 5 mathrm{m} ). The maximum
amount of work done when he
A. Move it over an inclined plane
B. Moves it over a horizontal surface
c. Lifts it vertically upwardd
D. None of these
11
729A man throws the bricks to the height of ( 12 m ) where they reach with a speed of
( 12 m / s . ) If he throws the bricks such that theyjust reach this height, then what percentage of energy will he save?
A . ( 19 % )
B. 38%
c. ( 57 % )
D. 76%
11
73014. Find how much mass m will rise if 4 m falls away. Blocks
are at rest and in equilibrium.
m
4m
Fig. 8.218
11
731The graph above shows the magnitude of the force applied to an initially stationary ( 20 k g ) curling rock over time.
Find out the velocity of the rock after the force has been applied to it?
A ( .1 .25 mathrm{m} / mathrm{s} )
в. ( 5 m / s )
( mathrm{c} cdot 10 mathrm{m} / mathrm{s} )
D. ( 25 m / s )
E. ( 50 m / s )
11
732Work-energy theorem is valid in the
presence of
A. All types of forces
B. Internal force only
c. conservative forces only
D. Non-conservative forces only
11
7336. A force F = -K (yi + xj) (where K is a positive constant)
acts on a particle moving in the x-y plane. Starting from
the origin, the particle is taken along the positive x-axis to
the point (a,0), and then parallel to the y-axis to the point
(a, a). The total work done by the force F on the particle is
(IIT JEE, 1998)
a. -2Ka? b. 2Ka? c. -Ka? d. Ka?
11
734The angle between two vectors ( vec{A}= ) (4,-2,5) and ( vec{B}=(3,1,-2) ) is:
A ( cdot 60^{circ} )
в. ( 30^{circ} )
( c cdot 90^{0} )
D. ( 45^{circ} )
11
73514. The potential energy o, in joule, of a particle of mass 1
kg, moving in the x-y plane, obeys the law o = 3x + 4y,
where (x, y) are the coordinates of the particle in metre.
If the particle is at rest at (6,4) at time t = 0, then
a. The particle has constant acceleration.
b. The work done by the external forces, the position
of rest of the particle and the instant of the particle
crossing the x-axis is 25 J.
c. The speed of the particle when it crosses the y-axis is
10 ms.
d. The coordinates of the particle at time t = 4 s are
(-18, -28)
11
736( mathbf{A} )
( 0.5 mathrm{kg} ) block slides from the point ( mathrm{A} ) on a horizontal track with an initial speed ( 3 mathrm{m} / mathrm{s} ) towards a weightless horizontal spring of length ( 1 mathrm{m} ) and force constant
2 N/m. The part AB of the Track is frictionless and the part BC has the coefficient of static and kinetic friction
as 0.22 and 0.20 respectively. If the distance ( A B ) and ( B D ) are ( 2 m ) and 2.14 m
respectively, find the total distance through which the block moves before it comes to rest completely.
( left(g=10 m / s^{2}right) )
11
737An artificial satellite of mass ( m ) is
moving in circular orbit at a height equal to the radius ( R ) of the earth.
Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One part of the satellite stops just after the explosion. The increase in the mechanical energy of the system due to explosion will be (Given:
acceleration due to gravity on the surface of earth is ( g ) )
A. ( m g R )
в. ( frac{m g R}{2} )
c. ( frac{m g R}{4} )
D. ( frac{3 m g R}{4} )
11
738A block of mass ( m ) is projected with velocity ( u ) forwards another identical
block with has a massless spring attached to its face. The spring constant of the spring is ( k ) and blocks are on smooth horizontal surface.

Maximum compression in the spring is:
A ( cdot u sqrt{frac{2 m}{k}} )
в. ( u sqrt{frac{m}{k}} )
c. ( u sqrt{frac{m}{2 k}} )
D. ( u sqrt{frac{m}{4 k}} )

11
739If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k} . ) Then, the
value of ( alpha ) is :
A ( cdot frac{-1}{2} )
B. – –
( c cdot frac{1}{2} )
D. 1
11
740A ball is thrown at an angle of incidence
( boldsymbol{theta}^{prime} ) on a horizontal plane such that the incident direction and the reflected
direction are at right angles to each other if the coefficient of restitution is
‘e’ then’ ( theta ) ‘is equal to
A ( cdot tan ^{-1}(e) )
B ( cdot tan ^{-1}(2 e) )
c. ( tan ^{-1}(sqrt{2} e) )
D. ( tan ^{-1}(sqrt{e}) )
11
741Two inclined friction less tracks, one
gradual and the other steep meet at ( boldsymbol{A} )
from where two stones are allowed to
slide down from rest, one on each track.
Will the stones reach the bottom at the
same time? Will they reach there with
the same speed? Explain. Given ( boldsymbol{theta}_{mathbf{1}}= )
( mathbf{3 0}^{0}, boldsymbol{theta}_{2}=mathbf{6 0}^{0}, ) and ( boldsymbol{h}=mathbf{1 0} boldsymbol{m}, ) what are
the speeds and times taken by the two
stones ?
11
742A body of mass ( 4 mathrm{kg} ) moving with a velocity of ( 9 mathrm{m} / mathrm{s} ). Collides with a body of ( 8 mathrm{kg} ) at rest. The coefficient of restitution is ( 0.33 . ) After collision the
velocity of body having mass ( 4 mathrm{kg} ) is:
( A cdot 1 mathrm{m} / mathrm{s} )
B. ( 4 mathrm{m} / mathrm{s} )
( c cdot 3 m / s )
D. ( 9 mathrm{m} / mathrm{s} )
11
743A ball dropped from a ( 20 m ) height loses
( 40 % ) of its energy on hitting the ground. Upto what height does the ball rebound?
( A cdot 28 m )
в. ( 8 m )
( c .12 m )
D. 20m
11
744A plastic ball falls from a height of 4.9 metre and rebounds several times from
the floor. What is the coefficient of
restitution during the impact with the floor if 1.3 seconds pass from the first impact to the second one?
A . 0.9
B. ( 0 . )
( c .0 .7 )
D. 0.8
11
745Work done by centripetal force in revolving a satellite around the earth is
A . zero
B. unity
c. infinity
D. nothing can be decided
11
746A ride in an amusement park called
scream machine swings the riders
around a complete vertical circle during
the course of the ride.
Identify where on the ride both PE and
KE are equal?
A. Point ( A )
B. Point B
c. Point ( C )
D. Point D
E . Point E
11
747Which one of the following energies cannot be possessed by a body at rest?
A. Potential energy
B. Kinetic energy
C. Thermal energy
D. Magnetic energy
11
748toppr
the following graphs violates the law of
conservation of energy?
3
( c )
( D )
11
749If ( g ) is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( boldsymbol{m} )
raised from the surface of the earth to a
height equal to the radius ( R ) of the earth
is
A. ( 2 m g R )
в. ( frac{1}{2} m g R )
c. ( frac{1}{4} m g R )
D. ( m g R )
11
750A gravitational field is present in a
region. A point mass is shifted from ( boldsymbol{A} )
to ( B, ) along different paths shown in the
figure. If ( W_{1}, W_{2} ) and ( W_{3} ) represent the
work done by gravitational force for
respective paths, then
( mathbf{A} cdot W_{1}=W_{2}=W_{3} )
В. ( W_{1}>W_{2}>W_{3} )
c. ( W_{1}>W_{3}>W_{2} )
D. none of these
11
75131. The ratio of magnitude of work done by camel on the load
during accelerated motion to retarded motion is
a. 3:5 b. 2.2:1 c. 1:1 d. 5:3
11
752A ( 0.098-k g ) block slides down a
frictionless track as shown in Fig. The time taken by the block to move
from ( A ) to ( B ) is:
( ^{A} cdot frac{1}{sqrt{g}} )
в. ( frac{2}{sqrt{g}} )
c. ( frac{3}{sqrt{g}} )
D. ( frac{4}{sqrt{g}} )
11
753If a ship of mass ( 4 times 10^{7} ) kg initially at
rest is pulled by a force of ( 5 times 10^{4} mathrm{N} )
through a distance of 4 m, then the
speed of the ship will be (resistance due to water is negligible)
( mathbf{A} cdot 5 m s^{-1} )
B . ( 1.5 mathrm{ms}^{-1} )
( mathrm{c} cdot 60 mathrm{ms}^{-1} )
D. ( 0.1 mathrm{ms}^{-1} )
11
754A particle of mass ( m ) moving in ( x ) direction with speed ( 2 v ) is hit by another
particle of mass ( 2 m ) moving in the ( y ) direction with speed ( v ). If the collisioni is
perfectly inelastic, the percentage of the energy retained by the colliding particles after the collision is close to
A . ( 56 % )
B. 80%
c. ( 35 % )
D. 44%
11
755A body dropped freely from a height h onto a horizontal plane, bounces up and down and finally comes to rest. The coefficient of restitution is e, the ratio
of distance travelled in two consecutive
rebounds
A ( .1: e )
B . ( e: 1 )
( mathbf{c} cdot 1: e^{2} )
D. ( e^{2}: 1 )
11
756Two protons are brought nearer; what will be the effect on potential energy of
system?
11
757The maximum vertical distance
through which a fully dressed astronaut canjump on the earth is ( 0.5 mathrm{m} ). If mean density of the moon is two thirds that of the earth and radius is one quarter that of the earth, the maximum vertical
distance through which he can jump on the moon and the ratio of time of
duration of the jump on the moon to
that on the earth are.
A. ( 3 mathrm{m}, 6: )
в. 6 m, 3:
( c cdot 3 m, 1: 6 )
D. ( 6 mathrm{m}, 1: 6 )
11
758If ( n ) balls hit elastically and normally on a surface per unit time and all the balls are of mass ( m ) moving with the same
velocity ( u, ) then force on the surface is:
( mathbf{A} cdot m times u times n )
В . ( 2 times m times u times n )
c. ( frac{1}{2} times m u^{2} n )
D. ( m u^{2} n )
11
759Statement 1: The scalar product of two
vector can be zero.
Statement 2:If two vector are
perpendicular to each other, their scalar product will be zero.
A ( cdot ) a) Statement- -1 is false, statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- – is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false
11
760An vehicle has a mass of 1500 kg. What must be the force between the vehicle
and the road if the vehicle is to be
stopped with a negative acceleration of ( 1.7 m s^{-2} ? )
A. ( 2550 N ) in a direction opposite to that of the vehicle
B. ( 2550 N ) in a direction same to that of the vehicle
c. ( 1550 N ) in a direction opposite to that of the vehicle
D. ( 1550 N ) in a same opposite to that of the vehicle
11
761A boy is moving on a straight road against a frictional force of ( 5 N . ) After
travelling a distance of ( 1.5 k m, ) he forgets the correct path at a round about (see fig.) of radius ( 100 m ) However, he moves on the circular path
for one and half cycle and then he moves
forward upto ( 2.0 k m . ) Calculate the work
done by him ( (pi=3.14) )
11
762The potential energy of an object of a mass m moving in xy plane in a conservative field is given by U=ax+by, where ( x ) and ( y ) are position coordinates of the object. Find magnitude of acceleration :-
A ( cdot frac{sqrt{a^{2}+b^{2}}}{2 m} )
( ^{text {В } cdot frac{a^{2}+b^{2}}{m}} )
c. ( sqrt{a^{2}+b^{2}} )
D. None
11
763When the load on a wire is slowly increased from 3 to ( 5 k g w t ), the
elongation increases from 0.61 to 1.02 ( m m ). The work done during the extension of wire is
( mathbf{A} cdot 0.16 J )
в. ( 0.016 J )
c. 1.6 .5
D. 16.5
11
764Illustration 8.46 A body of mass m hangs by
an inextensible string that passes over a smooth
mass less pulley that is fitted with a light spring
of stiffness k as shown in Fig. 8.99. If the body
is released from rest and the spring is released,
calculate the maximum elongation of the
spring
Fig. 8.99
11
765A moving block having mass ( m ), collides with another stationary block having mass ( 4 m . ) The lighter block comes to
rest after collision. When the initial
velocity of the lighter block is ( v ), then the value of coefficient of restitution ( (e) ) will
be:
A . 0.5
B. 0.25
c. 0.4
D. 0.8
11
766The velocity of a body moving in a straight line is increased by applying a constant force ( F ) for some distance in
the direction of the motion. The increase
in the kinetic energy of the body is equal to
A. the potential energy of the body.
B. the work done by the force on the body.
c. the momentum of the body.
D. the torque on the body.
11
76776. A particle of mass m slides along a curved-flat-curved
track. The curved portions of the track are smooth. If the
particle is released at the top of one of the curved portions.
the particle comes to rest at flat portion of length I and of
1 Minette after covering a distance of
Fig. 8.254
b. _H_
31
2U kinetic
Mkinetic
11
768A object of mass ( 40 k g ) having velocity
( 4 m / s ) collides with another object ( m= )
( 60 k g ) having velocity ( 2 m / s . ) The
collision is perfectly inelastic. The loss in energy is
A . ( 110 J )
в. ( 48 J )
( mathrm{c} .3925 )
D. ( 440 J )
11
7694. A body is attached to a spring whose other end is fixed.
If the spring is elongated by x, its potential energy is
U= 5×2, where x is in metre and U is in joule. U-x graph is
V
(c)
(d)
11
770A sphere of mass ( m ) is moving with a velocity ( (4 hat{i}-hat{j}) m / s ) hits a surface and rebounds with a velocity ( (hat{i}+3 hat{j}) m / s . ) The coefficient of restitution between the sphere and the
surface is ( k / 16 . ) find the value of ( k )
( A cdot 9 )
B. 8
( c cdot 7 )
D. 6
11
771A particle has potential energy dependent on its position on the ( x ) axis,
represented by the function ( U(x)= )
( e^{2 x}+1 ) for all real values of ( x ) where
( U(x) ) and ( x ) are given in standard units.
The force it feels at position ( x=1 ) is
closest to
A. ( 7.39 N )
B. ( 8.39 N )
c. ( -8.39 N )
D. ( 14.8 N )
E. ( -14.8 N )
11
772If a vector ( vec{A} ) makes an angles ( alpha, beta ) and
( Y ) respectively with the ( x, y ) and ( z ) axes
respectively. Then ( sin ^{2} alpha+sin ^{2} beta )
( +sin ^{2} gamma ) is equal to
( mathbf{A} cdot mathbf{0} )
B. 1
c. 2
D. 3
11
773What is the velocity of the cart just after the first collision?
A ( cdot frac{-m v_{0}}{m+M} )
в. ( frac{M v_{0}}{m+M} )
c. ( frac{M-m}{M+m} v_{0} )
D. ( frac{2 M}{m+M} v_{0} )
11
774A bullet of mass 125 gm leaves a rifle with a velocity of ( 500 m s^{-1} ). The rifle
recoils with a velocity of ( 5 m s^{-1} ). Find
the mass of the rifle.
( A cdot 100 mathrm{kg} )
B. 12.5 kgg
( c cdot 1.25 mathrm{kg} )
D. 125 kg
11
775A sphere rolling on a horizontal rough
surface collides elastically with a
smooth vertical wall, as shown in
Figure. State which of the following statements is true or false.

After collision the friction the linear
force acts on the sphere such that it decreases the linear speed and
increases the angular speed.

11
776A body of mass ( 10 g m ) moving with a
velocity of ( u_{1} c m / s ) collides with a
stationary mass of ( 90 g ) m. The collision is perfectly elastic. Find the percentage loss of kinetic energy of the first body.
A . 36
B . 48
c. 64
D.
11
777Two identical balls are projected, one vertically up and the other at an angle of ( 30^{0} ) to the horizontal, with same
initial speed. The potential energy at the highest point is in the ratio:
A . 4: 3
B. 3:
( c cdot 4: )
D. 1:
11
778Which of the following graphs closely represents the kinetic energy ( (K) ) of a
freely falling body and its height ( (h) )
above the ground?
( A )
в.
c.
D.
11
779The volume of a colloidal particle ( V_{c} ) as
compared to the volume of a solute
particle in atrue solution ( V_{s} ) could be
A ( cdot frac{V_{c}}{V_{s}}=1 )
B. ( frac{V_{c}}{V_{s}}=10^{23} )
c. ( frac{V_{c}}{V_{s}}=10^{-3} )
D. ( frac{V_{c}}{V_{s}}=10^{3} )
11
780An object of mass ( m ) and velocity ( v_{0} )
strikes a rigid uniform rod of length ( l )
and mass ( m_{r} . ) The rod is hanging by a frictionless pivot from the ceiling. Immediately after striking the rod, the object continues forward but its speed
reduces to ( frac{v_{0}}{2} . ) The moment of inertia of
the rod about its centre of mass is
( I_{C M}=frac{1}{2} m_{r} l^{2} . ) For the collision to be
inelastic:
A. the rod and object are of equal mass
B. the rod is either heavier or lighter than the object
c. the rod is of negligible mass
D. none of these
11
781A block moving in air breaks into two
parts and the parts separate:
This question has multiple correct options
A. the total momentum must be conserved
B. the total kinetic energy must be conserved
C. the total momentum must change
D. the total kinetic energy must change
11
782Two particles of mass ( M_{A} ) and ( M_{B} ) and
there velocities are ( V_{A} ) and ( V_{B} )
respectively collides. After collision they inter changes their velocities then ratio of ( frac{boldsymbol{M}_{boldsymbol{A}}}{boldsymbol{M}_{boldsymbol{B}}} ) is:
A ( cdotleft(text { a) } frac{V_{A}}{V_{B}}right. )
в. (b) ( frac{V_{B}}{V_{A}} )
c.
(c) ( frac{V_{A}+V_{B}}{V_{B}-V_{A}} )
D. (d)
11
783The resultant of two forces, one double
then other in magnitude, is perpendicular to the smaller of the two
forces. The angle between the two forces
is
( A cdot 120^{circ} )
B. 60
( c cdot 90 )
D. 150
11
784A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?11
785Two particles of masses ( m ) and ( 2 m ) moving in opposite directions collide elastically with velocity ( 2 nu ) and ( nu ) respectively. Find their velocities after collision.
[
n stackrel{2 v}{longrightarrow} quad stackrel{v}{-2 m}
]
11
786Calculate the height through which a
body of mass ( 0.5 k g ) is lifted if the
energy spent in doing so is ( 1.0 J . ) (Take
( boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-2} mathbf{)} )
( A cdot 2 m )
в. ( 0.2 m )
( c .20 m )
D. ( 0.4 m )
11
787Three blocks are initially placed as shown in the figure. block ( A ) has mass
( m ) and initial velocity ( v ) to the right.
Block ( B ) with mass ( m ) and block ( C ) with
mass ( 4 m ) are both initially at rest.
Neglect friction. All collisions are
elastic. The final velocity of block ( boldsymbol{A} ) is :
A. ( 0.6 v ) to the left
B. ( 1.4 v ) to the left
( c . v ) to the left
D. ( 0.4 v ) to the right
11
788A ball falls vertically onto a floor with
momentum ( p ) and then bounces repeatedly, the coefficient of restitution is ( e . ) The total momentum imparted by
the ball to the floor is
A ( cdot rho(1+e) )
B. ( frac{1}{1-e} )
( ^{c} rholeft(frac{1+e}{1-e}right) )
( ^{mathrm{D}} rholeft(1-frac{1}{e}right) )
11
789Calculate the work required to be done to stop a car of ( 1500 mathrm{kg} ) moving at a velocity of ( 60 mathrm{km} / mathrm{h} ? )11
790A ball falls freely under gravity from rest. Name the kind of energy it will possess at the point from where it falls:
A. Maximum energy
B. Heat energy
c. Potential energy
D. Kinetic energy
11
791The angle between force ( overrightarrow{boldsymbol{F}}=(mathbf{3} hat{boldsymbol{i}}+ )
( 4 hat{j}-5 hat{k}) ) unit and displacement ( overrightarrow{boldsymbol{d}}= ) ( (5 hat{i}+4 hat{j}+3 hat{k}) ) unit is
( A cdot cos ^{-1}(0.16) )
B. ( cos ^{-1}(0.32) )
( mathbf{c} cdot cos ^{-1}(0.24) )
D ( cdot cos ^{-1}(0.64) )
11
792Energy required to move a body of mass
( mathrm{m} ) from an orbit of radius ( 2 mathrm{R} ) to ( 3 mathrm{R} ) is:
( ^{mathbf{A}} cdot frac{G M m}{12 R^{2}} )
в. ( frac{G M m}{3 R^{2}} )
c. ( frac{G M m}{8 R} )
D. ( frac{G M m}{6 R} )
11
793A boy is swinging on a swing such that his lowest and highest position are at heights of ( 2 m ) and ( 4.5 m ) respectively. His velocity at the lowest position is
A ( .2 .5 m s^{-} )
B. ( 7 m s^{-1} )
( mathrm{c} cdot 14 mathrm{ms}^{-1} )
D. ( 20 m s^{-1} )
11
794Mass ( m_{1} ) strikes ( m_{2} ) which is at rest.
The ratio of masses for which they will
collide again is : (Collisions between
ball and wall are elastic. Coefficient of
restitution between ( m_{1} ) and ( m_{2} ) is ( e )
and all the surfaces are smooth
A ( cdot frac{e}{2+e} )
B. ( frac{2 e}{2+e} )
( c )
( D )
11
795In which of the following work is being
done?
This question has multiple correct options
A. Man sitting on a bench
c. Climbing a tree to pluck
D. Pushing a wheelbarrow of bricks.
11
7963. The PE of a certain spring when stretched from natural
length through a distance 0.3 m is 5.6 J. Find the amount
of work in joule that must be done on this spring to stretch
it through an additional distance 0.15 m.
11
vertical position and touching a block of mass ( M ) which is a rest on a horizontal
surface. The rod is given a slight jerk
and it starts rotating about point ( boldsymbol{O} )
This causes the block to move forward
as shown. The rod loses contact with the
block at ( boldsymbol{theta}=mathbf{3 0}^{circ} ) All surfaces are
questions. The velocity of block when
the rod loses contact with the block is
A ( cdot frac{3 g l}{4} )
B. ( frac{5 g l}{4} )
c. ( frac{6 g l}{4} )
D. ( frac{7 g l}{4} )
11
798The distance AC is :
A . ( 20 mathrm{m} )
B. 30 ( m )
( c cdot 40 m )
D. ( 50 mathrm{m} )
11
799mole 8.1 Figure 8.167 a smooth circular path of radius
on the horizontal plane which is quarter of a circle A block
mass m is taken from position A to B under the action of a
constant force F. Calculate the work done by force F.
a. If it is always directed horizontally
b. If the block is pulled by a force F which is always
tangential to the surface
Block is pulled with a constant force F which is always
directed towards the point B
11
800Two bars of masses ( m_{1} ) and ( m_{2} )
connected by a weightless spring of stiffness ( kappa ) (figure shown above) rest on a smooth horizontal plane. Bar 2 is
shifted a small distance ( x ) to the left
and then released. If the velocity of the centre of inertia of the system after bar
breaks off the wall is given as ( v_{c m}= )
( frac{s x sqrt{m_{2} k}}{left(m_{1}+m_{2}right)} . ) Find ( s )
11
801At what value of ( eta ) will the velocity of the disc after the collision be equal to zero?
A. ( eta=4 )
В . ( eta=5 )
( mathbf{c} cdot eta=6 )
D. ( eta=7 )
11
802A man of mass ( mathrm{m} ) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
( W_{text {gravity}}= ) work done by gravity on the
man.
( W_{text {friction}}= ) work done by gravity on the
man.
( W_{text {man}}= ) work done by man
If in the previous problem, we replace the man by a block of mass ( mathrm{m} ) and release it from top of the inclined plane, and let it gain a speed ( v, ) then This question has multiple correct options
A ( cdot W_{f r i c t i o n}=-m g h+frac{1}{2} m v^{2} )
B. ( W_{text {gravity}}=-m g h )
C. ( W_{text {friction}}=0 )
D. ( W_{text {friction}}=-mu g x, ) where ( x ) is the horizontal distance covered and ( mu ) is the coefficient of friction between the block and the ground
11
803A force of 500 dyne acts on an object
where the object moves through ( 8 m ) in
the direction of force. Calcualate the
work done in this case
11
804A ( 20 mathrm{kg} ) object is lifted through a height of ( _{-1}-ldots- ) m when 784 J of work is
done on it.
[Assume ( left.boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2}right] )
( A cdot 2 )
B. 4
c. 7.84
D. 3.92
11
805What is the projection of ( vec{P} ) on ( vec{Q} ? )
A ( . vec{Q} . vec{P} )
в. ( hat{P} . hat{Q} )
c. ( vec{P} . vec{Q} )
D. ( vec{P} . hat{Q} )
11
806Given: ( vec{a} ) and ( vec{b} ) are unit vector, and ( theta ) be
the angle between them. Then ( frac{1-vec{a} cdot vec{b}}{1+vec{a} cdot vec{b}}= )
A ( cdot sin ^{2} frac{theta}{2} )
в. ( cos ^{2} frac{theta}{2} )
c. ( tan ^{2} frac{theta}{2} )
D. ( cot ^{2} frac{theta}{2} )
11
807The position function of a particle is
given by ( boldsymbol{x}(t)=boldsymbol{k} boldsymbol{t}^{5 / 2}, ) where ( boldsymbol{k} ) is a
constant.
If the particle starts at rest and is propelled through some distance ( d ) so
that the trajectory matches ( x(t), ) the
work done on the particle is
proportional to which power of ( t ? )
( mathbf{A} cdot t^{5} )
B ( cdot t^{3} )
( mathbf{c} cdot t^{5 / 2} )
( mathbf{D} cdot t^{3 / 2} )
E. Not enough information
11
808A bullet of mass 10 g moving with velocity of ( 1.5 mathrm{m} / mathrm{s} ) hits a thick wooden plank of mass 90 g. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank and both move with a certain speed. Calculate the speed with which plank containing the bullet moves?
A. ( 0.15 mathrm{m} / mathrm{s} )
B. ( 0.5 mathrm{m} / mathrm{s} )
( c cdot 1.5 mathrm{m} / mathrm{s} )
D. ( 2 mathrm{m} / mathrm{s} )
11
809A hammer of mass ( M ) falls from a
height ( h ) repeatedly to drive a pile of
mass ( m ) into the ground. The hammer
makes the pile penetrate in the ground
to a distance ( d ) in single blow.

Opposition to penetration is given by:
A ( cdot frac{m^{2} g h}{M+m d} )
B. ( frac{m^{2} g h}{(M+m) d}+(M+m) g )
c. ( frac{M^{2} g h}{M+m d} )
D. ( frac{m^{2} g h}{(m+M) d}-(M+m) g )

11
810n after hitting
ing the collision
18. A tennis ball is dropped on a horizontal smooth sure
It bounces back to its original position after b
the surface. The force on the ball during the col
is proportional to the length of compression of
ball. Which one of the following sketches desc
the variation of its kinetic energy K with time t
le t most
appropriately? The figures are only illustrative and not
the scale.
a.
K
b.
K
d.
K
11
811A bullet weighing 10 g is fired with a velocity of ( 800 m s^{-1} . ) After passing
through a mud wall ( 1 mathrm{m} ) thick, its
velocity decreases to ( 100 m s^{-1} ). Find the
average resistance offered by the mud wall.
11
812Two identical balls ( A ) and ( B ) are
released from the position shown in Fig.
1.205. They collide elastically with each other on the horizontal portion. The ratio
of heights attained by ( A ) and ( B ) after collision is (neglect friction)
( A cdot 1: 4 )
в. 2: 1
( c .4: 13 )
D. 2: 5
11
813A uniform metal sphere of radius ( boldsymbol{R} ) and
mass ( m ) is surrounded by a thin
uniform spherical shell of same mass
and radius ( 4 R ) The centre of the shell ( C )
falls on the surface of the inner sphere.
Find the gravitational fields at points ( A )
and B.
11
81423. An object of mass m slides down a hill of arbitrary shape
and after travelling a certain horizontal path stops because
of friction. The total vertical height descended is h. The
friction coefficient is different for different segments for
the entire path but is independent of the velocity and
direction of motion. The work that a tangential force must
perform to return the object to its initial position along the
same path is
a. mgh b. – mgh c. -2mgh d. 2mgh
11
815Given unit vectors ( overline{boldsymbol{m}}, overline{boldsymbol{n}} ) and ( overline{boldsymbol{p}} ) such that
angle between ( bar{m} ) and ( bar{n}= ) angle between ( bar{p} ) and ( (bar{m} times bar{n})=pi / 6 ) then
( [overline{boldsymbol{n}} overline{boldsymbol{p}} overline{boldsymbol{n}}]= )
A. ( sqrt{3} / 4 )
B. 3/4
( c cdot 1 / 4 )
D. none
11
816A chain of mass ( mathrm{m} ) and length Lis over hanging from the edge of a smooth horizontal table such that ( frac{1}{n} ) of its length is lying on the table. The work done in pulling the chain completely on to the table is
A ( cdot frac{m g L}{2 n^{2}} )
в. ( frac{m g L(n-1)^{2}}{2 n^{2}} )
c. ( frac{m g L(n-1)^{2}}{n^{2}} )
D. ( frac{m g L}{n^{2}} )
11
817A ( 1 mathrm{kg} ) block situated on a rough incline is connected to a spring of spring constant 100Nm-1100Nm-1 as shown
The block is released from rest with the
spring in the unstretched position. The
block moves ( 10 mathrm{cm} ) down the incline
before coming to rest. Find the
coefficient of friction between the block
and the incline. Assume that the spring
has a negligible mass and the pulley is frictionless.
11
818A body moves from point ( A ) and ( B ) under the action of a force, varying in
magnitude as shown in figure below.
Obtain the work done. Force is
expressed in newton and displacement
is in metre
11
819The work done in holding 15 kg suitcase while waiting for a bus for 45 minutes is :
( A cdot 675 J )
B. 40500
c. 4500
D. zero
11
820A particle hanging from a massless spring stretches it by ( 2 mathrm{cm} ) at earths surface. How much will the same
particle stretch the spring at a height of ( 2624 mathrm{km} ) from the surface of the earth? (Radius of earth ( =6400 mathrm{km} ) ).
A ( .1 mathrm{cm} )
B. ( 2 mathrm{cm} )
( mathrm{c} .3 .3 mathrm{cm} )
D. 4 cm
11
821A smooth sphere (mass ( 10 mathrm{kg} )
negligible radius) moves on a smooth
curved surface from the point with a
speed of ( 10 mathrm{m} / mathrm{s} ) as shown in figure. The
sphere reaches the point D passing
through point B. If the ground is taken
as reference, Then ( left[boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right] )
This question has multiple correct options
A. The total mechanical energy of the sphere at point A is zero
B. The total mechanical energy of the sphere at the point A is 2500 J
C. The kinetic energy at point B is 2500 J
D. The notential energy at point B is 0 J
11
822A man standing on the edge of the terrace of a high rise building throws a stone, vertically up with a speed of 20
( mathrm{m} / mathrm{s} . ) Two seconds later, an identical stone is thrown vertically downwards with the same speed of ( 20 mathrm{m} / mathrm{s} ). Then :
This question has multiple correct options
A. the relative velocity between the two stones remains constant till one hits the ground
B. both will have the same kinetic energy, when they hitt the ground
c. the time interval between their hitting the ground is 2 s
D. if the collision on the ground is perfectly elastic, both will rise to the same height above the ground
11
823Two bullets ( P ) and ( Q ), masses 10 and 20
g, are moving in the same direction towards a target with velocities of 20
and ( 10 mathrm{m} / mathrm{s} ) respectively. Which one of the bullets will pierce a greater distance through the target?
( A cdot P )
B.
c. Both will cover the same distance
D. Nothing can be decided
11
824The vector ( hat{i}+x hat{j}+3 hat{k} ) is rotated
through an angle ( theta ) and doubled in magnitude,then it becomes ( 4 hat{i}+(4 x- )
2)( hat{j}+2 hat{k} . ) The value of ( x ) are
A ( cdot-frac{2}{3}, 2 )
в. ( frac{1}{3}, 2 )
c. ( frac{2}{3}, 2 )
D. zero, 2
11
825In which of the following cases, is the
work done maximum?
( A )
B.
( mathbf{c} )
D.
11
826A uniform stationary sphere starts
rolling down from the upper end of the
surface as shown in the figure, and it
reaches the lower right end. Given, ( boldsymbol{H}= )
( 27 m ) and ( h=20 m . ) The sphere will fall
on the ground level at the following
distance from ( C . ) (Assume horizontal
projection)
( A cdot 12 m )
B. ( 24 m )
( c .36 m )
D. 48 m
11
827A 2 kg mass moving on a smooth frictionless surface with a velocity of ( 10 m s^{-1} ) hits another 2 kg mass kept at rest, in an inelastic collision. After
collision, if they move together,
A. they travel with a velocity of ( 5 m s^{-1} ) in the same direction
B. they travel with a velocity of ( 10 mathrm{ms}^{-1} ) in the same direction
c. they travel with a velocity of ( 10 m s^{-1} ) in the opposite direction
D. they travel with a velocity of ( 5 m s^{-1} ) in the opposite direction
11
828Find the angle that the vector ( vec{A}=2 hat{i}+ ) ( 3 hat{j}-hat{k} ) makes with y-axis.
A ( cdot theta=cos ^{-1}left(frac{3}{sqrt{14}}right) )
B. ( theta=cos ^{-1}left(frac{2}{sqrt{14}}right) )
( ^{mathrm{c}} cdot_{theta}=cos ^{-1}left(frac{3}{sqrt{16}}right) )
D. ( theta=cos ^{-1}left(frac{3}{sqrt{28}}right) )
11
829A bullet of mass ( m ) moving horizontally with a velocity ( v ) strikes a block of wood
of mass ( M ) and gets embedded in the block. The block is suspended from the ceiling by a massless string. The height to which block rises is:
( A )
[
frac{v^{2}}{2 g}left(frac{m}{M+m}right)^{2}
]
в.
[
frac{v^{2}}{2 g}left(frac{M+m}{m}right)^{2}
]
( ^{mathrm{c} cdot} frac{v^{2}}{2 g}left(frac{m}{M}right)^{2} )
( D )
[
frac{v^{2}}{2 g}left(frac{M}{m}right)^{2}
]
11
83029. Work done by the boy is
– mgh
6. mgh
mgh
mgh
d. None of above
11
831A metallic ball strikes a wall and falls
down whereas a tennis bail having the same mass and velocity bounces back.
The reason for this is that:
A. both suffer equal change in momentum.
B. the tennis ball suffers a greater change in momentum
c. metallic ball suffers a greater change in momentum.
D. the momentum of the tennis ball is less than that of the metallic ball
11
8329. A block of mass m is dropped onto a spring of constant
k from a height h. The second end of the spring is
attached to a second block of mass M as shown in Fig.
8.213. Find the minimum value of h so that the block M
bounces off the ground. if the block of mass m sticks to
the spring immediately after it comes into contact with it.
Fig. 8.213
11
833Kinetic energy of a body depends upon its:
A. mass
B. velocity
c. density
D. both A and
11
834Illustration 8.5 A force F = a + bx acts on a particle in
X-direction, where a and b are constants. Find the work done
by this force during the displacement from x, to X2.
11
835A box of weight ( 150 k g f ) has ( 1.47 k J )
of gravitational potential energy stored in it. Find the height of the box above the ground. Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{N} boldsymbol{k} boldsymbol{g}^{-1} )
A . ( 10 m )
в. 4.9 т
c. ( 2.45 m )
D. ( 1 m )
11
836If ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{boldsymbol{i}}+hat{boldsymbol{j}}-hat{boldsymbol{k}} ) and ( overrightarrow{boldsymbol{B}}=sqrt{mathbf{2}}(hat{boldsymbol{i}}+hat{boldsymbol{j}}) )
Find ( vec{A} . vec{B} ). Hence find the angle between ( vec{A} ) and ( vec{B} ). Also find the component of ( overrightarrow{boldsymbol{A}} ) along ( overrightarrow{boldsymbol{B}} )
11
837The force exerted by a compression device is given by ( F(x)=k x(x-l) ) for
( 0 leq x leq l, ) where ( l ) is the maximum
possible compression, ( x ) is the compression and ( k ) is the constant
Work done to compress the device by a distance ( d ) will be maximum when
A ( cdot d=frac{l}{4} )
в. ( d=frac{l}{sqrt{2}} )
( c cdot d=frac{l}{2} )
D. ( d=l )
11
838
Vi
Quvve
8. Which of the following statements is correct?
a. Kinetic energy of a system can be changed without
changing its momentum.
b. Kinetic energy of a system cannot be changed without
changing its momentum.
c. Momentum of a system cannot be change
11
839When two bodies stick together after collision, the collision is said to be:
A. partially elastic
B. elastic
c. inelastic
D. perfectly inelastic
11
840(a), (V) dll
)
7. In an ideal pulley particle system, mass
m, is connected with a vertical spring
of stiffness k. If mass m, is released from
rest, when the spring is undeformed,
find the maximum compression of the
reelle
Fig. 8.211
11
841A simple pendulum is released from ( boldsymbol{A} )
as shown in figure. If ( m ) and ( l ) represent
the mass of the bob and the length of
the pendulum respectively, the gain in
kinetic energy at ( B ) is then
A ( cdot frac{m g}{2} )
B. ( frac{m g}{sqrt{2}} )
( c )
D. ( frac{2}{sqrt{3}} m g l )
11
842A block is constrained to move along ( x )
axis under a force ( F=-2 x ). Here, ( F ) is in
newton and ( x ) in metre. Find the work
done by this force when the block is displaced from ( x=2 m ) to ( x=-4 ) m.
A . -4 J
B. -8J
c. -12
D. -16
11
843toppr
velocity of the chain suddenly and without frictional resistance or
interference from the support or from
statement (when ( x=0, text { then } v=0) )
(length of the chain is L and p is the
mass per unit length of the chain)
A ( cdot ) the velocity v of the chain as a function of ( x ) is ( sqrt{frac{2 g x}{3}} )
B. the acceferation of a of the falling chain as a function
fris ( frac{g}{3} )
C. the energy Q lost from the system as the last link leaves the plafform is ( frac{p g L^{2}}{6} )
D. tension at the middle point of falling chain is ( frac{p g x}{3} )
11
844Tllustration 8.22 A block of mass m is moving with an initial
velocity vo towards a stationary spring of stiffness k attached
to the wall as shown in Fig. 8.51.
m
000004
Fig. 8.51
a. Find the maximum compression in the spring.
b. Is the work done by the spring negative or positive?
11
845A body is projected at an angle of ( 60^{circ} ) with the horizontal. If its kinetic energy at maximum height is ( 10 mathrm{J} ), then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is :
A. half of the maximum height
B. two third of the maximum height
c. one sixth of the maximum height
D. insufficient data to solve the problem.
11
846During any collision
A. Momentum is conserved
B. Linetic energy is conserved
c. Both conserved
D. All
11
847A body of mass ( 6 k g ) is under a force of
( 6 N ) which causes displacement in it given by ( S=frac{t^{2}}{4} m ) where ‘t’ is time. The
work done by the force in ( 2 s ) is :
A . ( 12 . J )
в. ( 9 J )
( c .6 J )
D. ( 3 J )
11
848Which of the following is approximately the rate of solar energy (in ( mathbf{K W}) )
falling per ( mathbf{m}^{2} ) on the surface area of
the earth?
A .
в. 100
c. ( 0 . )
D. 0.0001
11
849In a gravity free space, a man of mass ( M ) standing at a height ( h ) above the floor throws a stone of mass ( boldsymbol{m} )
downwards with a speed ( u . ) When the stone reaches the floor, distance of the
man above the floor will be :
( A cdot h )
B. ( 2 h )
c. ( _{h}-frac{2 m h}{M} )
D. ( frac{m h}{M}+h )
11
850A plot of velocity versus time is shown
in figure. A single force acts on the body
The correct statement is
A. In moving from ( c ) to ( D ), work done by the force on the body is positive
B. In moving from B to C, work done by the force on the body is positive
c. In moving from A to B, the body does negative work
D. In moving from o to
A, work is done by the body and negative
11
851Two blocks ( A ) and ( B ) of masses ( m ) and
( 2 mathrm{m} ) respectively placed on a smooth floor are connected by a spring. A third body ( C ) of mass ( m ) moves with velocity
( boldsymbol{v}_{0} ) along the line joining ( mathbf{A} ) and ( mathbf{B} ) and collides elastically with A. At a certain instant of time after collision it is found
that the instantaneous velocities of ( A )
and ( mathrm{B} ) are same then :
A. the common velocity of A and B at time to is ( v / 3 ).
в.
[
text { the spring constant is } mathrm{k}=frac{3 m v_{0}^{2}}{2 x_{0}^{2}}
]
( c )
[
text { the spring constant is } mathrm{k}=frac{2 m v_{0}^{2}}{3 x_{0}^{2}}
]
D. none of these
11
852The total work done on a particle is
equal to the change in its kinetic
energy.
This statement is true for which of the
condition?
A. always
B. only if the forces acting on the body are conservative
C. only if the forces acting on the body are gravitational
D. only if the forces acting on the body are elastic.
11
853A man moves on a straight horizontal road with a block of mass ( 2 k g ) in his
hand. If he covers a distance of ( 40 m )
with an acceleration of ( 0.5 m / s^{2}, ) find
the work done by the man on the block during the motion.
11
854A ball which is at rest is dropped from height ( h ) metre. As it bounces off the
floor, its speed is ( 80 % ) of what it was just before touching the ground. The ball will then rise to nearly a height.
( mathbf{A} cdot 0.94 h )
B. ( 0.74 h )
c. ( 0.64 h )
D. ( 0.84 h )
11
855Illustration 8.6 The displacement of a particle of mass 3
on a horizontal smooth surface is a function of time given by
x==1 Find out the work done by the external agent for
the first one second.
11
85642. Two ends A and B of a smooth chain of mass m and length
I are situated as shown in Fig. 8.236. If an external agent
pulls A till it comes to same level of B, work done by
external agent is
sloveeelllllllll
somboooo 0000000000000000000
Fig. 8.2360
mgl
36
b. mgl
15
mgl
d. None of the above
11
857A mass of ( 1 k g ) is thrown up with velocity of ( 1000 m / s . ) After 5 second, it explodes
into two parts. One part of mass 400 g
moves soen with a velocity ( 25 m / s ) calculate the velocity of other part just after the explosion ( left(boldsymbol{g}=mathbf{1 0 m s}^{-mathbf{2}}right) )
11
858S. A wind-powered generator converts wind energy into
electrical energy. Assume that the generator converts a
fixed fraction of the wind energy intercepted by its blades
into electrical energy. For wind speed V, the electrical
power output will be proportional to (IIT JEE, 2000)
b. v2
c.
p
d.
A
11
859An object of mass ( mathrm{m} ) is tied to a string of length I and a variable force ( mathrm{F} ) is applied on it which brings the string
gradually at angle ( theta ) with the vertical Find the work done by the force ( F )
11
860An object is displaced from point ( mathrm{A}(2 mathrm{m} ) ( 3 m, 4 m) ) to a point ( B(1 m, 2 m, 3 m) ) under a constant force ( overrightarrow{boldsymbol{F}}= ) ( (2 hat{i}+3 hat{j}+4 hat{k}) N . ) Find the work done by this force in this process.
A. ( -9 J )
( J )
B. ( 9 J )
c. ( -18 J )
D. ( 18 J )
11
861A catapult throws a stone of mass 0.10 kg with a velocity of ( 30 mathrm{m} / mathrm{s} ). If ( 25 % ) of the PE of the elastic band is wasted
during transmission, find the magnitude of PE.
11
862The work done in shifting a particle of mass ( m ) from the centre of earth to the
surface of the earth is
A. ( -m g R )
B. ( frac{1}{2} m g R )
c. zero
D. ( m g R )
11
863A rubber ball drops from a height h and after rebounding twice from the ground, it rises to h/2. The co – efficient of
restitution is
A ( cdot frac{1}{2} )
D.
11
864A ball of mass ( m ) moving at a speed ( v )
collides with another ball of mass ( 3 mathrm{m} ) at
rest. The lighter block comes to rest after collision. The coefficient of
restitution is-
A ( cdot frac{1}{2} )
B. ( frac{2}{3} )
( c cdot frac{1}{4} )
D. None of these.
11
865Illustration 8.4 A force F = 6xî +2yj displaces a body
from 7 = 3ỉ +8j to iz = 5 – 4. Find the work done by
the force.
OL
W
11
866A stone of mass ( 10 mathrm{kg} ) is lying at the bed of a lake 5 m deep. If the relative density
of the stone is ( 2, ) the amount of work
done to bring it to the top of the lake will
be
( mathbf{A} cdot 250 J )
B. ( 258 J )
c. ( 345 J )
D. ( 385 J )
11
867The kinetic energy of the body after the
collision is
A ( cdot frac{11 m v^{2}}{54} )
B. ( frac{m v^{2}}{108} )
c. ( frac{17 m v^{2}}{54} )
D. ( frac{17 m v^{2}}{108} )
11
868A sphere ‘P’ of mass ‘m’ moving with velocity ‘u’ collides head-on with another sphere ‘Q’ of mass ‘m’ which is at rest. The ratio of final velocity of ‘Q’ to initial velocity of ‘P’ is ( . cdot(e= )
coefficient of restitution)
A ( cdot frac{e-1}{2} )
( ^{mathrm{B}}left[frac{e+1}{2}right]^{1 / 2} )
c. ( frac{e+1}{2} )
( ^{mathrm{D} cdot}left[frac{e+1}{2}right]^{2} )
11
869An example of inelastic collision is:
A. scattering of ( alpha ) particle from a nucleus
B. collision of ideal gas molecules
C. collision of two steel balls lying on a frictionless table
D. collision of a bullet with a wooden block
11
87088. Water is drawn from a well in a 5 kg drum of capacity
55 L by two ropes connected to the top of the drum. The
linear mass density of each rope is 0.5 kgm . The work
done in lifting water to the ground from the surface of
water in the well 20 m below is (g = 10 ms?)
a. 1.4 x 104J
b. 1.5 x 104 J
c. 9.8 x 10 x 6J d. 18 J
11
871When a person stands on a weighing balance, working on the principle of Hooke’s law, it shows a reading of ( 60 mathrm{kg} )
after a long time and the spring gets compressed by ( 2.5 mathrm{cm} . ) If the person jumps on the balance from a height of ( mathbf{1 0} c boldsymbol{m}, ) the maximum reading of the balance will be
A. ( 60 mathrm{kg} )
в. ( 120 mathrm{kg} )
c. ( 180 mathrm{kg} )
D. 240 kg
11
872A block mass ‘ ( m^{prime} ) is released from rest
at point A. The compression in spring,
when the speed of block is maximum is:
A ( cdot frac{m g sin theta}{k} )
B. ( frac{2 m g sin theta}{k} )
( c cdot frac{m g cos theta}{k} )
D. ( frac{m g}{k} )
11
873The water stored in a
reservoir possesses:
A. Kinetic energy
B. Muscular energy
c. Potential energy
D. Magnetic energy
11
8743. A block of mass m lies on a wedge of mass M. The wedge
in turn lies on a smooth horizontal surface. Friction is
absent everywhere. The wedge-block system is released
from rest. All situations given in Column I are to be
estimated in duration the block undergoes a vertical
displacement h starting from rest. Match the statements in
Column I with the results in Column II. (g is acceleration
due to gravity.)
Fig. 8.293
Column I
Column II
i. Work done by normal reaction a. positive
acting on the block is
ii. Work done by normal reaction b. negative
(exerted by block) acting on the
wedge is
iii. The sum of work done by normal c. zero
reaction on the block and work
done by normal on wedge
iv. Net work done by all forces on d. less than mgh in
the block is
magnitude
11
875A cord is used to raise a block of mass
( m ) vertically through a distance ( d ) at a
constant downward acceleration ( boldsymbol{g} / mathbf{4} ) The work done by the cord is:
( mathbf{A} cdot m g d / 4 )
в. ( 3 M g d / 4 )
c. ( -3 M g d / 4 )
D. ( M g d )
11
876Graph shows the acceleration of ( 3 g )
particle as an applied force moves it
from rest along ( boldsymbol{x} ) – axis. The total work
done by the force on the particle by the
time the particle reaches ( boldsymbol{x}=mathbf{6 m}, ) is
equal to
11
877A body of mass 10 gm moving with a velocity of ( 20 mathrm{cm} s^{-1} ) collides with a stationary mass of ( 90 mathrm{gm} ). The collision is perfectly inelastic. Find the percentage loss of kinetic energy of
the system.
A.
B. 50
c. 90
D. 100
11
878One joule is approximately equal to:
A. 0.28 call ( l )
в. 0.32 сад ( l )
c. 0.24 call ( l )
D. 4.2 call ( l )
11
879A body is projected vertically up from a point on the ground. When it is at a height ( h ) above the ground, its kinetic
and potential energies are found to be in the ratio of ( 3: 2 . ) If the body rises to a
maximum height of ( H ) above the ground, then the ratio of ( boldsymbol{H}: boldsymbol{h} ) will be
A . 5: 3
B . 2: 1
c. 5: 2
D. 2: 5
11
880Which of the following physical quantity is different from others?
A. Displacement
B. Velocity
c. Force
D. Kinetic energy
11
881The angle made by ( overrightarrow{mathrm{j}}+overrightarrow{mathrm{k}} ) with ( mathrm{y} ) -axis is:
A ( cdot 60^{circ} )
B. ( 30^{circ} )
( mathbf{c} cdot 45^{circ} )
D. ( 90^{circ} )
11
882Two solid rubber balls, A and B having masses 200 and 400 g respectively are moving in opposite directions
with velocity of A equal to ( 0.3 m / s ). After collision the two balls come to rest, then the velocity of B is-
A. ( 0.15 mathrm{m} / mathrm{s} )
в. ( 1.5 mathrm{m} / mathrm{s} )
c. ( -0.15 mathrm{m} / mathrm{s} )
D. None of the above
11
883A body of mass 2 kg starts with an initial velocity ( 5 mathrm{m} / mathrm{s} ). If the body is acted upon by a time dependent force
(F) as shown in figure, then work done
on the body in 20 s is?
11
884A body of mass ( 3 k g ) is under a constant force which causes a displacement s in metres in it given by the relation ( s= ) ( frac{1}{3} t^{2}, ) where ( t ) is in a workdone by the
force in ( 2 s ) is
11
885A particle of mass ( boldsymbol{m}=12 boldsymbol{k} boldsymbol{g} ) falling
freely from rest under gravity and air resistance force ( (boldsymbol{F}) ). The velocity of the particle when reaches ground is ( 6 m / s )
Then total external work done on the
particle is
( mathbf{A} cdot 216 J )
в. ( (120-F) J )
( mathbf{c} .6 F J )
D. Data insufficient
11
886A force ( F ) is applied on a lawn mower at
an angle of ( 60^{circ} ) with the horizontal. If it
moves through a distance ( x ) in horizontal direction, the work done by
the force is:
A ( cdot frac{F x}{2} )
в. ( frac{sqrt{3} F x}{2} )
c. ( 2 F x )
D. None of the above
11
887( n ) elastic balls are placed at rest on a
smooth horizontal plane which is circular at the ends with radius ( r ) as
shown in the figure. The masses of the balls are ( m, frac{m}{2}, frac{m}{2^{2}} ldots ldots frac{m}{2^{n-1}} )
respectively. What is the minimum velocity which should be imparted to
the first ball of mass ( m ) such that ( n^{t h} )
ball completes the vertical circle:
A ( cdotleft(frac{3}{4}right)^{n-1} sqrt{5} g r )
В ( cdotleft(frac{4}{3}right)^{n-1} sqrt{5 g r} )
c. ( left(frac{3}{2}right)^{n-1} sqrt{5 g r} )
D ( cdotleft(frac{2}{3}right)^{n-1} sqrt{5 g r} )
11
888Book of mass ( 2 mathrm{kg} ) is lifted from floor to the table. The height between floor and the table is ( 1.5 mathrm{m} ). Calculate the work
done by gravitational force.
A . -30
B . -15 J
c. о
D. 15 J
E. 30
11
889A block of mass ( m ) moving at a speed ( v )
collides with another block of mass ( 2 m )
at rest. The lighter block comes to rest after collision. What is the coefficient of
restitution.
11
890A cart ( A ) of mass ( 50 k g ) moving at a
speed of ( 20 k m / h ) hits a lighter cart ( B )
of mass ( 20 mathrm{kg} ) moving towards it at a speed of ( 10 mathrm{km} / mathrm{h} ). The two carts cling to
each other. Find the change of
momentum of cart A.
11
891A wound watch spring has
energy.
A. mechanical
B. kinetic
C . potential
D. kinetic and potential
11
892Illustration 8.31
8.31 A 4.00-kg particle moves from the origin
A 4.00-kg particle moves
to position C, having coordinate x = 5.00 m and y
on the particle is the gravitational force acting in the
negative y direction. Using equation W=Far
ork done by the gravitational force on the
particle as it goes from O to Calong (a) OAT, (D)
(C) OC. Your results should all be identical. Why?
sequation W=FArcos O=F. AF.
(5.00,5.00)m
Fig. 8.68
11
893A force of ( 10 mathrm{N} ) is applied on an object at
rest of mass ( 2 mathrm{kg} ) placed on a smooth
surface. The kinetic energy after 5 s is
( J )
A . 124.6
в. 625
c. 312.5
D. 683.8
11
894A bullet is fired at a target with a velocity ( 80 mathrm{m} / mathrm{s} ) and penetrates ( 50 mathrm{cm} ) into it. If this bullet were fired into a
target ( 25 mathrm{cm} ) thick with equal velocity, with what velocity would it emerge, supposing the resistance to be uniform
and the same in both the cases?
A. ( sqrt{80} mathrm{m} / mathrm{s} )
в. ( frac{40}{sqrt{2}} m / s )
c. ( 40 m / s )
D. ( 40 sqrt{2} mathrm{m} / mathrm{s} )
11
895A particle of mass M moves along the ( x )
axis with speed ( V_{0} ) and collides and
sticks to a particle of mass ( m ) moving
with a speed ( V_{0} ) along y-axis. The velocity of the combined particle after the collision:
( ^{mathbf{A}} cdot frac{M hat{i}+m hat{j}}{(M+m)} V_{0} )
B. ( frac{m hat{i}+M hat{j}}{(M+m)} V_{0} )
c. ( (m hat{i}+M hat{j}) V_{0} )
D. Zero
11
896Angle (in rad) made by the vector ( sqrt{3} hat{i}+hat{j} ) with the ( x ) -axis:
A ( cdot frac{pi}{6} )
B.
( c cdot frac{pi}{3} )
D.
11
897A particle of mass ( m ) is located in a one dimensional potential field where potential energy is given by ( U(x)=A(1- ) ( cos p x), ) where ( A ) and ( p ) are constants. The period of small oscillations of the particle
A ( cdot 2 pi sqrt{frac{m}{A p^{2}}} )
в. ( pi sqrt{frac{m}{A P}} )
c. ( pi sqrt{frac{m}{A}} )
D. ( left(frac{1}{2 pi}right) sqrt{frac{A p}{m}} )
11
898A body of mass ( m ) is lifted up from the
surface of earth to a height three times the radius of the earth ( R ) The change in
potential energy of the body is
A. ( 3 m g R )
в. ( frac{5}{4} ) mg ( R )
c. ( frac{3}{4} m g R )
D. ( 2 m g R )
11
899The car ( A ) of mass ( 1500 k g ) travelling at
( 40 m / s ) collides with another car ( ^{prime} B^{prime} ) of
mass ( 1250 k g ) travelling at ( 25 m / s ) in the same direction. After collision the
velocity of car ‘ ( A^{prime} ) becomes ( 30 m / s )
calculate the velocity of car ( ^{prime} B^{prime} ) after the
collision.
11
900A cricket ball of mass ( mathrm{m} ) is hitted at the
angle ( 45^{circ} ) to the horizontal with velocity
v.lts kinetic energy at the topmost point is
( mathbf{A} cdot mathbf{0} )
B ( cdot frac{1}{2} m v^{2} )
c. ( frac{m v^{2}}{4} )
D. ( frac{m v^{2}}{2 sqrt{2}} )
11
901A vertical narrow smooth tube is bent
from it’s diameter such that one
semicircular part of the tube is
horizontal and the other part is vertical
A smooth ball is released from the
highest point of the tube. If the
maximum speed of ball is ( boldsymbol{x} boldsymbol{m} / boldsymbol{s}, ) then
the value of ( x ) is :
(neglect collision at bending) (take
( boldsymbol{R}=mathbf{2 . 5 m} ) and ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} )
11
902A truck and a car are moving on a smooth, level road such that the K.E.
associated with them is the same.
Brakes are applied to both of them simultaneously. Which one will cover a greater distance before it stops?
A . car
B. truck
c. the same distance
D. nothing can be decided
11
903Two identical balls of equal masses ( A )
and ( mathrm{B} ), are lying on a smooth surface as shown in the figure. Ball A hits the ball B (which is at rest) with a velocity ( v= ) ( 16 m s^{-1} . ) What should be the minimum
value of coefficient of restitution
between ( A ) and ( B ) so that ( B ) just reaches the highest point of inclined plane?
( left(g=10 m s^{-2}right) )
A ( cdot frac{2}{3} )
B. ( frac{1}{4} )
( c cdot frac{1}{2} )
D. ( frac{1}{3} )
11
904What is the nature of force between the
colliding bodies?
A. External
B. conservative
( c . ) Internal
D. Non conservative
11
905If ( g ) is acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ( m ) raised from the surface of earth to a height equal to the radius ( R ) of the earth is
( ^{mathbf{A}} cdot frac{1}{2}^{m g R} )
в. ( 2 m g R )
( mathrm{c} cdot m g R )
D. ( frac{1}{4} m g R )
11
90622. The potential energy curve for interaction between two
molecules is shown in Fig. 8.277. Which of the following
statements are true?
a. The molecules have maximum attraction for r=0A.
OHAB co
Fig. 8.277
b. The molecules have maximum kinetic energy for r =
OB.
c. The intermolecular force is zero for r = OB.
d. For the gaseous state, the depth BD of the potential energy
curve is much smaller than KT.
11
90778. A moving railway compartment has a spring of constant
k fixed to its front wall. A boy stretches this spring by
distance x and in the mean time the compartment moves
by a distance s. The work done by boy w.r.t. earth is
ロロロロロロ
AUW
Fig. 8.256
– kx²
b.
(kx) (s + x)
kxs
kx(stxts)
1
111
11
908A body is dropped from a certain height.
When it loses ( U ) amount of its energy it
acquires a velocity’ ( v^{prime} . ) The mass of the
body is:
A ( cdot 2 U / v^{2} )
B ( cdot 2 v / U^{2} )
c. ( 2 v / U )
D. ( U^{2} / 2 v )
11
909Derive an expression for work done in
sliding body down a rough inclined plane
11
910A uniform bar of mass ( M ) and length ( L )
collides with a horizontal surface.
Before collision, velocity of centre
of mass was ( v_{0} ) and no angular velocity. Just after collision, velocity of centre of
mass of bar becomes ( boldsymbol{v} ) in upward
direction as shown. Angular velocity ( omega )
of the bar just after impact is:
( A )
в.
c. ( frac{left(v_{0}+vright) cos theta}{L} )
( D )
11
91153. One end of an unstretched vertical spring is attached to the
ceiling and an object attached to the other end is slowly
lowered to its equilibrium position. If S is the gain in spring
energy and G is the loss in gravitational potential energy
in the process, then
a. S=G
b. S=2G
c. G= 2S
d. None of these
11
912The maximum vertical distance
through which a fully dressed astronaut canjump on the earth is ( 0.5 m . ) If mean
density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical
distance which he can jump on the
Moon and the ratio of the time of
duration of the jump on the Moon to hold on the earth are
в. ( 6 m, 3: ) ?
( c .3 m, 1: 6 )
D. ( 6 m, 1: 6 )
11
913A ball moving with velocity ( 2 m / s ) collides head on with another stationary
ball of double the mass. If the
coefficient of restitution is ( 0 cdot 5, ) then
their velocities ( (operatorname{in} m / s) ) after collision
will be
A . 0,1
в. 1,1
c. ( 1,0 cdot 5 )
D. 0,2
11
914A ball of mass m moving with velocity collides elastically with another ball of identical mass coming from the opposite direction with velocity ( 2 v ) Their velocities after collision are :
A . ( -v, 2 v )
в. ( -2 v, v )
c. ( v,-2 v )
D. ( 2 v,-v )
11
915A neutron in a nuclear reactor collides
head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is
A ( cdot frac{11}{12} )
B. ( frac{2}{11} )
c. ( frac{48}{121} )
D. ( frac{48}{169} )
11
916( underbrace{[L atop L} )11
917A body is moved in a direction opposite to the direction of force acting on it. Work is done is:
A. against the force
B. zero
c. along the force
D. none of these
11
918Potential energy of an object raised through a height h is ( (1 / 2 )
( left.m v^{2}, m g hright) )
11
work energy theorem
This question has multiple correct options
A. work done by all the conservative forces is equal to the decrease in potential energy.
B. work done by all the forces except the conservative forces is equal to the change in mechanical energy.
C. work done by all the forces is equal to the change in kinetic energy.
D. work done by all the forces is equal to the change in potential energy.
11
920Two vectors ( A ) and ( sqrt{3} A ) are acting
perpendicular to each other. What is the angle of resultant vector with ( boldsymbol{A} )
11
921A particle of mass ( m ) is moving along
( x- ) axis with speed ( v ) when it collides
with a particle of mass ( 2 m ) initially at
rest. After the collision, the first particle
has come to rest and the second
particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the
two places? ( (boldsymbol{theta}>mathbf{0}) )
A. each piece moves with speed ( v ).
B. each piece moves with speed ( v / 2 )
c. one of the piece moves with speed ( v / 2 ), the other moves with speed greater than ( v / 2 ).
D. each piece moves with speed greater than ( v / 2 )
11
weighs ( m^{prime} . ) Ejection of fuel gas is at a
constant rate of ( m_{0} ) per second with a
constant velocity of ( u_{r e l} ) relative to the
rocket. Final speed of rocket after the
complete burn out of the fuel is given by
( boldsymbol{v}= )
( ^{mathbf{A}} cdot_{u_{r e l}} log _{e} frac{m}{m^{prime}} )
в. ( quad u_{r e l} log _{e} frac{m_{0}}{m} )
( ^{mathrm{c}} cdot_{-u_{r e l}} log _{e} frac{m_{0}}{m^{prime}} )
D. ( -u_{r e l} frac{d m}{m} )
11
923elevated ends and a flat central part as shown in the Figure below. The flat portion BC has a length ( l=3.0 m . ) The
curved portions of the track are
frictionless. For the flat part the
coefficient of kinetic friction is ( mu_{k}= )
( 0.20, ) the particle is released at point ( A )
which is at height ( h=1.5 m ) above the
flat part of the track. Where does the
particle finally comes to rest?
B. The particle comes to rest at ( frac{1}{4} ) th distance from the point B of the flat part.
C. The particle comes to rest at ( frac{3}{4} ) th distance from the
point B of the flat part.
D. The particle comes to rest at point
11
924Two identical smooth balls are
projected from points 0 and ( A ) on the horizontal ground with same speed of projection. the angle of projection in
each case is ( 30^{circ} ) (see figure). The distance between 0 and ( A ) is 100 m. The
their respective points of projection. If the coefficient of restitution is ( 0.7, ) find
the speed of projection of either ball (in
( mathrm{m} / mathrm{s}) ) correct to nearest integer. (Take
( left.g=10 m s^{-2} text {and } sqrt{3}=1.7right) )
11
925A ball strikes a horizontal floor at
( 45^{circ} .25 % ) of its kinetic energy is lost
collision. Find the coefficient of
restitution
A .
в. ( frac{1}{sqrt{2}} )
c. ( frac{1}{sqrt{4}} )
D.
11
926A man applying a force ( boldsymbol{F} ) upon a stretched spring is stationary in a compartment moving with constant
speed ( v . ) If the compartment covers a
distance ( L ) in some time ( t, ) then
This question has multiple correct options
A. The man acting with force F on spring does the work ( (w)=F L )
B. The total work performed by man on the compartment with respect to ground is zero
c. The work done by friction acting on man with respect to ground is, (w) ( =F L )
D. The total work done by man with respect to ground is ( (w)=F L )
11
927A ball of mass ( 10 mathrm{kg} ) is moving with a velocity of ( 10 mathrm{m} / mathrm{s} ). It strikes another ball
of mass ( 5 mathrm{kg} ), which is moving in the same direction with a velocity of ( 4 mathrm{m} / mathrm{s} ) If the collision is elastic their
velocities after collision will be
respectively:
A ( cdot 12 mathrm{m} / mathrm{s}, 6 mathrm{m} / mathrm{s} )
B. ( 12 mathrm{m} / mathrm{s}, 25 mathrm{m} / mathrm{s} )
( c cdot 6 m / s, 12 m / s )
D. ( 8 mathrm{m} / mathrm{s}, 20 mathrm{m} / mathrm{s} )
11
928A bullet of mass m moving with a
velocity ( v_{1} ) strikes a suspended wooden
block of mass ( mathrm{M} ) as shown in the figure
and sticks to it. If the block rises to a
height h the initial velocity of the bullet
is-
A ( cdot frac{m+M}{m} sqrt{2 g h} )
( mathbf{B} cdot sqrt{2 g h} )
c. ( frac{M+m}{m} sqrt{g h} )
D. ( frac{m}{M+m} sqrt{2 g h} )
11
929A body is displaced from (0,0) to ( (1 m, 1 m) ) along the path ( x=y ) by a force ( boldsymbol{F}=left(boldsymbol{x}^{2} hat{boldsymbol{j}}+boldsymbol{y} hat{boldsymbol{i}}right) boldsymbol{N} . ) The work done
by this force will be :
A ( cdot frac{4}{3} J )
в. ( frac{5}{6} J )
( c cdot frac{3}{2} J )
D. ( frac{7}{5} J )
11
930A mass ( m ) is placed at point ( P ) lies on the axis of a ring of mass ( mathrm{M} ) and radius
( R ) at a distance ( R ) from its centre. The
gravitational force on mass ( mathrm{m} ) is then
( ^{mathbf{A}} cdot frac{G M m}{sqrt{2} R^{2}} )
в. ( frac{G M m}{2 R^{2}} )
c. ( frac{G M m}{2 sqrt{2} R^{2}} )
D. ( frac{G M m}{4 R^{2}} )
11
931A ball is dropped on to a horizontal plate from a height ( h=9 mathrm{m} ) above it. If the
coefficient of restitution is ( e=1 / 2, ) the
total distance travelled before the ball
comes to rest is
A . ( 10 mathrm{m} )
B. 15 ( m )
( c cdot 20 m )
D. 25 m
11
932A parallel beam of particles of mass ( m )
moving with velocities ( v ) impinges on
a wall at an angle ( theta ) to its normal. The number of particles per unit volume in the beam is ( n ). if the collision of
particles with the wall is elastic, then find the pressure exerted by this beam
on the wall.
11
933What do you understand by work?11
934A light rigid rod of length ( boldsymbol{L}=frac{8}{5} mathrm{m} )
hinged at one end has a bob of mass ( mathrm{m} )
attached to its other end. Find speed (in
( mathrm{m} / mathrm{s} ) ) of bob at the lowest point when rod is released from vertical position.
11
935( mathbf{A} )
1 kg stationary bomb is exploded in three parts having mass ratio 1: 1: 3
Parts having same mass move in perpendicular directions with velocity ( 30 m / s, ) then the velocity of bigger part will be:
( mathbf{A} cdot 10 sqrt{2} mathrm{m} / mathrm{s} )
В. ( frac{10}{sqrt{2}} m / s )
c. ( 15 sqrt{2} mathrm{m} / mathrm{s} )
D. ( frac{15}{sqrt{2}} m / s )
11
936Two bodies of masses ( 0.1 k g ) and ( 0.4 k g ) move towards each other with velocities
( 1 m / s ) and ( 0.1 m / s ) respectively. After
collision they stick together. In ( 10 s ) the combined mass travels
( mathbf{A} cdot 120 m )
B. ( 0.12 m )
( c .12 m )
D. ( 1.2 m )
11
937Which of the following is not an example of potential energy?
A. A vibrating pendulum at its maximum displacement from the mean position
B. A body at rest at some height from the ground
C. A wound clock-spring
D. A vibrating pendulum when it is just passing through the mean position
11
938A bullet of mass ( 20 g ) is moving with a
speed of ( 150 mathrm{ms}^{-1} . ) It strikes a target and is brought to rest after piercing 10 ( c m ) into it. Calculate the average force
of resistance offered by the target.
A ( .2500 mathrm{N} )
в. 2000 J
c. ( 2250 N )
D. 2100 J
11
939Light with an energy flux of ( 20 mathrm{W} / mathrm{cm}^{2} ) falls on a non-reflecting surface at normal incidence. If the surface has
an area of ( 30 mathrm{cm}^{2} ), the total
momentum delivered (for complete
absorption) during 30 minutes is :
A ( .3 .6 times 10^{-3} mathrm{kg} mathrm{m} / mathrm{s} )
B. ( 3.3 times 10^{-8} mathrm{kg} mathrm{m} / mathrm{s} )
c. ( 10.8 times 10^{4} mathrm{kg} mathrm{m} / mathrm{s} )
D. ( 1.08 times 10^{7} mathrm{kg} mathrm{m} / mathrm{s} )
11
940A body of mass ‘ ( m ) ‘ is raised to a height
( 10 R^{prime} ) from the surface of the Earth,
where ‘ ( R^{prime} ) is the radius of the Earth. The
increase in potential energy is ( G= ) universal constant of gravitation,
( M= ) mass of earth and ( g= ) acceleration due to gravity)
( ^{A} cdot frac{G M m}{11 R} )
в. ( frac{G M m}{10 R} )
c. ( frac{m g R}{11 G} )
D. ( frac{10 G M m}{11 R} )
11
941A car is going with a linear momentum
p. When brakes are applied, it comes to
a stop in a distance ( s ). If the same car
were going with a linear momentum ( 2 p ) and the brakes are applied, it comes to a stop in a distance of (assume that the
brake force is same in the two cases)
( mathbf{A} cdot 2 s )
B.
c. ( 4 s )
D.
11
942A bomb of mass 9 kg explodes into two pieces of masses ( 3 mathrm{kg} ) and 6 kg. The velocity of mass ( 3 mathrm{kg} ) is ( 16 mathrm{ms}^{-1} ). The
kinetic energy of mass ( 6 mathrm{kg} ) is
A . 96 J
B. 384 J
c. 192 J
D. 768 J
11
943A particle moves in such a way that its position vector at any time ( t ) is ( vec{r}=t hat{i}+ ) ( frac{1}{2} t^{2} hat{j}+t hat{k} . ) Find as a function of time
(i) the velocity ( left(frac{d vec{r}}{d t}right) )
(ii) the speed ( left(left|frac{d vec{r}}{d t}right|right) )
(iii) the acceleration ( left(frac{boldsymbol{d} overrightarrow{boldsymbol{v}}}{boldsymbol{d} boldsymbol{t}}right) )
(iv) the magnitude of the acceleration
(v) the magnitude of the component of acceleration along velocity (called tangential acceleration)
(vi) the magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).
11
944A pair of starts rotates about a common
centre of mass. One of the stars has a
mass ( M ) and the other ( m ). Their centres
are a distance ( d ) apart, ( d ) being large
compared to the size of either star. Derive an expression for the period of
revolution of the stars about their
common centre of mass. Compare their angular momenta and kinetic energies.
11
945A block of mass ( 2.0 mathrm{kg} ) is pushed down
an inclined plane of inclination ( 37^{circ} ) with
a force of ( 20 N ) acting parallel to the incline. It is found that the block moves
on the incline with an acceleration of
( 10 m / s^{2} . ) If the block started from rest, find the work done
(a) by the applied force in the first second
A . 100
B. 105
c. 150
D. 200
11
946Block A has a weight of 300N and block
B has a weight of 50 N. If the coefficient
of kinetic friction between the incline
and block ( A ) is ( mu_{k}=0.2 . ) Determine the speed of block A after it moves ( 1 mathrm{m} ) down
the plane, starting from rest. Neglect the mass of the cord and pulleys.
11
947The energy required to raise a given volume of water from a well can be
A. Mega watts
B. Mega newton
c. Mega joules
D. Kilo watts
11
948If a body of mass ( 200 g ) falls from a
height ( 200 m ) and its total potential
energy is conserved into kinetic energy, at the point of contact of the body with the surface, then decrease in potential
energy of the body at the contact is
begin{tabular}{l}
A. 9005 \
hline
end{tabular}
в. ( 500 J )
c. ( 400 J )
D. ( 200 J )
11
949If a simple pendulum of mass ( boldsymbol{m} ) is
displaced by a distance of ( x ) from its
mean position, then find the potential energy stored in it.
11
950A body when acted upon by a force of
10 ( k g f ), gets displaced by ( 0.5 m ) normal to the force. Calculate the work done by
the force, when the displacement is in the direction of force.
A . ( 5 . J )
в. ( 500 J )
c. ( 0.5 J )
D. ( 50 J )
11
951i ule paul in between
tol surface. A
4. A long block A is at rest on a smooth horizontal surface. A
small block B whose mass is half of mass of A is placed on
A at one end and is given an initial velocity u as shown in
Fig. 8.274. The coefficient of friction between the blocks
is u.
HB
Smooth
Fig. 8.274
a. Finally both move with a common velocity 2u/3.
b. Acceleration of B relative to A initially is 3ug/2 towards
left.
c. Magnitude of total work done by friction is equal to
the final kinetic energy of the system.
d. The ratio of initial to final momentum of the system
is 1.
Choose the correct statement(s) from the following
11
952A block ( A, ) whose weight is ( 200 N ), is
pulled up a slope of length ( 5 m ) by
means of a constant force ( boldsymbol{F}(=mathbf{1 5 0} boldsymbol{N}) )
as illustrated in Figure.
What is the work done by the force ( boldsymbol{F} ) in
moving the block ( A, 5 m ) along the
slope?
A ( .450 J )
B. ( 600 J )
( c .0 J )
D. ( 750 J )
11
953A body of volume ( V ) and density ( rho ) is initially submerged in a liquid of density ( rho^{prime} . ) If it lifted through a height ( h ) in the liquid, its potential energy will:
A . increase by ( h Vleft(rho-rho^{prime}right) g )
B. decrease by ( h Vleft(rho-rho^{prime}right) g )
C . increase by ( h V_{rho g / rho} )
D. decrease by ( h V_{rho g / rho} )
11
954Determine the loss in kinetic energy of the system as whole as a result of the
collision.
( ^{mathbf{A}} cdot frac{1}{6} m v^{2} )
в. ( frac{1}{7}^{m v^{2}} )
( mathrm{c} cdot m v^{2} )
D. ( frac{m v^{2}}{5} )
11
955A glass marble dropped from a certain height above the horizontal surface reaches the surface in time ( t ) and then
continues to bounce up and down. The time in which the marble finally comes to rest is:
( mathbf{A} cdot e^{n} t )
B . ( e^{2} t )
( ^{mathbf{c}} cdot tleft[frac{1+e}{1-e}right] )
D. ( tleft[frac{1-e}{1+e}right] )
11
956A ( 0.50 k g ) object moves in a horizontal circular track with a radius of ( 2.5 m . ) An
external force of ( 3.0 N, ) always tangent
to the track, causes the object to speed
up as it goes around. The work done by the external force as the mass makes
one revolution is:
A ( .24 J )
B. ( 47 J )
c. ( 58 J )
D. ( 67 J )
11
957The negative of the distance rate of change of potential energy is equal to:
A. force acting on the particle in the direction of displacement
B. acceleration of the particle, perpendicular to displacement
c. power
D. impulse
11
958A block of mass ( 50 mathrm{kg} ) is projected
horizontally on a rough horizontal floor.
The coefficient of friction between the
block and the floor is ( 0.1 . ) The block
strikes a light spring of stiffness ( boldsymbol{k}= )
( 100 N / m ) with a velocity ( 2 m / s . ) The
maximum compression of the spring is
( A cdot 1 m )
3. ( 2 m )
11
959A sphere A impinges directly on an identical sphere ( mathrm{B} ) at rest. If e is the coefficient of restitution then the ratio
of the velocities of ( A ) and ( B ) after impact
is
A ( cdot frac{1+e}{1-e} )
в. ( frac{1-e}{1+e} )
c. ( frac{e}{1-e} )
D. ( frac{e}{1+e} )
11
960Which quantity of a two particles system depend only on the separation between the two particles?
A. Kinetic energy
B. Total mechanical energy
c. Potential energy
D. Both (A) and (B)
11
961A ball is dropped from a height of ( 1 mathrm{m} ). if coefficient of restitution between the
surface and the ball is ( 0.6, ) the ball
rebounds to a height of
( A cdot 0.6 m )
B. 0.4 ( m )
( c cdot 1 m )
D. 0.31 ( m )
11
962Figure shows a wedge ( A ) of mass ( 6 mathrm{m} )
smooth semicircular groove of radius a
( =8.4 mathrm{m} ) placed on a smooth horizontal
surface. A small block B of mass m is
released from a position in groove where its radius is horizontal. Find the
speed (in ( mathrm{ms}^{-1} ) ) of bigger block when
smaller block reaches its bottommost
position
A. ( 3 m / s )
B. ( 2 m / s )
( c .7 m / s )
( mathbf{D} cdot 4 m / s )
11
963If a body is taken up to a height of ( 1600 mathrm{km} ) from the earth’s surface, then the percentage loss of gravitational force acting on that body will be –
(Radius of earth ( R_{e}=6400 mathrm{km} ) ).
A . 50%
B. 36%
c. 25%
D. 10%
11
964According to the definition of oblique collision in the paragraph, which of the following collision cannot be oblique?
A. Collision between two point masses.
B. Collision between two rings of same radius
c. collision between two rings of different radius
D. All the above
11
965A force of ( 5 N ) is applied on a ( 20 k g ) mass at rest. the work done in the third
second is:-
A ( cdot frac{25}{8} J )
в. ( frac{25}{4} J )
c. ( 12 J )
D. 25J
11
966Identify which of the following quantities remain conserved during an elastic collision?
A. momentum only
B. momentum and potential energy
c. kinetic energy only
D. momentum and kinetic energy
E. momentum end velocity
11
967A loud speaker converts:
A. electrical energy into sound energy
B. sound energy into electrical energy
C. mechanical energy into sound energy
D. sound energy into mechanical energy
11
968rolling on a smooth horizontal surface
with velocity ( V ) and angular velocity ( omega )
(where ( V=omega r) . ) The sphere collides
with a sharp edge on the wall as shown
in the figure. The coefficient of friction
between the sphere and the edge ( mu= )
1/5. Just after the collision the angular
velocity of the sphere becomes equal to
zero. The linear velocity of the sphere
just after the collision is equal to:
( mathbf{A} cdot V )
B. ( underline{V} ) ( overline{5} )
c. ( frac{3 V}{5} )
D. ( frac{V}{6} )
11
969Two satellites ( A ) and ( B ) of the same
mass are revolving around the earth in the concentric circular orbits such that
the distance of satellite ( B ) from the
centre of the earth is thrice as
compared to the distance of the
satellite ( A ) from the centre of the earth.
The ratio of the centripetal force acting on ( B ) as compared to that on ( A ) is
A ( cdot frac{1}{3} )
B. 3
c. ( frac{1}{9} )
D. ( frac{1}{sqrt{3}} )
11
970Illustration 3.34 A body constrained to move along the z-axis
of a co-ordinate system is subjected to a constant force F given
by F=-i +2j+3k newton where i, j, and ſ represent unit
vectors along X-, y, and z-axes of the system, respectively.
Calculate the work done by this force in displacing the body
through a distance of 4 m along the z-axis.
11
971A ( 12 k g ) bomb at rest explodes into two
pieces of ( 4 k g ) and ( 8 k g . ) If the momentum
of ( 4 k g ) piece is ( 20 N s, ) the kinetic energy
of the ( 8 k g ) piece is:
A ( .25 J )
B. ( 20 J )
c. ( 50 J )
D. ( 40 J )
11
972In one – dimensional head on
collision, the relative velocity of approach before collision is equal to:
A. relative velocity of separation after collision
B. ( e ) times relative velocity of separation after collision
c. ( 1 / e ) times relative velocity of separation after collision
D. sum of the velocities after collision
11
973The velocity of a particle is ( overrightarrow{boldsymbol{v}}=mathbf{6} hat{mathbf{i}}+ )
( 2 hat{j}-2 hat{k} . ) The component of the velocity parallel to vector ( vec{a}=hat{i}+hat{j}+hat{k} ) is :-
( mathbf{A} cdot 6 hat{i}+2 hat{j}+2 hat{k} )
B . ( 2 hat{i}+2 hat{j}+2 hat{k} )
( mathbf{c} cdot hat{i}+hat{j}+hat{k} )
D. ( 6 hat{i}+2 hat{j}-2 hat{k} )
11
974A body of mass ( 2 mathrm{kg} ) is thrown vertically upwards with an initial velocity of 20 ( mathrm{m} / mathrm{s} . ) What ( mathrm{m}: ) potential energy at the end of ( 2 s ? g=10 m / s^{2} )11
975A car is accelerated on a leveled road
and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car
A. does not change
B. becomes twice to that of initial
c. becomes 4 times that of initial
D. becomes 16 times that of initial
11
976Explain by an example that a body may posses energy when it is not in motion.11
977Two water droplets combine to from a
large drop in this process energy is
11
97811. The work done by the man is
a. mgl b. mgh c. mg
d. mg(l – h)
11
979If ( A ) and ( B ) are two perpendicular vectors given by ( bar{A}=5 bar{i}+7 bar{j}+3 bar{k}, ) and ( 4 bar{B}= )
( 2 bar{i}+2 bar{j}+c bar{k}, ) then the value of ( c ) is:
( A cdot-2 )
B. 8
( c .-7 )
( D cdot-8 )
11
980A certain force acting on a body of mass 2kg increase its velocity from 6m/s to ( 15 mathrm{m} / mathrm{s} ) in ( 2 mathrm{s} ). The work done by the force during this interval is?
A. 27
B. 3J
c. ( 94.5 mathrm{J} )
D. 1890
11
981Hall
Hallo

25. If in the previous problem, we replace the man by a block
of mass m and release it from top of the inclined plane,
and let it gain a speed v, then
a. W friction = -mgh + = mv
b. W gravity = -mgh
c. W friction = 0
d. W friction = – umgx, where x is the horizontal distance
covered and u is the coefficient of friction between
the block and the ground.
11
982If ( vec{A}=2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to ( vec{B}=4 hat{j}-4 hat{i}+alpha hat{k}, ) then the value of ‘ ( alpha^{prime} )
is
A .
B.
c. -1
D. ( frac{1}{-2} )
11
983Marbles, each of mass ( 1 mathrm{g} ) are dropped from a height of ( 10 mathrm{m} ) on to a horizontal
smooth metal surface at the rate of 50
per second. Find the force on the surface. If the surface were inclined to
the horizontal at an angle of ( 60^{circ}, ) what would be force on it be? Assume
collisions to be elastic. ( g=9.8 m / s^{2} )
A. ( 1.2 N ; 0.7 N )
в. ( 1.4 N ; 0.5 N )
c. ( 1.4 N ; 0.7 N )
D. ( 0.4 N ; 0.4 N )
11
984A mass of ( 20 mathrm{kg} ) moving with a speed of ( 10 m / s ) collides with another stationary mass of 5 kg. As a result of the collision,
the two masses stick together. The kinetic energy of the composite mass
will be
( mathbf{A} cdot 600 J )
в. ( 1000 J )
c. ( 800 J )
D. ( 1200 J )
11
985tilustration 8.8 Consider a variable force F=(3x + 5) N acting
on a body and if it is displaced from x=2 m tox=4 m, calculate
the work done by this force.
11
986A force ( F ) acting on an object varies
with distance ( x ) as shown in the figure.
The work done by the force in moving
the object from ( x=0 ) and ( x=20 m ) is
A . ( 500 J )
B. ( 1000 J )
c. ( 1500 J )
D. ( 2000 J )
11
987The potential energy of a particle in a space is given by ( U=x^{2}+y^{2} ). Find the
force associated with this potential
energy:
A ( .-2 x hat{i}-2 y hat{j} )
B . ( 2 x hat{i}-2 y hat{j} )
c. ( -2 x hat{i}+2 y hat{j} )
D. ( 2 x hat{i}+2 y hat{j} )
11
988Read the assertion and reason carefully
to mark the correct option out of the
options given below:
Assertion: At height ( h ) from ground and
at depth ( h ) below ground, where ( h )
is approximately equal to ( 0.62 R )
the value of ( g ) acceleration due to
gravity is same.

Reason: Value of ( g ) decreases both
sides, in going up and down.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true

11
989An object is acted on by a retarding force of ( 10 N ) and at a particular instant
its kinetic energy is ( 6 J . ) The object will
come to rest after it has travelled a
distance of:
( A cdot 3 )
( frac{5}{5} mathrm{m} )
в. ( frac{5}{3} ) m
c. ( 4 mathrm{m} )
D. 16
11
990A bullet of mass ( mathrm{m} ) is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by a distance d. Then the velocity of the bullet is :
A. ( k d sqrt{M / m} )
в. ( frac{d}{M} sqrt{k m} )
c. ( frac{d}{m} sqrt{k M} )
D. ( frac{k M}{m} sqrt{d} )
11
991A body of mass 3 kg hits a wall at an
angle of ( 600 & ) returns at the same angle. The impact time was0.2 s. Calculate the force exerted on the wall:
A. ( 150 sqrt{3} N )
В. ( 50 sqrt{3} N )
c. ( 100 mathrm{N} )
D. ( 75 sqrt{3} N )
11
992A toy car of mass ( 5 mathrm{kg} ) moves up a ramp
under the influence of force ( F ) plotted
against displacement. The maximum height attained is given by
A ( cdot y_{max }=20 mathrm{m} )
B ( cdot y_{max }=15 mathrm{m} )
( mathbf{c} cdot y_{max }=11 m )
( y_{max }=5 m )
11
993A freely falling body converts:
A. kinetic energy into potential energy
B. potential energy into kinetic energy
C. chemical energy into kinetic energy
D. potential energy into chemical energy
11
994The block is moved from A to C along
three different paths. Find the Work done by friction when the block is
displaced from ( A ) to ( B ) and then from ( B ) to
( mathrm{C} )
A. ( W=-mu m g(a+b) )
в. ( W=-mu m g )
C. ( W=-mu m g(a+b) / 2 )
D. None of the above
11
995A man of mass ( 50 mathrm{kg} ) falls freely from a height of ( 40 mathrm{m} ) into a swimming pool and just come to rest at the bottom of the pool. Assume that the average upward force on the man due to water is ( 1000 mathrm{N} . ) If depth of water in the pool is ( d )
then ( boldsymbol{d} ) is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
A. 20
B. ( 40 mathrm{m} )
( c cdot 10 m )
( D .5 mathrm{m} )
11
996A particle of mass m moving with a velocity v makes a head on elastic
collision with another particle of the same mass initially at rest. The velocity of the first particle after collision is
( A )
B. ( v / 2 )
c. ( 2 v )
D.
11
997A particle in a certain conservative force field has a potential energy given by ( U=frac{20 x y}{z} . ) The force exerted on it is?
A ( cdotleft(frac{20 y}{z}right) hat{i}+left(frac{20 x}{z}right) hat{j}+left(frac{20 x y}{z^{2}}right) hat{k} )
B. ( -left(frac{20 y}{z}right) hat{i}-left(frac{20 x}{z}right) hat{j}+left(frac{20 x y}{z^{2}}right) hat{k} )
( ^{mathrm{c}} cdotleft(frac{20 y}{z}right) hat{i}-left(frac{20 x}{z}right) hat{j}-left(frac{20 x y}{z^{2}}right) hat{k} )
D ( cdotleft(frac{20 y}{z}right) hat{i}+left(frac{20 x}{z}right) hat{j}-left(frac{20 x y}{z^{2}}right) hat{k} )
11
998A body falls from a height of 16 m and
rebounds to a height of 4 m. The coefficient of restitution is
A ( cdot frac{1}{4} )
B. ( frac{1}{2} )
( c cdot frac{3}{4} )
D.
11
99985. A 500-kg car, moving with a velocity of 36 kmh on a
straight road unidirectionally, doubles its velocity in 1 min.
The average power delivered by the engine for doubling
the velocity is
a. 750 W b. 1050 W c. 1150 W d. 1250 W
Tn11
11
1000A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the
coefficient of restitution, then what will be the ratio of velocity of two balls after collision?
A ( cdot frac{1-e}{1+e} )
в. ( frac{e-1}{e+1} )
c. ( frac{1+e}{1-e} )
D. ( frac{e+1}{e-1} )
11
1001A particle of mass ( m_{1} ) collides elastically with a stationary particle of
( operatorname{mass} boldsymbol{m}_{2}left(boldsymbol{m}_{1}>boldsymbol{m}_{2}right) . ) The maximum
angle through which the striking particle may deviate as a result of the collision is given as ( sin theta_{1 max }=frac{x m_{2}}{m_{1}} )
Find ( boldsymbol{x} )
11
1002mg sinumg CUSO
52. The given plot shows the variation of U, the potential
energy of interaction between two particles, with the
distance separating them, r.
UA
(
BD
C
Fig. 8.243
1. B and D are equilibrium points.
2. C is a point of stable equilibrium.
3. The force of interaction between the two particles
is attractive between points C and B, and repulsive
between points D and E on the curve.
4. The force of interaction between the particles is
repulsive between points C and A.
Which of the above statements are correct?
a. 1 and 3 b. 1 and 4 c. 2 and 4 d. 2 and 3
C
1
11
11
1003Illustration 8.23 In the previous illustration, consider the
situation when the string is completely compressed. Then it
begins to relax and will come to its original length.
a. What is the work done by the spring during the period?
b. Is the work done by the spring positive or negative?
11
1004The amount of work done is pumping water out of a cubical vessel of height
( mathrm{m} ) is nearly (Given ( rho_{w a t e r}=1000 mathrm{kg} / mathrm{m}^{3} )
A . 5,000
в. 10,000
c. 5 J
D. 10 J
11
1005A bullet moving with a speed of
( 100 m s^{-1} ) canjust penetrate two
planks of equal thickness. Then, the number of such planks penetrated by the same bullet when the speed is
doubled will be:
( A cdot 6 )
B. 10
( c cdot 4 )
D.
11
1006A mass is suspended from the end of a
spring. When the system is oscillating the amplitude of oscillation is ( 4 mathrm{cm} ) and the maximum kinetic energy of
oscillation of the system is 1 joule.
Then the force constant of the spring is:
A. ( 2500 mathrm{N} / mathrm{m} )
в. ( 1250 mathrm{N} / mathrm{m} )
c. ( 500 mathrm{N} / mathrm{m} )
D. ( 250 mathrm{N} / mathrm{m} )
11
1007In elastic collision, ( A ) is conserved while
in inelastic collision ( B ) is conserved.
I.Momentum
II.Kinetic Energy
III.Potential Energy
A. ( A= ) ।, ॥ ( B=1, ) II
в. ( A= ) ।, ॥ ( B=1 )
c. ( A=| ) ( B= ) ॥, ॥ ॥
D. ( A=| ) ( B=1, ) II
11
1008A sphere of mass ( 50 k g ) is attached by a
second sphere of mass ( 90 mathrm{kg} ) with a
force equal to a weight of ( 0.5 m g ) and
their centres are ( 20 mathrm{cm} ) apart.
The gravitational constant is.
A ( .4 .2 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{2} )
B. ( 6.23 times 10^{-15} mathrm{Nm}^{2} mathrm{kg}^{2} )
c. ( 3.3 times 10^{-11} N m^{2} k g^{2} )
D. ( 4.4 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{2} )
11
1009Find the cosine of the angle between the vectors ( overrightarrow{boldsymbol{A}}=(mathbf{3} hat{boldsymbol{i}}+hat{boldsymbol{j}}+mathbf{2} hat{boldsymbol{k}}) boldsymbol{a n d} hat{boldsymbol{B}}= )
( (2 hat{i}-2 hat{j}+4 hat{k}) )
A ( cdot frac{3}{sqrt{21}} )
B. ( frac{sqrt{12}}{sqrt{21}} )
c. ( frac{9}{sqrt{21}} )
D. ( frac{3}{sqrt{12}} )
11
1010Assertion
Velocity time graph of two particles undergoing head-on collsion is shown in the figure. If collision is inelastic then
value of y must be less than ( x )
Reason

Coefficient of restitution(e) ( = ) velocity of |velocity of
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
1011A billiard ball of mass ( M ) moving with
velocity ( v_{1} ) collides with another ball of
the same mass but at rest. If the
collision is elastic the angle of divergence after the collision is
A ( cdot 0^{circ} )
B. ( 30^{circ} )
( c cdot 90^{circ} )
D. ( 45^{circ} )
11
1012A ( 30 g ) bullet initially travelling at ( 120 m / s ) penetrates ( 12 c m ) into a
wooden block. The average resistance by the wooden block is
A ( .2850 N )
в. 22000N
c. ( 2000 N )
D. 1800N
11
1013Which of the following statements
about kinetic energy (K.E.) is true?
A. All objects moving with the same velocity have the same K.E
B. The K.E. of a body will quadruple if its velocity doubles
C. As the velocity of a body increases, its K.E. decreases
D. The K.E. of a body is independent of its mass
11
1014(i) With reference to their direction of
action, how does a centripetal force differ from a centrifugal force?
(ii) State the Principle of conservation of energy.
(iii) Name the form of energy which a body may possess even when it is not in motion.
11
1015A bullet moving with a velocity of ( 200 mathrm{cm} / mathrm{s} ) penetrates a wooden block and comes to rest after traversing ( 4 mathrm{cm} ) inside it. What velocity is needed for travelling distance of ( 9 mathrm{cm} ) in same
block
A. ( 100 mathrm{cm} / mathrm{s} )
B. ( 136.2 mathrm{cm} / mathrm{s} )
c. ( 300 mathrm{cm} / mathrm{s} )
D. ( 250 mathrm{cm} / mathrm{s} )
11
1016Two bodies of unequal masses are dropped from the top of building. Which of the following is equal for both bodies at any instance?
A. Speed
B. Force of gravity
c. Potential energy
D. Kinetic energy
11
1017How soon will the frame come to the
orientation shown in figure (b) after
collision?
( ^{A} cdot frac{pi l}{4 v} )
B. ( frac{7 pi l}{8 v} )
c. ( frac{pi l}{v} )
D. ( frac{7 pi l}{4 v} )
11
1018( operatorname{mass} m=2 k g ) are connected to the
ends of an ideal spring having force
constant ( boldsymbol{k}=mathbf{1 0 0 0} boldsymbol{N m}^{-1} . ) System of
these blocks and spring is placed on a rough floor. Coefficient of friction
between blocks and floor is ( mu=0.5 )
Block B is pressed towards left so that
spring gets compressed.
Initial minimum compression ( boldsymbol{x}_{mathbf{0}} ) of
spring such that block A leaves contact
with the wall when system is released is:
( mathbf{A} cdot 3 mathrm{cm} )
B. ( 4 mathrm{cm} )
( mathbf{c} .5 mathrm{cm} )
D. ( 6 mathrm{cm} )
11
1019A particle of mass ( m_{1} ) moving at
certain velocity collides elastically
head on with a particle of mass ( m_{2} ) at rest. After collision their velocities will
be in the ratio of
A ( cdot frac{m_{1}-m_{2}}{m_{1}+m_{2}} )
в. ( frac{m_{1}-m_{2}}{2left(m_{1}+m_{2}right)} )
c. ( frac{2 m_{1}}{m_{1}-m_{2}} )
D. ( frac{m_{1}-m_{2}}{2 m_{1}} )
11
1020The ( P E ) of a ( 2 k g ) particle, free to move along ( x ) -axis is given by ( V(x)= ) ( left(frac{x^{3}}{3}-frac{x^{2}}{2}right) J . ) The total mechanical energy of the particle is ( 4 J . ) Maximum
speed ( left(operatorname{in} m s^{-1}right) ) is
A ( cdot frac{1}{sqrt{2}} )
B. ( sqrt{2} )
c. ( frac{3}{sqrt{2}} )
D. ( frac{5}{sqrt{6}} )
11
1021The gravitational potential energy of an isolated system of three particles, each of mass ( m ), at the three corners of an
equilateral triangle of side ( l ) is
( ^{text {A }}-frac{G m^{2}}{l} )
в. ( -frac{G m^{2}}{2 l} )
c. ( -frac{2 G m^{2}}{l} )
D. ( -frac{3 G m^{2}}{l} )
11
1022(ii) while climbing up a slope of height
( 10 mathrm{m}left(g=10 m s^{-2}right) ? )
A ( .5 k J^{2} )
( begin{array}{ll}2 & text { 2 } \ text { 2 } & text { 2 }end{array} )
в. ( 50 k J )
c. ( 100 k J^{2} )
D. ( 5 k J )
11
1023A mass ( m_{1} ) moves with a grate velocity.
It strikes another mass ( m_{2} ) at rest in
head-on collision. It comes back along
its path with low speed after collision. Then :
( mathbf{A} cdot m_{1}>m_{2} )
В. ( m_{1}<m_{2} )
( mathbf{c} cdot m_{1}=m_{2} )
D. there is no relation between ( m_{1} ) and ( m_{2} )
11
1024The slope of kinetic energy and displacement curve for a particle in motion will be
A. Equal to the acceleration of the particle
B. Directly proportional to the acceleration of the particl
C . Inversely proportional to the acceleration of the particle
D. None of the above
11
1025A bullet of mass ( m ) hits a target of mass ( M ) hanging by a string and gets embedded in it. If the block rises to a
height ( h ) as a result of this collision, the
velocity of the bullet before the collision
is:
A. ( v=sqrt{2 g h} )
B. ( v=sqrt{2 g h}left(1+frac{m}{M}right) )
c. ( v=sqrt{2 g h}left(1+frac{M}{m}right) )
D. ( v=sqrt{2 g h}left(1-frac{m}{M}right) )
11
1026Five particles each of mass ‘ ( m ) ‘ are kept
at five vertices of a regular pentagon. A sixth particle of mass ‘ ( M^{prime} ) is kept at
centre of the pentagon’ ( O ) ‘. Distance
between ‘ ( M ) ‘ and ‘ ( m ) ‘ is ‘a’. Find
(i) net force on ( ^{prime} boldsymbol{M}^{prime} )
(ii) magnitude of net force on ‘ ( M^{prime} ) if any one particle is removed from one of the vertices.
11
1027If force ( overrightarrow{boldsymbol{F}}=4 hat{hat{boldsymbol{i}}}+5 hat{boldsymbol{j}} ) and displacement
( vec{S}=3 hat{i}+6 hat{j} ) then the work done is
A ( .4 times 3 J )
B. ( 5 times 6 )
( c cdot 6 times 3 )
D. ( 4 times 6 )
11
1028A bullet of mass ( 8 g ) strikes a vertical
wooden plank ( 5 c m ) thick with a velocity of ( 200 m / s ) in a horizontal direction and emerges out of at ( 150 mathrm{m} / mathrm{s} ) in same direction find retarding force bullet experience in wood for what additional thickness bullet will just emerge on
other side
11
1029State and derive work energy theorem.11
1030A raised hammer possesses:
A. K.E. only
B. gravitational P.E.
c. electrical energy
D. sound energy
11
1031Certain force acting on a ( 20 mathrm{kg} ) mass
changes its velocity from ( 5 m s^{-1} ) to
( 2 m s^{-1} . ) Calculate the work done by the
force
A. ( -210 J )
B. ( 210 J )
c. -105 J.
D. ( 420 J )
11
1032The angle made by the vector ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+ )
( 3 hat{j} ) with ( y ) -axis is:
A ( cdot tan ^{-1}left(frac{3}{2}right) )
B. ( tan ^{-1}left(frac{2}{3}right) )
c. ( sin ^{-1}left(frac{2}{3}right) )
D. ( cos ^{-1}left(frac{3}{2}right) )
11
1033A uniform solid sphere of mass ( mathrm{M} ) and
radius ( R ) is kept on the horizontal
surface.

Find potential energy of the solid
sphere
A ( cdot frac{m g R}{2} )
в. тg R
( c cdot frac{m g R}{4} )
D. ( frac{2 m g}{B} )

11
1034A bomb of ( 12 k g ) divides in two parts
whose ratio of masses is ( 1: 3 . ) If kinetic
energy of smaller part is ( 216 J ), then
momentum of bigger part in ( k g- )
( boldsymbol{m} / boldsymbol{s e c} ) will be
A . 36
B. 72
c. 108
D. Data is incomplete
11
1035A mass ( m ) moves with a velocity ( v ) and collides inelastically with another identical mass. After collision, the 1 st
mass moves with velocity ( frac{v}{sqrt{3}} ) in a
direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision
A ( cdot frac{2 v}{sqrt{3}} )
B. ( frac{v}{sqrt{3}} )
( ^{c} cdot sqrt{frac{2}{3}} )
D. The situation of the problem is not possible without external impulse
11
1036There is an isolated planet having mass 2M and radius 2R, where M and R are
the mass and radius of the earth.
simple pendulum having mass ( mathrm{m} ) and length ( mathrm{R} ) is made to small oscillations on the planet. Find the time period of SHM of the pendulum in second. (Take ( left.pi=3.00, mathrm{g}=10 mathrm{m} / mathrm{s}^{2}, sqrt{2}=1.41right) )
A. 8000
B. 6768 s
c. 9000 s
D. 7968 s
11
1037Two astronauts, each of mass ( 75 k g ), are
floating next to each other in space, outside the space shuttle. They push each other through a distance of an arm’s length ( =1 m ) each with a force of
( 300 N ).If the final relative velocity of the
two, w.r.t each other is ( V_{0} m / s, ) find the value of ( frac{left(V_{0}right)^{2}}{4}( ) Note that both astronauts are displaced by ( 1 boldsymbol{m} )
11
1038Find the velocity of a body of mass ( 100 g )
having a kinetic energy of ( 20 J )
11
1039The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of ( sqrt{3 g l} ). Find the angle rotated by the string before it becomes slack.11
1040A force acts on a ( 3 g ) particle in such a
way that position of the particle as a function of time is given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}- )
( 4 t^{2}+t^{3}, ) where ( x ) is in metre and ( t ) is in
sec. The work done during the first ( 4 s ) is
A. 570 mJ
B. 450 mJ
c. ( 490 mathrm{mJ} )
D. 528 mJ
11
1041A ( 20 g ) bullet passes through a plate of
mass ( 1 k g ) and finally comes to rest
inside another plate of mass ( 2980 g ). It
makes the plates move from rest to
same velocity. The percentage loss in velocity of bullet between the plate is:
( A )
B . ( 50 % )
( c .75 % )
D. ( 25 % )
11
1042If two forces ( boldsymbol{F}_{1}=mathbf{2} hat{mathbf{i}}+mathbf{4} hat{boldsymbol{k}} boldsymbol{F}_{2}=mathbf{3} hat{boldsymbol{j}}+ )
( 2 hat{k} ) acts on one body and displaces it from (1,0,0) to (2,1,1) find net work done
11
1043‘lg. 8.206, the pulley shown is smooth. The spring and
me string are light. Block B slides down from the top along
mxed rough wedge of inclination e. Assuming that the
block reaches the end of the wedge, find the speed
block at the end. Take the coefficient of frict
the block and the wedge to be u and that the spring was
relaxed when the block was released from the top of the
wedge.
m
B
h
w
WWW
Fig. 8.206
11
1044A solid cylinder of mass ( 2 mathrm{Kg} ) and radius
( 0.2 mathrm{m} ) is rotating about its own
axis without friction with angular
velocity 3 rad/s. A particle of mass 0.5
( mathrm{Kg} ) and moving with a velocity of ( 5 mathrm{m} / mathrm{s} ) strikes the cylinder and sticks to it as
shown in. The velocity of the system after the particle sticks it will be
11
1045DOOR 13 8 upwalu.
Illustration 8.43 A block of mass m strikes a light pan fitted
with a vertical spring after falling through a distance h. If the
stiffness of the spring is k, find the maximum compression
of the spring
heelll
-00000
Fig. 8.95
11
1046A smooth steel ball strikes a fixed
smooth steel plate at an angle ( theta ) with the vertical. If ‘e’ is the coefficient of
restitution, the angle at which the rebounce will take place with the vertical is
A ( cdot alpha=tan ^{-1}left(frac{tan theta}{e}right) )
B. ( alpha=tan ^{-1}left(frac{cot theta}{e}right) )
c. ( _{alpha=tan ^{-1}left(frac{sin theta}{e}right)} )
D・ ( alpha=tan ^{-1}left(frac{e}{tan theta}right) )
11
1047A ball is bouncing down a flight of stairs. The coefficient of restitution is ( e )
The height of each step is ( d ) and the ball descends one step each bounce. After each bounce it rebounds to a height ( h )
above the next lower step. The height is large compared with the width of step so that the impacts are effectively head-on. Find the relationship between
( boldsymbol{h} ) and ( boldsymbol{d} )
A ( cdot h=frac{d}{1-e^{2}} )
в. ( h=frac{d}{1+e^{2}} )
c. ( h=frac{d}{1+e} )
D. ( h=sqrt{frac{d}{1-e^{2}}} )
11
1048A uniform rod of length ( L ) rests on a frictionless horizontal surface. The rod
is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed ( v ) strikes the rod at
its centre and becomes embedded in it.
The mass of the bullet is one-sixth the
mass of the rod. The ratio of the kinetic
energy of the system before the collision to the kinetic energy of the bullet after the collision is ( frac{1}{x} . ) Find the value of ( x )
11
104922. What is the minimum value of x for which the ball can
reach the point of projection after reaching C?
a. 2Rb
. SR
c. 3R
11
1050A body dropped freely from a height hon to a horizontal plane, bounces up and
down and finally comes to rest.The coefficient of restitution is e. The ratio
of velocities at the beginning and after two rebounds is
A ( cdot 1: e )
B. e:
( c cdot 1: e^{3} )
D. ( e^{2}: 1 )
11
1051Assertion
In elastic collision, kinetic energy is
conserved.
Reason
Energy is always 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
1052A particle of mass ( m_{1} ) moving with
velocity ( v ) strikes with a mass ( m_{2} ) at rest, then the condition for maximum
transfer of kinetic energy is :
( mathbf{A} cdot m_{1}>>m_{2} )
в. ( m_{2}>>m_{2} )
( mathbf{c} cdot m_{1}=m_{2} )
D . ( m_{1}=2 m_{2} )
11
1053A ball of mass ‘m’ moving horizontally
which velocity ‘u’ hits a wedge of mass
( M^{prime} . ) The wedge is situated on a smooth
horizontal source. If after striking with wedge the ball starts moving in vertica
direction and the wedge starts moving
in horizontal plane. Calculated
a) The velocity of wedge ( V )
b) The velocity (v) at which the ball
moves in vertical direction.
c) The impulse imparted by the ball on
the wedge.
d) The coefficient of restitution ( e=? )
11
1054The potential energy of a particle of mass ( 5 k g ) moving in the ( x ) -y plane is given by the equation, ( U=-7 x+24 y )
Joule. Here ( x ) and ( y ) are in the meter at
( boldsymbol{t}=mathbf{0}, ) the particle is at the origin and moving with velocity ( (2 i+3 j) m / s . ) The
magnitude of the acceleration of the particle is:
A ( .3 m / s^{2} )
в. ( 5 m / s^{2} )
c. ( 31 m / s^{2} )
D. ( 15 m / s^{2} )
11
1055A body of mass ( 3 mathrm{kg} ) is under a force which causes a displacement in it, given by ( s=t^{2} / 3(text { in } mathrm{m}) . ) Find the work
done by the force in 2 second.
A . 2
B . 3.8
c. 5.2 J
D . 2.6
11
1056Assertion
A body is moved from ( x=2 ) to ( x=1 )
under a force ( boldsymbol{F}=mathbf{4} boldsymbol{x} ), the work done by
this force is negative.
Reason
Force and displacement are in opposite directions.
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
1057Two particles of equal mass ( m ) go around in a circle of radius ( R ) under the action of
their mutual gravitational attraction. The
speed of each particle is ( v ). Find value of ( v )
( ^{mathrm{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G m}right)} )
в. ( v=sqrt{left(frac{G m}{2 R}right)} )
c. ( v=frac{1}{2} sqrt{left(frac{G m}{R}right)} )
D. ( v=sqrt{left(frac{4 G m}{R}right)} )
11
1058A block of mass ( 10 mathrm{kg} ) is pulled by a constant horizontal force of ( 19 mathrm{N} ) and it
is displaced by ( 15 mathrm{m} ) across the floor. Calculate the work done.
A . 1.3
в. 30 J
c. 285 J
D. 5586 J
E. 1
11
1059The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of
energy?
A. Yes
B. No
c. Yes, at certain instants
D. None of the above
11
1060A body of mass travels in a straight line with a velocity ( v=k x^{3 / 2} ) where ( k ) is a
constant. The work done in displacing the body from ( x=0 ) to ( x ) is proportional
to:
( mathbf{A} cdot x^{1 / 2} )
B. ( x^{2} )
c. ( x^{3} )
D. ( x^{5 / 2} )
11
1061A ( 10 mathrm{kg} ) mass moves along ( mathrm{X} ) -axis. Its
acceleration as a functions of its
position is shown in the figure. What is
the total work done on the mass by the
force as the mass moves from ( x=0 ) to
( x=8 mathrm{cm} ? )
( mathbf{A} cdot 8 times 10^{-2} J )
В. ( 16 times 10^{-2} J )
C. ( 4 times 10^{-4} J )
D. ( 1.6 times 10^{-3} J )
11
1062A ball of mass ( 4 mathrm{kg} ) moving on a smooth horizontal surface makes an elastic collision with another ball of mass ( mathrm{m} ) at
rest in the line of motion of first ball, if
after collision first ball moves in the
same direction with one fourth of its
velocity before collision, then mass of
second ball is :
( A cdot 4 mathrm{kg} )
B. 4.4 kgg ( g g )
c. ( 2.4 mathrm{kg} )
D. ( 2 mathrm{kg} )
11
106387. In the above question, if equal forces are applied on two
springs, then
a. More work is done on Q
b. More work is done on P
c. Heir force constants will become equal
d. Equal work is done on both the springs
oo
11
106441. If the total mechanical energy of the particle is 25 J, then
it can be found in region
a. -10<x<-5 and 6<x< 15
b. -10<x<0 and 6<x< 10
c. -5<x< 6
d. -10<x< 10
11
1065Which of the following statement is
wrong for acceleration due to gravity.
A. ( g ) decreases on going above the surface of earth
B. ( g ) increases on going below the surface of earth
( mathrm{C} cdot g ) is maximum at pole
D. ( g ) increases on going from equator to poles
11
1066The potential energy of a body is given by ( U=A-B x^{2} ) (where ( x ) is the
displacement). The magnitude of force acting on the particle is
A. Constant
B. Proportional to ( x )
c. Proportional to ( x^{2} )
D. Inversely proportional to
11
1067Derive the expression for gravitational potential energy?11
1068A body moves a distance of ( 10 mathrm{m} ) long a straight line under the action of force of
5N. If the work done is 25 joules, the angle which the force makes with the
direction of motion of the body is:
A . ( 0^{circ} )
B. ( 30^{circ} )
( c cdot 60^{circ} )
D. ( 90^{circ} )
11
1069If a vector ( A ) is given as ( A=4 hat{i}+3 hat{j}+ ) ( 12 hat{k}, ) then the angle subtended with the
x-axis is :
( ^{mathbf{A}} cdot sin ^{-1}left[frac{4}{13}right] )
B. ( sin ^{-1}left[frac{3}{13}right] )
( ^{mathbf{c}} cdot cos ^{-1}left[frac{3}{13}right] )
D. ( cos ^{-1}left[frac{4}{13}right] )
11
1070A small ball moves toward right with a velocity ( v ). It collides with the wall and
returns back and continues to and fro
motion. If the average speed for first to and fro motion of the ball is ( (2 / 3) v, ) find the coefficient of restitution of impact.
11
1071The speed of the block when it reaches
the point ( Q ) is
( mathbf{A} cdot 5 m s^{-1} )
B. ( 10 m s^{-1} )
c. ( 10 sqrt{3} mathrm{ms}^{-1} )
D. ( 20 mathrm{ms}^{-1} )
11
1072Calculate the displacement for a body, if the workdone is ( 130 mathrm{J} ) and force
applied is ( 19.5 mathrm{N} )
A. 6.66 m
B. 130 ( m )
( c .2535 mathrm{m} )
D. 20 ( m )
11
1073A ball of mass ( m ) is thrown vertically up
with an initial velocity so as to reach a
height ( h . ) The correct statement is:
A. potential energy of the ball at the ground is ( m g h )
B. kinetic energy imparted to the ball at the ground is zero
c. kinetic energy of the ball at the highest point is ( m g h )
D. potential energy of the ball at the highest point is ( m g h )
11
1074A mass ( m_{1} ) with initial speed ( v_{0} ) in the
positive ( x ) -direction collides with a
( operatorname{mass} boldsymbol{m}_{2}=2 boldsymbol{m}_{1} ) which is initially at
rest at the origin, as shown in figure.
After the collision ( m_{1} ) moves off with
speed ( boldsymbol{v}_{1}=boldsymbol{v}_{0} / 2 ) in the negative ( boldsymbol{y} )
direction, and ( m_{2} ) moves off with speed
( v_{2} ) at angle ( theta . ) Determine ( tan theta, ) and find
( v_{2} ) in terms of ( v_{0} )
11
1075A massless platform is kept on a light elastic spring, as shown in the figure.
When particle of mass ( 0.1 mathrm{kg} ) is dropped on the pan from a height of ( 0.24 mathrm{m} ), the
particle strikes the pan, and the spring
is compressed by ( 0.01 mathrm{m} . ) From what
height should the particle be dropped to
cause a compression of ( 0.04 mathrm{m} ? )
A. ( 0.96 mathrm{m} )
B . ( 2.96 mathrm{m} )
c. 3.96 ( m )
D. ( 0.48 mathrm{m} )
11
1076A stick of mass ( mathrm{m} ) and length lis pivoted at one end and is displacement trough an angle ( theta ). The increase in
potential energy is
11
1077The distance of two planets from the Sun are ( 10^{13} ) and ( 10^{12} mathrm{m}, ) respectively. The ratio
of time periods of these two planets is
A. ( frac{1}{sqrt{10}} )
B. 100
c. ( frac{10}{sqrt{10}} )
D. ( sqrt{10} )
11
10786. In which of the following cases can the work done increase
the potential energy?
a. Both conservative and non-conservative forces
b. Conservative force only
c. Non-conservative force only
d. Neither conservative nor non-conservative forces.
11
10797. The extra power required is
a. 0.4 W b. 0.08 W c. 0.04 W
d. 0.2 W
11
1080A car is moving at ( 100 mathrm{km} / mathrm{h} ). If the mass of the car is ( 950 k g ), its kinetic energy is:
в. ( 0.367 M J )
c. ( 3.67 M J )
D. 3.67J
11
1081In a tug of war, the team that exerts a
larger tangential force on the ground wins, winning team not moving. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. Which of the following work is negative?
A. work by the ground on the winning team.
B. work done by string on the winning team.
c. work by ground on the losing team.
D. total external work on the two teams.
11
1082The gravitational potential due to earth at infinite distance from it is zero. Let
the gravitational potential at a point ( boldsymbol{P} ) be ( -5 J k g^{-1} . ) Suppose, we arbitrarily assume the gravitational potential at infinity to be ( +10 J k g^{-1} ), then the gravitational potential at ( boldsymbol{P} ) will be
( mathbf{A} cdot-5 J k g^{-1} )
( mathbf{B} cdot+5 J k g^{-1} )
c. ( -15 J k g^{-1} )
( mathbf{D} cdot+15 J k g^{-1} )
11
1083The force ( F ) acting on a particle moving
in a straight line is shown below. What is the work done by the force on the particle in the 1st metre of the trajectory?
( A cdot 5 J )
В. ( 10 J )
( c .15 J )
D. 2.5 5
11
1084If a vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{i}-4 hat{j}+alpha hat{k}, ) then the
value of ( alpha ) is
11
1085The graph of kinetic energy (K) of a body versus velocity (v) is represented as
A. hyperbola
B. parabola
c. straight line
D. none of these
11
1086A chain of length ( L ) and mass ( m ) is placed upon a smooth surface. The length of BA is ( (boldsymbol{L}-boldsymbol{b}) ). Calculate the
velocity of the chain when its end
reaches B.
B. ( 2 sqrt{frac{g sin theta}{L}}left(L^{2}-b^{2}right) )
c. ( sqrt{frac{g sin theta}{L}left(L^{2}-b^{2}right)} )
D. ( sqrt{frac{g sin theta}{2 L}}left(L^{2}-b^{2}right) )
11
1087The relation between displacement ( x )
and time ( t ) for a body of mass ( 2 K g ) moving under the action of a force is given by ( x=frac{t^{3}}{3}, ) where ( x ) is in meter and
( t ) in second, calculate the work done by
the body in first 2 seconds.
11
1088Expression for potential energy11
1089Two satellites ( A ) and ( B ) of masses ( m_{1} )
and ( m_{2}left(m_{1}=2 m_{2}right) ) are moving in
circular orbits of radii ( r_{1} ) and
( r_{2}left(r_{1}=4 r_{2}right), ) respectively, around the
earth. If their periods are ( T_{A} ) and ( T_{B} )
then the ratio ( T_{A} / T_{B} ) is
A .4
B . 16
( c cdot 2 )
D. 8
11
1090A force ( F=10 sqrt{2} N ) acts an angle of
( 45^{circ} ) above the horizontal on a ( 2 k g ) block
placed on a rough horizontal surface. The coefficient of friction between the
block and surface is 0.2 Find the work
done by the force ( F ) on the block in ( 5 s )
initially the block is at rest. [Take ( g= )
( left.mathbf{1 0} / boldsymbol{s}^{2}right] )
( mathbf{A} cdot 250 J )
В. ( 2500 J )
c. ( 500 J )
D. ( 50 J )
11
1091If one body collides with another body of same mass at rest inelastically, the ratio of their speeds after collision shall
be-
( A )
в. ( frac{1-e}{1+e} )
c. ( frac{1+e}{1-e} )
( D cdot 1 )
11
1092Illustration 8.64 An automobile of mass m accelerates,
starting from rest, while the engine supplies constant power
P, its position and instantaneous velocity changes w.rt, time
assuming the automobile starts from rest.
11
1093Let ( A, B ) and ( C ) are unit vectors
suppose ( A . B=A . C=0 ) and angle between ( B ) and ( C ) is ( frac{pi}{6} ) then
A ( . A=pm 2(B times C) )
B. ( A=pm sqrt{2}(B times C) )
c. ( A=pm 3(B times C) )
D. ( A=pm sqrt{3}(B times C) )
11
1094Two balls of equal masses are thrown upwards along the same vertical line at
an interval of 2 seconds with the same
initial velocity of ( 39.2 m s^{-1} . ) The total
time of flight of each ball, if they collide at a certain height, and the collision is perfectly inelastic, will be
A. ( 5 s ) and ( 3 s )
B. ( 10 s ) and ( 6 s )
c. ( 5 sqrt{15 s} ) and ( 3 sqrt{15 s} )
D. ( (5+sqrt{15}) s ) and ( (3+sqrt{15}) s )
11
1095Two forces whose magnitudes are in the ratio 3: 5 give a resultant of ( 28 N . ) If the
angle of their inclination is ( 60^{circ} ), find the magnitude of each force.
11
1096The angle ( theta ) between the vector ( p=hat{i}+ ) ( hat{j}+hat{k} ) and unit vector along ( x ) -axis is
( ^{A} cdot cos ^{-1}left(frac{1}{sqrt{3}}right) )
в. ( cos ^{-1}left(frac{1}{sqrt{2}}right) )
( ^{mathrm{c}} cdot cos ^{-1}left(frac{sqrt{3}}{2}right) )
D. ( cos ^{-1}left(frac{1}{2}right) )
11
1097A force of ( 10 N ) is applied along ( x- ) axis calculate amount of work done to
displace body from (2,3) to (-1,4)
11
1098The flowing water of a river possesses
energy.
A. gravitational
B. potential
c. electrical
D. kinetic
11
1099Find the components of ( overrightarrow{boldsymbol{a}}=2 hat{boldsymbol{i}}+boldsymbol{3} boldsymbol{j} )
along the directions of vectors ( hat{i}+hat{j} ) and
( hat{mathbf{i}}-hat{boldsymbol{j}} )
11
1100The moving striker of the carom board
will possess- – – energy
A. Kinetic
B. Potential
c. solar
D. Electric
11
1101A water jet, whose cross sectional are is
‘a’ strikes a wall making an angle ‘ ( boldsymbol{theta}^{prime} )
with the normal and rebounds
elastically. The velocity of water of
density ‘d’ is v. Force exerted on wall is
A ( cdot 2 a v^{2} d cos theta )
B. ( 2 a v^{2} d sin theta )
c. 2 avd ( cos theta )
D. avd cose
11
1102A ( 30 mathrm{kg} ) child climbs 15 meters up a tree when he stops to have a look around. What is the child’s potential energy in joules? [Assume ( left.g=10 m / s^{2}right] )
A . 1500
B. 3000
c. 4500
D. 6000
11
1103Prove work energy theorem for a constant force.11
1104What is the work done by a force of ( 2 mathrm{N} ) in displacing a body by ( 2 mathrm{m} ) in the direction of the force?
A ( cdot 4 J^{2} )
в. ( 6 J )
c. ( 4 J )
D. ( 48 J )
11
1105The work done by an external agent to shift a point mass from infinity to the centre of the earth is W. Then choose the
correct relation.
A. ( w=0 )
B. ( w>0 )
( c cdot w<0 )
D. ( w leq 0 )
11
1106When a body of mass ( m_{1} ) moving with uniform velocity ( 40 m s^{-1} ) collides with
another body of mass ( m_{2} ) at rest, then the two together begin to move with
uniform velocity of ( 30 m s^{-1} . ) The ratio of the mass (i.e., ( frac{m_{1}}{m_{2}} ) ) of the two bodies will be
A .1: 3
в. 3: 1
c. 1: 1.33
D. 1: 0.75
11
1107If ( g ) is the acceleration due to gravity on
the earth’s surface, the gain in the potential energy of an object of mass ( boldsymbol{m} )
raised from the surface of the earth to a
height equal to the radius ( R ) of the earth
is
( ^{mathbf{A}} cdot frac{1}{2}^{m g R} )
в. ( 2 m g R )
( ^{mathrm{c}} cdot frac{1}{4}^{m g R} )
D. ( m g R )
11
11081. TOULD
54. The potential energy function associated with the force
E = 4 xyl + 2x² } is
a. U=-2 xły
b. U=-2xy + constant
c. U = 2xy + constant d. Not defined
1
11
1109Assertion
The change in kinetic energy of a particle is equal to the work done on it by the net force.
Reason
Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
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
1110A body of volume ( V ) and density ( rho ) is raised through height ( h, ) in a liquid of density ( sigma(sigma<rho) . ) The increment in
potential energy of the body is (Given acceleration due to gravity ( =g ) ):
A. ( V rho g h )
в. V( sigma g h )
c. ( V(rho+sigma) g h )
D. ( V(rho-sigma) g h )
11
1111Two identical balls ( A ) and ( B ) are kept on a smooth table as shown. B collides with
A with speed v. For different conditions mentioned in List I, match with speed of A after collision given in List II.
11
1112By applying a force ( boldsymbol{F}=(mathbf{3} boldsymbol{x} boldsymbol{y}-mathbf{5} boldsymbol{z}) boldsymbol{j}+ )
( 4 z k ) a particle is moved along the path
( boldsymbol{y}=boldsymbol{x}^{2} ) from point ( (boldsymbol{0}, boldsymbol{0}, boldsymbol{0}) ) to the point
( (2,4,0) . ) The work done by the ( F ) on the particle is (all values are in SI units)
( A )
в. ( frac{140}{5} J )
c. ( frac{232}{5} J )
D.
11
1113A car is accelerating on a levelled plane and acquires a velocity 3 times of its initial velocity. During this process, the potential energy of the car
A. does not change
B. becomes 1.5 times that of initial potential energy
c. becomes 3 times that of initial potential energy
D. becomes 9 times that of initial potential energy
11
1114The kinetic energy of a body of mass ( boldsymbol{m} )
moving with a velocity ( v ) is given by:
A ( cdot m v^{2} )
в. ( frac{1}{2} m v^{2} )
( mathrm{c} cdot 2 mathrm{mv}^{2} )
D. ( frac{1}{2} m^{2} v^{2} )
11
1115A vessel containing ( 50 k g ) of water of height ( 15 m ) is placed above the ground. Assuming the gravitational potential energy at ground to be zero. What will be the gravitational potential energy of water in the vessel ? ( left(boldsymbol{g}=mathbf{1 0 m} boldsymbol{s}^{-mathbf{2}}right) )
A . ( 0 . J )
в. ( 750 J )
c. ( 3750 J )
D. ( 7500 J )
11
1116A bullet fired into a trunk of a tree loses
( 1 / 4 ) of its kinetic energy in traveling a distance of ( 5 mathrm{cm} . ) Assuming constant
retardation before stopping, it travels a further distance of
A. ( 150 mathrm{cm} )
B. ( 1.5 mathrm{cm} )
c. ( 1.25 mathrm{cm} )
D. ( 15 mathrm{cm} )
11
1117A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of
restitution is e:
A ( cdot frac{1-e}{1+e} )
в. ( frac{e-1}{e+1} )
c. ( frac{1+e}{1-e} )
D. ( frac{e+1}{e-1} )
11
1118Illustration 8.38 The potential energy of configuration
changes in x and y directions as U = kxy, where k is a positive
constant. Find the force acting on the particle of the system
as the function of x and y.
11
111913. The speed y reached by a car of mass m in travelling a
distance x, driven with constant power P, is given by
3xP
(3xP)1/2
a.
v=
b.
y=
m
m
(3xP)1/3
(3xP)
V=
d.
y =
m
11
1120The linear momentum of a particle is given by ( boldsymbol{P}=(boldsymbol{a} sin boldsymbol{t} hat{boldsymbol{i}}-boldsymbol{a} cos boldsymbol{t} hat{boldsymbol{j}}) ) kg-
( mathrm{m} / mathrm{s} ) A force ( overrightarrow{boldsymbol{F}} ) is acting on the particle Select correct alternative/s
A. Linear momentum ( vec{P} ) of particle is always parallel to
B. Linear momentum ( vec{P} ) of particle is always perpendicular to ( vec{F} )
c. Linear momentum ( vec{P} ) is always constant
D. Magnitude of linear momentum is constant with respect to time
11
1121If a ball is thrown upwards from the
Surface of earth:
A. The earth remains stationary while the ball moves upwards
B. The ball remains stationary while the earth moves downwards
C. The ball and earth both moves towards each other
D. The ball and earth both move away from each other
11
1122The decrease in potential energy between top position ( A ) and bottom position B is,
( =boldsymbol{m} boldsymbol{g} boldsymbol{r}-(-boldsymbol{m} boldsymbol{g} boldsymbol{r})=boldsymbol{2 m} boldsymbol{g} boldsymbol{r} quad ldots )
This must be equal to the increase in kinetic energy, when particle move from ( A ) to ( B )
i.e. ( frac{1}{2} boldsymbol{m} boldsymbol{v}_{2}^{2}-frac{1}{2} boldsymbol{m} boldsymbol{v}_{1}^{2} )
11
1123In the elastic collision of heavy vehicle
moving with a velocity ( 10 mathrm{ms}^{-1} ) and a small stone at rest, the stone will fly away with a velocity equal to:
A. ( 40 mathrm{ms}^{-1} )
B. 20 ( mathrm{ms}^{-1} )
( c cdot 10 mathrm{ms}^{-1} )
( D cdot 5 mathrm{ms}^{-1} )
11
112439. If the collision of ball with the building is elastic, then the
angle with the horizontal at which the ball will rebound
from the top of the building is
a. 60° b. 45º c. 30° d. None
11
11253. A force of F = 2xi +2j+3zÂ N is acting on a particle.
Find the work done by this force in displacing the body
from (1, 2, 3) m to (3, 6, 1) m.
a. -10 J b . 100 J c. 10 J d. 1J
11
1126A body of mass ( 0.2 mathrm{kg} ) dropped from a height ‘6 m’. If ( e=frac{1}{sqrt{6}} ) then K.E. lost
during its first bounce from the ground
is
( mathbf{A} cdot 1.96 J )
B. ( 9.8 J )
c. 19.6 .5
D. zero
11
gas particles from both sides as shown
in the figure. The solid dots are
representing the molecules hitting from left side and the faint dots are the
molecules hitting from right side. The
mass of these gas particles is ( boldsymbol{m}= )
( 10^{-26} k g ) and velocity before hitting is
( v_{0}=5 m / s . ) Volume density of the gas
particles on both sides is ( n=10^{25} ) per
( m^{3} . ) Each beam has an area ( A=1 m^{2} )
and the collisions are perfectly elastic.
What is the external force ( F ) (in newton)
required to move the plate with a
constant velocity ( boldsymbol{v}=2 boldsymbol{m} / boldsymbol{s} )
11
1128A body of mass ( 2 k g ) initially at rest moves under the action of an applied
horizontal force of ( 7 N ) on a table with
coefficient of kinetic friction ( =mathbf{0 . 1} )
Compute the Work done by the applied force in ( 10 s )
в. ( 890 J )
c. ( 1000 J )
D. ( 5000 J )
11
1129A particle moves along the ( x ) -axis from
( x=0 ) to ( x=5 m ) under the influence of
a force ( F(text { in } N) ) given by ( F=3 x^{2}- )
( 2 x+7 . ) Calculate the work done by this
force
11
1130An object of mass ( 5 k g ) falls from rest
through a vertical distance of ( 20 m ) and
attains a velocity of ( 10 mathrm{m} / mathrm{s} ). How much work is done by the resistance of air on
the object? ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
A . ( 250 J )
В. ( -650 J )
c. ( -750 J )
D. ( 950 J )
11
1131An aeroplane flying in the sky
possesses:
A. Kinetic but not Potential Energy
B. Potential but not Kinetic Energy
C. Both Kinetic and Potential energy
D. Neither Kinetic nor potential energy
11
1132The angles which the vector ( vec{A}=3 hat{i}+ ) ( 6 widehat{j}+2 widehat{k} ) makes with the co-ordinate
axes are:
A ( cdot cos ^{-1} frac{3}{7}, cos ^{-1} frac{4}{7}, cos ^{-1} frac{1}{7} )
B. ( cos ^{-1} frac{3}{7}, cos ^{-1} frac{6}{7}, cos ^{-1} frac{2}{7} )
C ( cdot cos ^{-1} frac{4}{7}, cos ^{-1} frac{5}{7}, cos ^{-1} frac{3}{7} )
D. None of these
11
1133A small ball is rolled with speed u from point A along a smooth
circular track as shown in Fig. 8.281. If x = 3R, then
X
A

B
Reference
level
Fig. 8.281
21. Determine the required speed u so that the ball returns
to A, the point of projection after passing through C, the
highest point.
127 8. VER
NININ
11
1134If collision between the balls is
completely inelastic, then :
A. there is no loss of kinetic energy of the system
B. entire kinetic energy of the system is lost
C. kinetic energy loss in the system is less than 50%
D. kinetic energy loss in the system is more than 50%
11
1135Pick the odd one out from the following based on the nature of energy possessed by them. (moving car, water stored in a tank, a book on a table,
ceiling fan in OFF position)
11
1136Two balls ( A ) and ( B ) having masses ( m ) kg and ( 2 m mathrm{kg}, ) moving with speeds ( 21 mathrm{m} / mathrm{s} ) and ( 4 mathrm{m} / mathrm{s} ) respectively in opposite direction, collide head on. After collision ( A ) moves with a speed of ( 1 mathrm{m} / mathrm{s} ) in the same direction, then incorrect
statement is :
A. The velocity of B after collision is 6 ( mathrm{m} / mathrm{s} ) opposite to the direction before collision
B. The coefficient of resitution is 0.2
c. The loss of kinetic energy due to collision is ( (200 mathrm{m}) ) )
D. The impulse of the force between the two ball is ( (40 mathrm{m}) ) Ns
11
1137A body is hanging from a rigid support by an extensible string of length ( L ). It is struck inelastically by an identical body of mass ( m ) with horizontal velocity ( v= )
( sqrt{2 g l}, ) the tension in the string
increases just after striking by:
A . ( m g )
в. ( 3 m g )
c. ( 2 m g )
D. None of these
11
1138How much work is done in raising a stone of mass ( 5 mathrm{kg} ) and relative density
3 lying at the bed of a lake through
height of 3 meter? (Take ( g=10 m s^{-2} ) ):
A . 25 J
B. 100
c. 75 J
D. none
11
1139Identify the mismatch of the following.
A. Photo diode – optical signal
B. LED – spontaneous emission
C. Diode laser – stimulated emission
D. Solar cell – electrical energy into light
E. Photo conducting cell – photo detector
11
1140How much work does a person do in
pushing a box with a force of 20 N over a distance of ( 8.0 mathrm{m} ) in the direction of the
force?
A . 1.6
B . 16 J
c. 160
D. 1600
E. 16000
11
1141State work-energy theorem. Prove it for
a variable force.
11
1142A chain of length ( l ) and mass ( m ) lies of
the surface of a smooth hemisphere of
radius ( R>1 ) with one end tied to the
top of the hemisphere. Taking base of the hemisphere as reference line, find
the gravitational potential energy of the
chain.
11
1143A rocket of initial mass 6000 kg ejects
mass at a constant rate of ( 16 k g / s ) with
constant relative speed of ( 11 k m / s ) What is the acceleration of the rocket a
minute after the blast? (Neglect gravity)
( mathbf{A} cdot 28.7 mathrm{m} / mathrm{s}^{2} )
B . ( 34.9 mathrm{m} / mathrm{s}^{2} )
c. ( 39.4 mathrm{m} / mathrm{s}^{2} )
D. ( 27.8 mathrm{m} / mathrm{s}^{2} )
11
1144What are the advantages of wind
energy?
11
1145Three small bodies of identical masses
can move along a straight line. The central body (2) is initially at rest and
bodies 1 and 3 are at a distance ( L ) and ( 2 L )
from the central body respectively.
Bodies 1 and 3 move towards body 2
with speeds ( v_{0} ) each. The collision
between 1 and 2 is perfectly elastic and the collision between body 2 and 3 is perfectly inelastic. After all the collisions are over
A. all the bodies come to rest
B. the body 1 moves towards left, bodies 2 and 3 move towards right
c. body 2 remains at rest and other bodies 1 and 3 turn back
D. all the bodies move towards right.
11
1146How is work done by a force measured
when the force:
(i) is in the direction of displacement.
( (i i) ) is at an angle to the direction of displacement.
11
1147Three vectors ( vec{P}, vec{Q}, vec{R} ) are such that the ( |overrightarrow{boldsymbol{P}}|=|overrightarrow{boldsymbol{Q}}|,|overrightarrow{boldsymbol{R}}|=sqrt{mathbf{2}}|overrightarrow{boldsymbol{P}}| ) and ( overrightarrow{boldsymbol{P}}+overrightarrow{boldsymbol{Q}} )
( +vec{R}=0 . ) The angle between ( vec{P} ) and ( vec{Q}, vec{Q} ) and ( vec{R} ) and ( vec{P} ) and ( vec{R} ) will be respectively.
B . ( 90^{circ}, 45^{circ} ), ( 45^{circ} )
c. ( 45^{circ}, 90^{circ}, 90^{circ} )
D . ( 45^{circ}, 135^{circ}, 135^{circ} )
11
1148In above shown figure, a ball of mass 4 kg slides over frictionless surface and
strikes the post with velocity of ( 1 mathrm{m} / mathrm{s} )
and rebounds toward the north at the
same speed. The change in the magnitude of the eastward component
of the momentum of the disk is:
A. ( -4 k g-m / s )
в. ( -1 k g-m / s )
c. ( 0 k g-m / s )
D. ( 1 k g-m / s )
E . ( 4 k g-m / s )
11
1149A force is applied to box of mass ( 4 mathrm{kg} ) and it changes the velocity from ( 3 mathrm{m} / mathrm{s} ) to ( 6 mathrm{m} / mathrm{s} ) in ( 8 mathrm{s} ). Determine the work done
by force during the this process.
A . 27 J
B. 54 J
c. 72 J
D. 96 J
E. cannot be determined from the information given
11
1150Initial speed of the bullet is
A ( .549 m / s )
B. ( 502 m / s )
c. ( 475 mathrm{m} / mathrm{s} )
D. ( 624 mathrm{m} / mathrm{s} )
11
1151Consider elastic collision of a particle of mass ( m ) moving with a velocity ( u ) with
another particle of the same mass at rest. After the collision the projectile and the stuck particle move in
directions making angles ( theta_{1} ) and ( theta_{2} )
respectively with the initial direction
of motion. The sum of the angles ( boldsymbol{theta}_{1}+boldsymbol{theta}_{2} )
is
11
1152If ( vec{A} cdot vec{B}=vec{A} times vec{B}, ) then angle between ( vec{A} ) and ( vec{B} ) is
A . 45
B. 30
( c cdot 60^{circ} )
D. ( 90^{circ} )
11
1153A proton moving with a velocity of ( 1.25 times 10^{5} mathrm{m} / mathrm{s} ) collides with a
stationary helium atom. The velocity of proton after collision is
( mathbf{A} cdot 0.75 times 10^{5} m s^{-1} )
B . ( 7.5 times 10^{5} mathrm{ms}^{-1} )
c. ( -7.5 times 10^{5} mathrm{ms}^{-1} )
D. ( 0 m s^{-1} )
11
1154Two balls initially moving in same
direction with speed ( 10 m s^{-1} ) and
( 5 m s^{-1} ) make a head-on collision. After
collision, they move with speed ( 4 m s^{-1} )
and ( 6 m s^{-1} ) in the same direction. Coefficient of restitution of collision is :
A . 0.2
B. 0.4
( c cdot 0.6 )
D. 0.8
11
1155The atmospheric pressure and height of barometer column is ( 10^{5} P_{a} ) and ( 760 mathrm{mm} )
respectively on the earth surface. If the barometer is taken to moon then column height will be
A . zero
B. 76 mm
c. ( 126.6 mathrm{mm} )
D. 760 mm
11
1156Two identical blocks ( A ) and ( B ), each of
mass ‘m’ resting on a smooth horizontal surface, are inter connected by spring of stiffness ‘K’. If the block B is acted on by
a horizontal force ‘ ( mathrm{F}^{prime} ) and the elongation
of the spring is ‘e’, the relative acceleration between the
blocks is equal to
A ( cdot frac{F}{2 m} )
B. ( frac{F-K e}{m} )
( mathbf{c} cdot frac{F-2 K e}{m} )
D. ( frac{K e}{m} )
11
1157The kinetic energy acquired by a mass ( mathrm{m} ) after travelling a fixed distance from rest under the action of constant force
is
A. directly proportional to velocity.
B. directly proportional to m.
c. independent of m.
D. inversely proportional to ( mathrm{m} ).
11
1158A force ( F=left(3 x^{2}+2 x-7right) N ) acts on a
( 2 k g ) body as a result of which the body gets displaced from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=mathbf{5} boldsymbol{m} )
The work done by the force will be:
A . ( 5 . J )
B. ( 70 J )
( mathrm{c} .115 mathrm{J} )
D. ( 270 J )
11
1159An automobile engine propels a ( 1000 mathrm{kg} ) car ( A ) along a leveled road at a speed of ( 36 k m h^{-1} . ) The frictional force is 100
N. Suppose after traveling a distance of ( 200 mathrm{m}, ) this car collides with another
stationary car ( mathrm{B} ) of the same mass and comes to rest. Let Its engine also stop at the same time. Now, car B starts
moving on the same level road without getting its engine started. Find the speed of the car B just after the collision.
A. ( 36 mathrm{km} / mathrm{h} )
B. 72 km/h
( mathbf{c} cdot 18 mathrm{km} / mathrm{h} )
D. ( 100 mathrm{km} / mathrm{h} )
11
11602. 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
1161Which of the following possesses potential energy?
A. Moving vehicle on the road
B. A running athlete
D. A stretched rubber band
11
1162Find the projection of ( vec{A}=2 hat{i}-hat{j}+ )
( A cdot frac{5}{sqrt{6}} )
B. ( frac{7}{10} )
( c cdot frac{6}{sqrt{5}} )
D. ( \$ \$ ) frac ( {5 text { ) ( } mid text { sqre }{3}} )
11
1163A uniform chain of length ( 2 m ) is kept on
a table such that a length of ( 50 mathrm{cm} )
hangs freely from the edge of the table. The total mass of the chain is ( 5 k g . ) What
is the work done in pulling the entire chain on the table. (in J)
A . 7.2
B. 3
c. 4.6
D. 12
11
1164A particle of mass m is moving in a circular path of
constant radius r such that its centripetal acceleration a.
varies with time t as a = krt, where k is a constant. The
power delivered to the particles by the force acting on it is
(IIT JEE, 1987)
b. mk?r?t
d. Zero
a. 2tmk?r?t
(mkt p215)
11
1165A satellite is revolving round the earth
with orbital speed ( v_{0} ). If it is imagined to stop suddenly, the speed with which it will strike the surface of the earth would
be ( left(v_{e}- ) escape speed of a body from right. earth’s surface)
A ( cdot frac{v_{e}^{2}}{v_{0}} )
в. ( v_{0} )
c. ( sqrt{v_{e}^{2}-v_{0}^{2}} )
D. ( sqrt{v_{e}^{2}-2 v_{0}^{2}} )
11
116662 Block A is hanging from a vertical spring and is at rest.
Block B strikes block A with velocity v and sticks to it.
Then the value of v for which the spring just attains natural
length is
m
in
Fig. 8.247
(60mg²
a. V k
b. som?
a. 10mg?
C. V
d. None of these
11
1167A bag of wheat weighs 100 kg. To what height should it be raised, so that its potential energy may be ( 9800 mathrm{J}(g= )
( left.9.8 m s^{-2}right) )
11
1168A homogeneous rod ( X Y ) of length ( L ) and
mass ( M ) is pivoted at the centre ( C )
such that it can rotate freely in the vertical plane. Initially, the rod is in the horizontal position. A blob of wax of
same mass ( M ) as that of the rod falls
vertically with the speed ( V ) and sticks
to the rod midway between points ( C )
and ( Y . ) If the rod rotates with angular
speed ( omega ) what will be angular speed in
terms of ( boldsymbol{V} ) and ( boldsymbol{L} ) ?
11
1169At what height above the ground must a mass of ( 5 mathrm{kg} ) be to have its P.E. equal in value to the K.E. possessed by it when it moves with a velocity of ( 10 mathrm{m} / mathrm{s} ? )
(Assume ( boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2} )
A. ( 1 mathrm{m} )
B. ( 5 mathrm{m} )
( c cdot 10 m )
D. 50 ( m )
11
1170A force of ( 5 mathrm{N}, ) making an angle ( theta ) with
the horizontal, acting on an object displaces it by ( 0.4 mathrm{m} ) along the horizontal direction. If the object gains kinetic energy of 1 J, the horizontal component of the force is?
A . ( 1.5 mathrm{N} )
в. 2.5 N
c. 3.5 N
D. 4.5 N
11
1171Assertion The angle between the two vectors ( (hat{i}+ )
( hat{boldsymbol{j}}) ) and ( (hat{boldsymbol{j}}+hat{boldsymbol{k}}) ) is ( frac{pi}{3} ) radian
Reason
Angle between two vectors ( vec{A} ) and ( vec{B} ) given by ( boldsymbol{theta}=cos ^{-1}left(frac{vec{A} cdot vec{B}}{A B}right) )
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
1172Why are shockers used in scooters and
cars? Explain.
A. decreases friction
B. Increase the time of impact
c. increases friction
D. decorative
11
1173Energy required to break a bond of DNA is approximately
( A cdot-1 e V )
B. 0.1 ev
c. ( sim 0.01 mathrm{ev} )
D. 2.1 ev
11
117424. A toy gun uses a spring of force constant K. Before being
triggered in the upward direction, the spring is compressed
by a distance x. If the mass of the shot is m, on being
triggered, it will go up to a maximum height of
Kr?
b.
*?
mg
Kmg
R2
d. Kºr?
2mg
mg
11
1175The assembly of two discs as shown in figure is placed on a rough horizontal surface and the front disc is given an
initial angular velocity ( omega_{0} ) Determine the final linear and angular velocity when both the discs start rolling. It is given that friction is sufficient 10
sustain rolling in the rear wheel from the starting of motion
11
1176What happened when a rubber band is
stretched?
11
1177What is work done in holding a body of mass ( 20 mathrm{kg} ) at a height of ( 2 mathrm{m} ) above the
ground? ( left(g=10 m / s^{2}right) )
A . ( 40 mathrm{J} )
B. 400 J
c. ( 10 J )
D. zero
11
1178A bullet is fired from a rifle. If rifle
recoils freely, then K.E. of the rifle is:
A. less than that of the bullet
B. more than that of the bullet
c. same as that of the bullettet
D. equal or less than that of the bullet
11
1179Assertion
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision
Reason
Principle of conservation of momentum holds true for all kinds of collision
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
1180A skater of mass m standing on ice throws a stone of mass M with a velocity of ( V ) in a horizontal direction. The
distance over which the skater will move back (the coefficient of friction
between the skater and the ice is ( mu ) ):
( ^{mathbf{A}} cdot frac{M^{2} V^{2}}{2 m mu g} )
в. ( frac{M V^{2}}{2 m^{2} mu g} )
( ^{mathrm{c}} cdot frac{M^{2} V^{2}}{2 m^{2} mu g} )
D. ( frac{M^{2} V^{2}}{2 m^{2} mu^{2} g} )
11
1181A 50 gram bead slides on a frictionless
wire as shown above. At what point on
the wire will the bead come to a
complete stop? The initial speed at ( C ) is ( sqrt{2 g h} )
A. Point ( A )
B. Point B
c. Point ( c )
D. Point D
E. Point E
11
1182During collision
a) There is a change in momenta of individual bodies
b) The change in total momentum of the system of colliding particle is zero
c) The change in total energy is zero
d) The law of conservation of
momentum is not valid
A. only a ( & ) b are true
B. only b & c are true
( c cdot a, b & c ) are true
D. b, c & d are true
11
1183An athelete diving off a high spring board can perform a variety of physical moments in the air before entering the water below. Which one of the following parameters will remain constant during the fall? The athelete’s:
A. linear velocity
B. linear momentum
c. moment of inertia
D. angular momentum
11
1184If vector ( vec{A}=hat{i}+c hat{j}+5 hat{k} ) and vector
( vec{B}=2 hat{i}+hat{j}-hat{k} ) are perpendicular,then calculate the value of ( c )
11
1185A bead of mass ( mathrm{m} ) kept at the top of a
smooth hemispherical wedge of mass M and radius R, is gently pushed
towards right. As a result, the wedge slides due left. Find the a. speed of the
wedge
b. magnitude of velocity of the bead relative to the wedge
11
1186An object is dropped from a height ( h ) from the ground. Every time it his the ground it looses ( 50 % ) of its kinetic energy. The total distance covered as
( rightarrow infty ) is:
( mathbf{A} cdot 2 h )
B . ( infty )
c. ( frac{5}{3} h )
D. ( frac{8}{3} h )
11
1187If there is a nonzero net force acting on an object for some time, which of the following must be true?
I. The object is gaining kinetic energy
II. The object experiences displacement
III. There is work being done on the object
A. I only
B. I and II only
c. I and III only
D. Il and III only
E . I, II, and III
11
1188A box of mass ( mathrm{m} ) slides down a
frictionless inclined plane of Iength L and vertical height h. Calculate the kinetic energy at the bottom of plane.
A . mgl
в. mghh
c. ( mathrm{mgL} / mathrm{h} )
D. ( operatorname{mgh} / mathrm{L} )
E. mghL
11
118949. A particle is projected along a horizontal field whose
coefficient of friction varies as u = AIV, where r is the
distance from the origin in metres and A is a positive
constant. The initial distance of the particle is 1 m from the
origin and its velocity is radially outwards. The minimum
initial velocity at this point so the particle never stops is
a..
b. 2./8A
c. √28A
d. 4/qA
T
I LIA
11
1190The mass of a spaceship is 1000 kg. It is to be launched from the earths
surface out into free space. The value of ( g ) and ( R(text { radius of earth) are } 10 m / s )
and ( 6400 mathrm{km} ) respectively. The required energy for this work will be:
A ( cdot 6.4 times 10^{11} J )
( J )
В. ( 6.4 times 10^{8} J )
c. ( 6.4 times 10^{9} J )
D. ( 6.4 times 10^{10} J )
11
1191Find the components of vector ( overrightarrow{boldsymbol{a}}=mathbf{3} hat{mathbf{i}}+ )
( 4 hat{j} ) along the direction of vectors ( hat{i}+hat{j} & ) ( hat{mathbf{i}}-hat{boldsymbol{j}} )
A ( cdot frac{7}{2}(hat{i}+hat{j}),-frac{1}{2}(hat{i}-hat{j}) )
B ( cdot frac{1}{2}(hat{i}+hat{j}),-frac{7}{2}(hat{i}-hat{j}) )
c. ( frac{-7}{2}(hat{i}+hat{j}),-frac{1}{2}(hat{i}-hat{j}) )
D ( cdot frac{7}{2}(hat{i}+hat{j}), frac{1}{2}(hat{i}-hat{j}) )
11
1192Hail storms are observed to strike the
surface of the frozen lake at 30 with the
vertical and rebiund at 60 with the
vertical. Then:
11
1193What is the angle between vector ( vec{A}= ) ( hat{mathbf{i}}+hat{mathbf{j}}+sqrt{mathbf{2}} hat{boldsymbol{k}} ) and the z-axis :
A ( cdot 0^{circ} )
B . 45
( c cdot 60 )
D. ( 90^{circ} )
11
1194A uniform disc of mass ( m ) is fitted
(pivoted smoothly) with a rod of mass
( m / 2 . ) If the bottom of the rod is pulled
with a velocity ( v, ) it moves without changing its angle of orientation and the disc rolls without sliding. Find the
kinetic energy of the system ( (r o d+ )
( operatorname{disc} )
11
1195A non-zero vector ( vec{a} ) is parallel to the line
of intersection of the plane ( boldsymbol{P}_{1} ) determined by ( hat{i}+hat{j} ) and ( hat{i}-2 hat{j} ) and plane ( P_{2} ) determined by vector ( 2 hat{i}+ ) ( hat{j} ) and ( 3 hat{i}+2 hat{k}, ) then angle between ( vec{a} ) and vector ( hat{i}-2 hat{j}+2 hat{k} ) is
A ( cdot frac{pi}{4} )
в.
( c cdot frac{pi}{3} )
D. ( pi )
11
1196Match the following list 1 to list 211
1197If ( R ) is radius of the earth and ( W ) is work
done in lifting a body from the ground to an altitude ( R ), the work which should be
done in lifting it further to twice that altitude is:
A ( cdot frac{W}{2} )
B. ( W )
c. ( frac{W}{3} )
D. ( 3 W )
11
1198A body falling from a height of ( 10 m )
rebounds from hard floor. If it loses ( 20 % )
energy in the impact, then coefficient of restitution is
A . 0.89
B. 0.56
c. 0.23
D. 0.18
11
1199Three identical point masses, each of
mass ( 1 k g ) lie in the ( x ) -y plane at points ( (0,0),(0,0.2 m) ) and ( (0.2 m, 0) . ) The
gravitational force on the mass at the origin is
A ( cdot 1.67 times 10^{-9}(hat{i}+hat{j}) N )
B. ( 3.34 times 10^{-10}(hat{i}+hat{j}) N )
c. ( 1.67 times 10^{9}(hat{i}-hat{j}) N )
D. ( 3.34 times 10^{10}(hat{i}-hat{j}) N )
11
1200Given ( overline{boldsymbol{a}}+overline{boldsymbol{b}}+overrightarrow{boldsymbol{c}}+overline{boldsymbol{d}}=mathbf{0}, ) which of the
following statements is/are not a
correct statement?
A ( cdot vec{a}, vec{b}, vec{c} ) and ( vec{d} ) must be a null vector.
B. The magnitude of ( ( vec{a}+vec{c} ) ) equals the magnitude of ( a(vec{b}+vec{d}) )
C. The magnitude of ( vec{a} ) can never be greater than the summ of the magnitudes of ( vec{b}, vec{c} ) and ( vec{d} )
D. ( b+vec{c} ) must He in the plane of ( vec{a} ) and ( vec{d} ) if ( vec{a} ) and ( vec{d} ) are not collinear and in the line of ( vec{a} ) and ( bar{d} ), if they are collinear.
11
1201Show that kinetic energy is always lost
in inelastic collision.
11
1202An object mass ( 10 mathrm{kg} ) falls from rest through a vertical distance of ( 10 mathrm{m} ) and acquires a velocity of ( 10 mathrm{m} / mathrm{s} ). The work done by the push of air on the object is ( left(g=10 m / s^{2}right) )
A. 500 J
B . -500 J
c. 250
D . -250J
11
1203A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is
given an initial velocity of ( 4 m s^{-1} ) by applying a force. The trolley comes to rest after traversing a distance of ( 16 mathrm{m} ) How much work is done on the
trolley?
A. ०
B. 320 J
c. ( 120 mathrm{J} )
D. 250 J
11
1204Calculate the work required to be done
to stop a car of ( 1500 mathrm{kg} ) moving at a
velocity of ( 60 mathrm{kmh}^{-1} )
в. 208333 Л
c. -209333 J
D. ( -207333 J )
11
1205The gravitational force between two objects is proportional to ( frac{1}{R} ) (and not as ( left.frac{1}{R^{2}}right) ) where ( R ) is separation between them then a particle in a circular orbit under such a force would have its orbital speed
( nu ) proportional to
A ( cdot frac{1}{R^{2}} )
B . ( R^{0} )
c. ( R^{text {। }} )
D. ( frac{1}{R} )
11
1206Vector ( vec{a} ) has components ( boldsymbol{a}_{boldsymbol{x}}=mathbf{3}, boldsymbol{a}_{boldsymbol{y}}= )
4. Find the components of a vector ( overrightarrow{boldsymbol{c}} )
which is perpendicular to ( vec{a} ) and has a
magnitude of 5 units.
A ( cdot c_{x}=pm 4, c_{y}=mp 3 )
B . ( c_{x}=pm 3, c_{y}=mp 4 )
C ( cdot c_{x}=pm 2, c_{y}=mp 3 )
D. ( c_{x}=pm 3, c_{y}=mp 2 )
11
1207A mass ( m ) is thrown vertically upward
into air with initial speed ( u . ) A constant
force ( F ) due to air resistance acts on the
mass during it’s travel. Taking into
account the work done against air drag, the maximum distance covered by the mass to reach the top is (Given acceleration due to gravity ( =g ) )
A ( cdot frac{u^{2}}{2 g} )
в. ( frac{u^{2}}{2 g+2 F / m} )
с. ( frac{u^{2}}{2 g+F / m} )
D. ( frac{u^{2}}{g+F / m} )
11
1208external = AX +20
Illustration 8.40 A block is placed on the top of a plane
inclined at 37° with horizontal. The length of the plane is 5 m.
The block slides down the plane and reaches the bottom.
5 m
37°
Fig. 8.90
a. Find the speed of the block at the bottom if the inclined
plane is smooth.
b. Find the speed of the block at the bottom if the coefficient
of friction is 0.25.
11
1209Two balls ( A ) and ( B ) having masses ( 1 k g )
and ( 2 k g ) moving with speeds ( 21 m / s )
and ( 4 m / s ) respectively in opposite direction, collide head on. After collision
( A ) moves with a speed of 1 m/ ( s ) in the same direction, then the coefficient of
restitution is :
A . 0.1
B. 0.2
c. 0.4
D. None
11
1210Two small particles of equal masses
start moving in opposite directions
from a point ( A ) in a horizontal circular
orbit. Their tangential velocities are ( boldsymbol{v} )
and ( 2 v ) respectively, as shown in the
figure. Between collisions, the particles
move with constant speeds. After making how many elastic collisions, other than that at ( A ), these two
particles will again reach the point ( A ) ?
A . 4
B. 3
( c cdot 2 )
D.
11
1211What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.11
1212Which of the following graphs depicts the variation of ( mathrm{KE} ) of a ball, bouncing on
a horizontal floor with height? (neglect
air resistances)
( A )
B.
( c )
D. None of these
11
1213the value of ( x ) at which ( F_{x} ) is zero.
( A cdot x=2 m )
B. ( x=4 ) m
( c cdot x=6 m )
D. ( x=8 ) m
11
121410. In Fig. 8.304, find the velocity of m, in ms when m2
falls by 9 m.
u = 0.1 m
m2
Fig. 8.304
= m; m2 = 2m (take g = 10 ms?).
Given m
11
( M_{A}=2 M ) and ( M_{B}=M, ) as indicated
in the figure. The two masses are initially oriented along the Y-axis and connected by a rod of negligible mass of length ( mathrm{D} ), forming a rigid body. A force of magnitude ( boldsymbol{F}=|overrightarrow{boldsymbol{F}}| ) along the X-axis is
applied to the object at ( mathrm{B} ) at ( t=0 ) for ( mathrm{a} )
short time interval ( delta t . ) Neglect gravity. The expression for the magnitude of angular velocity of the system after the
collision is:
A ( cdot frac{F delta t}{M D D} )
в. ( frac{2 F delta t}{3 M D} )
c. ( frac{F delta t}{2 M D} )
D. ( frac{3 F delta t}{2 M D} )
11
1216A bullet fired into a fixed target loses half of its velocity after penetrating ( 3 mathrm{cm} ) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
( mathbf{A} .3 .0 mathrm{cm} )
B. ( 2.0 mathrm{cm} )
c. ( 1.5 mathrm{cm} )
D. ( 1.0 mathrm{cm} )
11
1217A ball of mass m makes perfectly elastic head-on collision with a ball of mass nm which is initially at rest. Show
that the fractional transfer of energy by the first ball is ( 4 n /(1+n)^{2} . ) Deduce the
value of ( n ) for which the transfer is
maximum.
11
1218A sphere of mass ( m_{1}=2 k g ) collides
with a sphere of mass ( m_{2}=3 k g ) which
is at rest. Mass ( m_{1} ) will move at right angles to the line,joining centres at the time of collision, if the coefficient of
restitution is :
( A cdot 4 / 9 )
в. ( 1 / 2 )
( c cdot frac{2}{3} )
D. ( sqrt{2 / 3} )
11
1219Identify the energy changes in the following two cases –
( A: A ) car moving up a hill
B : Photographic film is exposed to sun-
light
A. In ‘A’ mechanical energy in moving car is converted to potential energy and in ‘B’ potential energy is converted to chemical energy
B. In’A’ potential energy in moving car is converted to kinetic energy and in ‘B’ chemical energy is converted to light energy.
C. In’A’ kinetic energy in moving car is converted to potential energy and in ‘B’ potential energy is converted to light energy.
D. In’A’ kinetic energy is moving car is converted to potential energy and in ‘B’ light energy is converted to chemical energy.
11
122010. A particle, which is constrained to move along the x-axis,
is subjected to a force in the same direction which varies
with the distance x of the particle from the origin as F(x)
= kx + ar. Here k and a are positive constants. For x >
0, the functional form of the potential energy U (x) of the
particle is
(IIT JEE, 2002)
U(x)
b.
U(x)
U(x)

d.
11
1221A uniform chain of length ( 2 m ) is kept on
a table such that a length of ( 60 mathrm{cm} ) hanging freely from the edge of the table. The total mass of the chain is
( 4 k g . ) The work done is pulling the entire
chain on the table (Take ( left.g=m s^{-2}right) )
A . ( 12.9 J )
B. ( 6.3 J )
c. ( 3.6 J )
D . ( 2.0 J )
11
1222Find out the potential energy of the force ( boldsymbol{F}=boldsymbol{y} hat{boldsymbol{i}}+boldsymbol{x} hat{boldsymbol{j}} boldsymbol{N} )
A. ( -x y+c )
B. ( x y+c )
c. ( -x y-c )
D. ( x y-c )
11
1223Suppose a ball of mass ( mathrm{m} ) is thrown vertically upward with an initial speed ( v ) Its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentums of the ball
are same. Is this an example of conservation of momentum?
A. Yes
B. No
c. Sometimes
D. None of these
11
1224Maximum velocity of block during
subsequent motion of the system after
release of ball is :
A ( cdot[g L(1-cos theta)]^{1 / 2} )
B ( cdot[2 g L(1-cos theta)]^{1 / 2} )
( mathbf{c} cdot[g L(cos theta)]^{1 / 2} )
D. insufficient information
11
1225An object of mass 40 kg having velocity ( 4 hat{text { ì }} m / s ) collides with another objects of mass 40 kg having velocity ( 3 hat{i} ). If the collision is perfectly inelastic, then the loss of mechanical energy.
( A ). ( 250 J )
B. 100
c. 125
D. 35 J
11
1226A particle is moved from (0,0) to ( (a, a) ) under a free force ( overrightarrow{boldsymbol{F}}=(3 hat{boldsymbol{i}}+4 hat{boldsymbol{j}}) ) from
two paths, I is OP and path 2 is OQP. Let
( W_{1} ) and ( W_{2} ) be the work done by this force in these two paths. Then:
A. ( W_{1}=W_{2} )
в. ( W_{1}, W_{2} )
c. ( W_{2}-2 W_{1} )
D. ( W_{2}-4 W_{1} )
11
1227A ball falls from a height of ( 5 m ) and strikes the roof of a lift. If at time of
collision, lift is moving in the upward
direction with a velocity of ( 1 mathrm{ms}^{-1} ). Then the velocity with which the ball rebounds after collision will be :
A ( cdot 13 mathrm{ms}^{-1} ) upwards
B. ( 12 mathrm{ms}^{-1} ) downwards
C. ( 12 mathrm{ms}^{-1} ) upwards
D. ( 11 mathrm{ms}^{-1} ) downwards
11
1228A simple pendulum oscillates freely between points ( A ) and ( B ) We now put a peg (nail) at some point ( C )
as shown. As the pendulum moves from
At to the right, the string will bend at ( C ) and the pendulum will go to its extreme point D. Ignoring friction, the point D.
A. Will lie on the line AB
B. Will lie above the line AB
c. will lie below the line ( A B )
D. Will concide with B
11
1229A body of mass ( 1 k g ) falls from a height
of ( 5 m . ) How much energy does it
possess at any instant? (Consider ( boldsymbol{g}= )
( left.10 m s^{-2}right) )
A . ( 25 J )
в. ( 50 J )
c. 0
D. can not be determined with the help of given data
11
1230What is the minimum energy required
to lunch a satellite of mass ( m ) from the
surface of a planet of mass ( M ) and radius ( R ) In a circular orbit at an
altitude of ( 2 R ? )
A ( cdot frac{2 G m M}{3 R} )
в. ( frac{G m M}{2 R} )
c. ( frac{G m M}{3 R} )
D. ( frac{5 G m M}{6 R} )
11
12311. The displacement x in meter of a particle of mass m kg
moving in one dimension under the action of a force is
related to the time t in second by the equation x = (1-3).
The work done by the force (in joules) in first six seconds
is
a. 18m
b. Zero
c. 9m/2
d. 36m
11
1232If ( hat{i}, hat{j} ) and ( widehat{k} ) are unit vectors along ( mathbf{x}, mathbf{y} ) and z axes respectively. the angle ( theta ) between the vector ( hat{mathbf{i}}+widehat{mathbf{j}}+widehat{boldsymbol{k}} ) and vector
( widehat{boldsymbol{i}} )
A ( cdot theta=cos ^{-1}left(frac{1}{sqrt{3}}right) )
В ( cdot theta=sin ^{-1}left(frac{1}{sqrt{3}}right) )
C ( cdot theta=cos ^{-1}left(frac{sqrt{3}}{2}right) )
D. ( theta=sin ^{-1}left(frac{sqrt{3}}{2}right) )
11
1233If ( g ) is the acceleration due to gravity on
the surface of the earth, the gain in potential energy of an object of mass ( boldsymbol{m} )
raised from the earth’s surface to a
height equal to the radius ( R ) of the earth is
( ^{mathrm{A}} cdot frac{m g R}{4} )
в. ( frac{m g R}{2} )
( mathbf{c} cdot m g R )
D. ( 2 m g R )
11
1234A ball of mass m moving with a constant velocity strikes against a ball
of same mass at rest. If ( e= )
coefficient of restitution, then what
will be the ratio of velocity of two balls
after collision?
A ( frac{1-e}{1+e} )
в. ( frac{e-1}{e+1} )
c. ( frac{1+e}{1-e} )
D. ( frac{2+e}{e-1} )
11
1235A pair of bullocks exerts a force of ( 140 N ) on a plough. The field being
ploughed is 15 m long. How much work
is done in ploughing the length of the field?
11
1236Obtain the angle between ( vec{A}+vec{B} ) and ( vec{A}-vec{B} ) if ( vec{A}=2 hat{i}+3 hat{j} ) and ( vec{B}=hat{i}-2 hat{j} )
( ^{A} cdot cos ^{-1}left(frac{4}{sqrt{65}}right) )
в. ( pi-cos ^{-1}left(frac{4}{sqrt{65}}right) )
( ^{mathrm{c}} cdot sin ^{-1}left(frac{4}{sqrt{65}}right) )
D. ( -sin ^{-1}left(frac{4}{sqrt{65}}right) )
11
1237Find the ratio of speed of B with ( mathbf{A} ) ( left(i . e frac{V_{B}}{V_{A}}right) ) when all collisions end :
( A )
B. 2
( c cdot 3 )
( D )
11
1238Name the type of energy (kinetic energy
( boldsymbol{K} ) or potential energy ( boldsymbol{U} ) ) possessed in the following case.
A piece of stone placed on the roof
A. ( U )
в. ( K )
c. ( U ) and ( K )
D. No energy
11
1239A body of mass ( 10 k g ) is moving with a
velocity ( 20 m s^{-1} . ) If the mass of the body is doubled and its velocity is halved, find the ratio of the initia
kinetic energy to the final kinetic
energy.
11
1240What is the velocity of centre of mass after the collision?
( A cdot vec{V}_{0} )
в. ( frac{vec{V}_{0}}{3} )
( c cdot frac{vec{V}_{0}}{6} )
( D )
11
1241A thin hollow sphere of mass ( m ) is
completely filled with an ideal liquid of
mass ( m . ) When sphere rolls with a
velocity ( v, ) kinetic energy of the system is equal to:
A ( cdot m v^{2} / 2 )
B. ( m v^{2} )
C. ( 4 m v^{2} / 3 )
D. ( 4 mathrm{mv}^{2} / 5 )
11
124236. During the displacement, which of the curves shown in the
graph best represents the work done on the spring block
system by the applied force?
a. 1 b. 2 . c. 3 d. 4
11
1243A molecule in a gas container hits a
horizontal wall with speed ( 200 mathrm{m} s^{-1} )
and angle ( 30^{0} ) with the normal, and
rebounds with the same speed. Is momentum conserved in the collision?
Is the collision elastic or inelastic?
11
124414. A 2144 kg freight car roles along rails with negligible
friction. The car is brought to rest by a combination of two
coiled springs as illustrated in Fig. 8.308. Both springs are
described by Hooke’s law with k, = 1600 Nm” and k, =
3400 Nm. After the first spring compresses a distance of
30.0 cm, the second spring acts with the first to increase
the force as additional compression occurs as shown in
the graph in Fig. 8.309. The car comes to rest 50.0 cm
after first contracting the two-spring system. Find the car’s
initial speed (in x 10-Nm).
common
Fig. 8.308
Total force (N)
10
50
20 20 40
Distance (cm)
Fig. 8.309
11
1245The vector ( hat{B}=4 hat{i}+2 hat{j}-S hat{k} ) is
perpendicular to the vector ( overrightarrow{boldsymbol{A}}=mathbf{3} hat{mathbf{i}}+ )
( hat{boldsymbol{j}}+boldsymbol{2} hat{boldsymbol{k}} ) if ( boldsymbol{S}= )
( A )
B. 7
( c cdot 6 )
D. 8
11
1246A ball is thrown from ground at an angle
( theta ) with horizontal and with an initial
speed ( u_{0} . ) For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when
it hits the ground for the first time is ( V_{1} )
After hitting the ground, the ball rebounds at the same angle ( theta ) but with
a reduced speed of ( u_{0} / alpha . ) Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of
motion is ( 0.8 V_{1}, ) the value of ( alpha ) is
11
1247An overhead tank having some water
possesses energy.
A. Kinetic
B. Potential
c. Thermal
D. Electrical
11
124865. The kinetic energy acquired by a mass m in travelling a
certain distance d, starting from rest, under the action of
a force F such that the force F is directly proportional to
tis
a. Directly proportional to t
b. Independent of t
c. Directly proportional to t
d. Directly proportional to t
1:1..
: 1.
1.
11
1249When a car of mass ( 1200 mathrm{kg} ) is moving
with a velocity of ( 15 mathrm{ms}^{-1} ) on a rough horizontal road. Its engine is switched off. How far does the car travel before it
comes to rest if the coefficient of
kinetic friction between the road and
tyres of the car is ( 0.5 ?left(g=10 m s^{-2}right) )
( mathbf{A} cdot 6.2 m )
в. 20 ( m )
c. ( 22.5 m )
D. 30
11
1250A box of weight ( 150 k g f ) has
gravitational potential energy stored in it equal to ( 14700 J ). Find the height of the box above the ground. (Take ( g= )
( 9.8 N k g^{-1} )
( mathbf{A} cdot 10 mathrm{cm} )
B. ( 10 k m )
( c .1 m )
D. ( 10 m )
11
1251During inelastic collision of two
particles.
( mathbf{A} cdot(K E)_{text {final }}=(K E)_{text {initial }} )
B. ( (K E)_{text {final }} ) must be greater than ( (K E)_{text {initial}} )
( mathbf{C} cdot(K E)_{text {final}} ) must be less than ( (K E)_{text {initial}} )
D. ( (K E)_{text {final }} ) must be greater or less than ( (K E)_{text {initial }} )
11
1252Simple pendulum of length I has a
maximum angular displacement ( theta ). The maximum kinetic energy of the bob is?
A . ( m g mid(1-cos theta) )
B. ( 0.5 mathrm{mgl} )
c. ( mathrm{mg} )
D. 2mgl
11
1253A uniform chain of length ( 2 m ) is kept on a table such that a length of ( 60 mathrm{cm} ) hangs freely from the edge of the table. The total mass of the chain is ( 4 k g )
What is the work done in pulling the
entire chain on the table?
A .125
( J )
B. 3.6 J
( c .7 .25 )
D. ( 1200 J )
11
125427. A spring is compressed between two toy carts of masses
m, and my. When the toy carts are released, the spring
exerts on each toy cart equal and opposite forces for the
same small time t. If the coefficients of friction u between
the ground and the toy carts are equal, then the magnitude
of displacements of the toy carts are in the ratio
11
125517. The maximum positive displacement x is
a. 273 m
b. 2 m
c. 4 m
d. V2 m
11
1256A ball of mass ( m ) moving with a speed
( 2 v_{0} ) collides head-on with an identical
ball at rest. If ( e ) is the coefficient of
restitution, then what will be the ratio of velocity of two balls after collision?
A ( cdot frac{1-e}{1+e} )
в. ( frac{1+e}{1-e} )
c. ( frac{e-1}{e+1} )
D. ( frac{e+1}{e-1} )
11
1257Define coefficient of restitution.11
1258( hat{text { i }} ) and ( hat{j} ) are unit vectors along along ( x ) and ( y- ) axis respectively. What is the magnitude and direction of the vectors ( hat{mathbf{i}}+hat{text { jand }} hat{boldsymbol{i}}-hat{boldsymbol{j}} ) ?What are the
components of a vector ( A=2 hat{i}+3 hat{j} ) along the directions of ( hat{i}+hat{j} ) and ( hat{i}-hat{j} )
? [You may use graphical method]
11
1259A force ( overrightarrow{boldsymbol{F}}=(mathbf{5} hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}} 2 hat{boldsymbol{k}}) boldsymbol{N} quad ) is
applied over a partivle which displaces it from its origin to the point ( vec{r}= ) ( (2 hat{i}-hat{j}) m . ) The work done on the particle in joules is then
A . -7
B. +7
( c cdot+10 )
D. +13
11
1260In a smooth stationary cart of length ( d )
a small block is projected along it’s length with velocity v towards front.
Coefficient of restitution for each
collision is e. The cart rests on a smooth
ground and can move freely. The time taken by block to come to rest w,r.t cart
is
( A )
B. ( frac{e d}{(l+e) v} )
( c cdot d )
D. infinite
11
1261A body moving at ( 2 mathrm{m} / mathrm{s} ) can be stopped over a distance ( x ). If its kinetic energy is
doubled, how long will it go before coming to rest, retarding force remains unchanged?
( A )
B . ( 2 x )
c. ( 4 x )
D. ( 8 x )
11
1262Show that in case of one-dimensional
elastic collision of two bodies, the relative
velocity of separation after the collision
is equal to the relative velocity of approach before the collision.
11
1263A body having kinetic energy ( k ) moving on a rough horizontal surface is stopped at a distance ( x ) by constant frictional
force. The force of friction exerted on the
body is
A ( cdot frac{k}{x} )
B. ( frac{sqrt{k}}{x} )
c. ( frac{k}{sqrt{x}} )
D. ( k x )
11
1264A car of mass 2000 kg changes its
speed from ( 18 mathrm{km} / mathrm{h} ) to ( 90 mathrm{km} / mathrm{hr} ). Find
the work done by the engine.
11
1265A body of mass ‘m’ is raised from the surface of earth to a point which is at a height ( 5 R ) from the surface of the earth.
The change in PE is
A. ( 5 mathrm{mgR} )
в. ( frac{2 m g R}{3} )
c. ( frac{4}{5} m g r )
D. ( frac{5 m g R}{6} )
11
1266Consider two solid uniform spherical
objects of the same density ( rho . ) One has
radius ( R ) and the other has radius ( 2 R )
They are in outer space where the
gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
( mathbf{A} cdot G pi^{2} R^{4} )
B. ( frac{128}{81} G pi^{2} R^{4} rho^{2} )
( ^{mathbf{C}} cdot frac{128}{81} G pi^{2} )
( stackrel{128}{87} G pi^{2} R^{2} )
11
1267A mass ( boldsymbol{m}=mathbf{1 4 k g} ) performing ( boldsymbol{S H} boldsymbol{M} ) as
displacement, ( boldsymbol{x}=(mathbf{0 . 5 m}) sin (boldsymbol{6} boldsymbol{t}+boldsymbol{pi}) )
Determine maximum K.E. of the mass
during its motion ( (text { in } boldsymbol{J}) )
A. ( frac{7 pi^{2}}{4} )
B . 49
c. 63
D. Data insufficient
11
1268When a body is whirled in a circle, the work done on it is
A. Positive
B. Negative
c. zero
D. Infinite
11
1269A planet whose mass and radius are
both half of that of earth. Acceleration
due to gravity(g) at its surface should
be:
A ( cdot 29.4 m / s e c^{2} )
в. ( 19.6 mathrm{m} / mathrm{sec}^{2} )
( mathrm{c} cdot 9.8 mathrm{m} / mathrm{sec}^{2} )
D. ( 4.9 mathrm{m} / mathrm{sec}^{2} )
11
1270A car of mass ( 1000 mathrm{kg} ) moving with a
speed ( 18 k m h^{-1} ) on a smooth road and
colliding with a horizontally mounted
spring of spring constnat ( 6.25 times )
( 10^{3} N m^{-1} . ) The maximum compression
of the spring is
A . ( 1 m )
B. ( 2 m )
( c .3 m )
D. ( 4 m )
11
1271A body of mass M was slowly hauled up a rough hill by a force ( F ) which at each point was directed along a tangent to the hill. Work done by the force.
This question has multiple correct options
A. Is independent of the shape of trajectory
B. Depends upon the vertical component of displacemen but is independent of horizontal component
c. Depends upon both the component
D. Does not depend upon the coefficient of friction
11
1272Potential energy increases with the
increase in :
A. work
B. Force
c. speed
D. Position
11
1273toppr
‘Igure. Ine coemcıent ( mu ) Is insurırcıent
to start pure rolling. The sphere slides a
length ( ell ) on the incline from rest and its
kinetic energy becomes K. Then, the work done by friction will be
A. ( -mu ) mglcos ( theta )
в. ( -m g ell sin theta+K )
( c )
( D )
11
1274The work done by a force ( overline{boldsymbol{F}}= )
( left(-6 x^{3} iright) N ) in displacing particle from
( boldsymbol{x}=boldsymbol{a} boldsymbol{m} boldsymbol{t} boldsymbol{o} boldsymbol{x}=-boldsymbol{2} boldsymbol{m} ) is
11
1275The work done on an object does not depends upon the:
A. displacement
B. force applied
c. angle between force and displacement
D. initial velocity of the object
11
1276The potential energy function for
a particle executing linear simple harmonic motion is given by
( V(x)=k x^{2} / 2, ) where ( k ) is the force
constant of the oscillator.
For ( boldsymbol{k}=mathbf{0 . 5} boldsymbol{N} boldsymbol{m}^{-1}, ) the ( operatorname{graph} ) of ( mathbf{V}(mathbf{x}) )
versus ( x ) is shown in Fig. Show that ( a )
particle of total energy 1 J moving under this potential must turn back when
it reaches ( boldsymbol{x}=pm mathbf{2 m} )
11
127721. A bob of mass m is projected with a horizontal velocity
V=
84 as shown in Fig. 8.224. In consequence, it moves
V 2
in a circular path in a vertical plane by the inextensible
string which passes over the smooth fixed peg. Find the
maximum angle that the bob swings in the left hand
side.
Up V
Fig. 8.224
11
1278Two bodies collide at the same
temperature. Which of the following must remain conserved?
(i) Velocity
(ii) Momentum
(iii) Kinetic energy
A. Only (i) and (ii)
B. Only (ii)
c. only (i) and (iii)
D. (i), (ii) and (iii)
11
1279If the constant forces ( 2 hat{i}-5 hat{j}+6 hat{k} ) and ( -hat{mathbf{i}}+mathbf{2} hat{mathbf{j}}-hat{boldsymbol{k}} ) act on a particle due to
which it is displaced from a point ( A(4,-3,-2) ) to a point ( B(6,1,-3) ) then the work done is
A . 15 unit
B. 9 unit
c. -15 unit
D. – 9 unit
11
1280Choose the correct option:
A. If only conservative forces act on a particle, the kinetic energy remains constant.
B. If the net force acting on an object is zero, then the object is at rest.
C. If net mechanical work is done on a body, the body must accelerate.
D. If net mechanical work is done on a body, the speed of body remains unchanged.
11
1281If a particle of ( 1 K g ) at mars is pushed through a distance of ( 5 m ). Calculate the
total work done. ( left(operatorname{given} mu_{m}=0.3 ) and right.
( left.boldsymbol{g}_{m}=mathbf{5} boldsymbol{m} / boldsymbol{s}^{2}right) )
A . ( 10 J )
в. 7.5 .5
( c .0 J )
D. None
11
1282A body of mass ( 1 k g ) is made to trave with a uniform acceleration of
( 30 mathrm{cm} / mathrm{s}^{2} ) over a distance of ( 2 mathrm{m} ), the work done is:
( mathbf{A} cdot 6 J )
в. ( 60 J )
( c .0 .6 . J )
D. 0.3 .5
11
1283Two satellites of earth, ( S_{1} ) and ( S_{2} ), are
moving in
the same orbit. The mass of ( S_{1} ) is four
times the
mass of ( S_{2} ). Which one of the following
statements is true?
A. The kinetic energies of the two satellites are
equal
B. The time period of ( S_{1} ) is four times that of ( S_{2} )
c. The potential energies of earth and satellite in
the two cases are equal
D. ( S_{1} ) and ( S_{2} ) are moving with the same speed
11
1284If the vector ( 6 hat{i}-3 hat{j}-6 hat{k} ) is decomposed into vectors parallel and perpendicular to the vector ( hat{i}+hat{j}+hat{k} )
then the vectors are
A ( .-(hat{i}+hat{j}+hat{k}) & 7 hat{i}-2 hat{j}-5 hat{k} )
B. ( -2(hat{i}+hat{j}+hat{k}) & 8 hat{i}-hat{j}-4 hat{k} )
( mathbf{c} cdot+2(hat{i}+hat{j}+hat{k}) & 8 hat{i}-hat{j}-4 hat{k} )
D. none
11
1285a. 8a b. 24a c. 160 d. Zero
72. In the position shown in Fig. 8.251, the spring is at its
natural length. The block of mass m is given a velocity
Vo towards the vertical support at t = 0. The coefficient of
friction between the block and the surface is given by u
= Ox, where a is a positive constant and x is the position
of the block from its starting position. The block comes
to rest for the first time at x, which is
VO
Fig. 8.251
m
b.
Vo
Vk + amg
m
vonas
d. None of these
1
.
c.
11
1286Statement 1:If ( vec{A} cdot vec{B}=vec{B} cdot vec{C} ) then ( vec{A} ) may
not always be equal to ( overrightarrow{boldsymbol{C}} ) Statement 2: The dot product of two vector involves cosine of the angle
between the two vectors.
A. a) Statement- – is false, Statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- – is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false
11
1287An object of mass ( 1 mathrm{kg} ) has a PE of 1 relative to the ground when it is at a height of:
A. ( 0.102 mathrm{m} )
B. ( 1 mathrm{m} )
c. ( 9.8 mathrm{m} )
D. 32 ( m )
11
1288Given ( k_{1}=1500 N m^{-1}, k_{2}= )
( mathbf{5 0 0} N boldsymbol{m}^{-1}, boldsymbol{m}_{1}=mathbf{2 k g}, boldsymbol{m}_{2}=mathbf{1 k g} . ) Find:
a. Potential energy stored in the springs in equilibrium, and
b. work done in slowly pulling down ( m_{2} )
by ( 8 mathrm{cm} )
11
1289When a rubber-bank is stretched by a distance ( x, ) it exerts a restoring force of magnitude ( F=a x+b x^{2} ) where ( a ) and ( b )
are constants. The work done in
stretching the unstretched rubber band
by ( boldsymbol{L} ) is:
( ^{mathrm{A}} cdot frac{a L^{2}}{2}+frac{b L^{3}}{3} )
( ^{mathrm{B}} cdot frac{1}{2}left(frac{a L^{2}}{2}+frac{b L^{3}}{3}right) )
( mathbf{c} cdot a L^{2}+b L^{3} )
D. ( frac{1}{2}left(a L^{2}+b L^{3}right) )
11
1290A bird flying in the sky has
A. K.E. only
B. P.E. only
C. Neither K.E. nor P.E.
D. Both K.E. and P.E.
11
1291A ball is dropped from height hon the ground level. If the coefficient of
restitution is e then the height
upto which the ball will go after ( n^{t h} )
jump will be-
( A cdot frac{h}{e^{2 n}} )
B. ( frac{e^{2 n}}{h} )
( mathbf{c} cdot h e^{n} )
D. ( h e^{2 n} )
11
1292A boy weighing ( 25 k g f ) climbs up from
the first floor at height ( 3 m ) above the
ground to the third floor at height ( 9 m )
above the ground. What will be the increase in the gravitational potential energy? Consider ( boldsymbol{g}=10 m s^{-2} )
( mathbf{A} cdot 1 k J )
B. ( 1.3 k J )
c. ( 1.5 k J )
D. None of these
11
1293( Q ) туре уочт question
rod. The rod can revolve in a vertical
plane around the point A. What horizontal velocity must be imparted to the end of the rod ( C ) to deflect it to the
horizontal position? (Given acceleration
due to gravity ( =g )
4. ( sqrt{2 g} )
( 3 cdot sqrt{2 cdot 4 g} )
( c cdot sqrt{3 g} )
( -sqrt{3.60} )
0
11
1294If ( vec{A} cdot vec{B}=0, ) the angle between the
vectors ( A ) and ( B ) will be:
A ( cdot 0^{circ} )
B. ( 60^{circ} )
( c cdot 90^{circ} )
( D cdot 180^{circ} )
11
1295A tunnel is dug along a diameter of the
earth. If ( M_{e} ) and ( R_{e} ) are the mass and
radius, respectively, of the earth, then
the force on a particle of mass ( m ) placed in the tunnel at a distance ( r ) from the
centre is :
( ^{mathbf{A}} cdot frac{G M_{e} m}{R_{e}^{3}} r )
в. ( frac{G M_{e} m}{R_{s}^{3} r} )
c. ( frac{G M_{e} m R_{e}^{3}}{r} )
( ^{mathrm{D}} cdot frac{G M_{e} m}{R^{2}} )
11
1296Value of v for which particle hit vertical
walls ( n ) times is ( left(x n+frac{5}{2}right) mathrm{m} / mathrm{s} ) and
finally hit the point ( A ) which is the centre point between the two vertical walls (all collison are elastic) Find ( x )
( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
11
1297The vector ( vec{A}=vec{i}+vec{j} ) where ( vec{i}, vec{j} ) are unit vectors along ( X ) and ( Y ) axes respectively makes an angle of with ( X )
axis.
( A cdot 0^{circ} )
B. ( 45^{circ} )
( c cdot 60 )
D. ( 90^{circ} )
11
1298A man of mass ( 60 k g ) climbs up a ( 20 m ) long staircase on the top of a building
10 ( m ) high. What is the work done by
him? ( left(text { Takeg }=10 m s^{-2}right) )
A. ( 12 k J ) J 5 J. 12 .
в. ( 6 k J )
c. ( 3 k J )
D. ( 18 k J )
11
1299A particle is projected vertically upwards from the surface of the
earth(radius R) with a kinetic energy equal to half of the minimum value
needed for it to escape. Find the height to which it rises above the surface of
earth.
11
1300A body of mass 5 kg falls from a height of ( 10 m ) to 4 m. Calculate the loss in
potential energy of the body. (Take ( g= ) ( left.10 m s^{-2}right) )
A . ( 0 . J )
в. ( 300000 J )
c. ( 3 J )
D. ( 300 J )
11
1301Two charges ( +5 mu C ) and ( -5 mu C )
separated by ( 4 m m ) form an electric dipole. The dipole is placed in a uniform
electric field of ( 4 times 10^{5} N / C . ) The work
done in rotating the electric dipole
through ( 180^{circ}, ) if it starts from the
positions of ( boldsymbol{theta}=mathbf{0} ) is
A. ( 4 m J )
в. ( 8 m J )
c. ( 12 m J )
D. ( 16 m J )
11
1302A bullet of mass ( m=50 ) gm strikes a bag of mass ( mathrm{M}=5 mathrm{kg} ) hanging from a fixed point, with a horizontal velocity ( bar{V}_{p} . ) If bullet sticks to the sand bag then just after collision the ratio of final
( & ) initial kinetic energy of the bullet is approximately:
A ( cdot 10^{-2} )
– ( ^{-2} )
B. ( 10^{-3} )
( mathbf{c} cdot 10^{-6} )
D. ( 10^{-4} )
11
1303Velocity of a particle of mass ( 2 mathrm{kg} ) changes from ( overrightarrow{boldsymbol{v}}_{1}=-2 widehat{boldsymbol{i}}-widehat{boldsymbol{2}} hat{boldsymbol{j}} boldsymbol{m} / boldsymbol{s} ) to
( overrightarrow{boldsymbol{v}}_{2}=(widehat{boldsymbol{i}}-widehat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} ) after colliding with a
plane surface
This question has multiple correct options
A. the angle made by the plane surface with the positive ( x ) -axis is ( 90^{circ}+tan ^{-1}left(frac{1}{3}right) )
B. the angle made by the plane surface with the positive x-axis is ( tan ^{-1}left(frac{1}{3}right) )
C. the direction of change in momentum makes an angle ( tan ^{-1}left(frac{1}{3}right) ) with the positive ( x ) -axis.
D. the direction of the change in momentum makes an angle ( 90^{circ}+tan ^{-1}left(frac{1}{3}right) ) with the plane surface.
11
1304A projectile is launched vertically upward. It explodes into two pieces at the top point of its trajectory. One piece has twice the mass of the other.
Immediately after the explosion,
the more massive piece has
kinetic energy ( boldsymbol{E} ). What is the total
kinetic energy of both pieces immediately after the explosion?
( mathbf{A} cdot 1.5 E )
B. ( 2 E )
( c .3 E )
D. not enough information to answer
11
1305If ( vec{A}=a hat{i}+2 hat{j}-5 hat{k}, vec{B}=2 hat{i}-hat{j}-4 hat{k} )
are perpendicular to each other, the
value of ( boldsymbol{a} ) is:
( A cdot 9 )
B. -9
( c cdot 4 )
( D cdot-4 )
11
130616. In Fig. 8.220, the light spring is of force constant k and
is on a smooth horizontal surface. Initially the spring is
relaxed. Calculate the work done by an external agent to
lower the hanging body of mass M slowly, till it remains
in equilibrium.
00000
От
Fig. 8.220
11
1307The average transnational KE of N2 molecules at NTP is-
( mathbf{A} cdot 0.15 J )
в. 0.036 .5
c. ( 0.032 J )
D. ( 152 J )
11
1308( vec{A}, vec{B} ) and ( vec{C} ) satisfy the relations, ( vec{A} cdot vec{B}=0 ) and ( vec{A} cdot vec{C}=0, ) then ( vec{A} ) is
parallel to
A . ( vec{B} )
в. ( vec{c} )
c. ( vec{B} times vec{C} )
D. 高广
11
1309A child pulls a toy bus through a distance of ( 8 mathrm{m} ) on a smooth horizontal
floor. The string held in the child’s hand
makes an angle of ( 60^{circ} ) with the horizontal surface. If the force applied by the child is 3 N. Calculate the work done by the child in pulling the toy car.
11
1310A steel ball strikes a fixed smooth steel
plate placed on a horizontal surface at an angle ( theta ) with the vertical. If the
coefficient of restitution is ( e ), the angle
at which the rebound will take place is
( A cdot theta )
B. ( tan ^{-1}left[frac{tan theta}{e}right] )
( c cdot e tan theta )
D. ( tan ^{-1}left[frac{e}{tan theta}right] )
11
1311In a one-dimensional collision between
two particles, their relative velocity is ( overrightarrow{v_{1}} ) before the collision and ( overrightarrow{v_{2}} ) after
collision:
A. ( overrightarrow{v_{1}}=overrightarrow{v_{2}} ) if the collision is elastic
B. ( overrightarrow{v_{1}}=-overrightarrow{v_{2}} ) if the collision is elastic
c. ( |overrightarrow{v_{2}}|=|overrightarrow{v_{1}}| ) in all cases
D. ( overrightarrow{v_{1}}=-k overrightarrow{v_{2}} ) in all cases, where ( k geq 1 )
11
13125. A stone tied to a string of length L is whirled in a vertical
circle with the other end of the string at the centre. At a
certain instant of time, the stone is at its lowest position,
and has a speed u. The magnitude of the change in its ve-
locity as it reaches a position where the string is horizontal
(IIT JEE, 1998)
a. Su² – 28L b. √2qL
d. /2cu² – 8L)
is
c. Su² – gl
11
1313Mass of a planet is ( 5 times 10^{24} mathrm{kg} ) and
radius is ( 6.1 times 10^{6} mathrm{m} . ) The energy
needed to send a 2 kg body into space from its surface, would be.
A. 9 joule
B. 18 joule
C. ( 2.2 times 10^{8} ) joule
D. ( 1.1 times 10^{8} ) joul
11
1314Force acting on a particle moving in a straight line varies with the velocities of
the particle as ( boldsymbol{F}=boldsymbol{K} . boldsymbol{V} . ) Where ( boldsymbol{K} ) is
constant. The work done by this force in time ( t ) is
A . ( K V t )
B. ( K^{2} V^{2} t^{2} )
c. ( K^{2} V t )
D. ( K V^{2} t )
11
1315The track shown in figure is frictionless.
The block B of mass ( m ) is pushed along the track with some speed. The collision
between ( A ) and ( B ) is perfectly elastic. With what velocity should the block ( A ) be
started to get the sleeping man
awakened ?
11
131610. An engine pumps up 100 kg of water through a height
of 10 m in 5 s. Given that the efficiency of the engine is
60%, what is the power of the engine? Take g =10 ms.
a. 33 kW b. 3.3 kW c. 0.33 kW d. 0.033 kW
11
1317A ball drops from a ceiling of a room, and after rebounding twice from the floor reaches a height equal to half that
of the ceiling. Show that coefficient of restitution is ( sqrt{frac{1}{2}} )
11
1318Equal net forces act on two different
blocks ( A ) and ( B ) of masses ( m ) and ( 4 m )
respectively. For same displacement, identify the correct statement.
A ‘ their kinetic energies are in the ratio ( frac{K_{A}}{K_{B}}=frac{1}{4} )
B. Their speeds are in the ratio ( frac{v_{A}}{v_{B}}=frac{1}{1} )
c. work done on the blocks are in the ratio ( frac{W_{A}}{W_{B}}=frac{1}{1} )
D. All of the above
11
1319The kinetic energy acquired by a mass ( mathrm{m} ) after travelling a fixed distance from rest under the action of constant force
is
A. directly proportional to ( sqrt{m} )
B. directly proportional to
c. independent of ( m )
D. directly proportional to ( frac{1}{sqrt{m}} )
11
1320With what speed must a ball be thrown
down for it to bounce 10 m higher
11
1321Fig. 8.
6. AB is a quarter of smooth circular track of radius R=6m
A particle P of mass 0.5 kg moves along the track from A
to B under the action of the following forces.
B
Fig. 8.210
a. A force Fı directed always towards the point B; its
magnitude is constant and is equal to 20 N.
b. A force F2 directed along the instantaneous tangent
to the circular track; its magnitude is (15 – 105) N,
where S is the distance travelled in metre.
C. A horizontal force of magnitude 30 N.
Find the work done by forces mentioned in
(a), (b) and (c)
11
1322A meter stick of mass 400 g is pivoted at one end and displaced through an angle ( 60^{0} . ) The increase in its potential energy is11
1323Two wires if same material and area if
cross section but with length in the
ratio 5: 3 are streached by the same
force. The ratio of work done in two
cases is
A . 5: 8
B. 8: 5
( c .5: 3 )
D. 3: 5
11
1324A solid iron ball A of radius ( r ) collids
head on with another stationary solid iron ball ( B ) of radius ( 2 r . ) The ratio of
their speeds just after the collision ( (e=0.5) ) is:
A . 3
B. 4
( c cdot 2 )
D.
11
1325A rope ladder with a length ( l ) carrying a man with a mass ( m ) at its end is
attached to the basket of a balloon with
a mass ( M . ) The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon,
the balloon descends by a height ( h ). The change in potential energy of the man is:
A ( . m g l )
в. ( M g(l-h) )
( c cdot 1 / 2 m g l )
D. ( m g(l-h) )
11
1326A bullet of mass 10 g moving with velocity of ( 100 mathrm{m} / mathrm{sec} ) hits a wooden log and penetrates it up to thickness of 5 ( mathrm{cm} . ) The resistance force of log is:
A . 200
B. 500 N
c. ( 1000 N )
D. 600 N
11
1327Find the maximum extension in the
spring
A ( cdot frac{1}{4} v_{0} sqrt{frac{m}{5 k}} )
В ( cdot frac{3}{4} v_{0} sqrt{frac{m}{5 k}} )
( ^{mathbf{c}} cdot frac{1}{3} v_{0} sqrt{frac{m}{5 k}} )
D. ( quad frac{1}{8} v_{0} sqrt{frac{m}{5 k}} )
11
1328Two point masses 1 and 2 move with
uniform velocities ( boldsymbol{v}_{1} ) and ( boldsymbol{v}_{2} )
respectively. Their initial position
vectors are ( r_{1} ) and ( r_{2}, ) respectively.
Which of the following should be satisfied for the collision of the point
masses?
A ( cdot frac{r_{1}-r_{2}}{left|r_{2}-r_{1}right|}=frac{v_{1}-v_{2}}{left|v_{2}-v_{1}right|} )
В. ( frac{r_{2}-r_{1}}{left|r_{1}-r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}-v_{1}right|} )
c. ( frac{r_{2}-r_{1}}{left|r_{2}+r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}+v_{1}right|} )
D. ( frac{r_{2}+r_{1}}{left|r_{2}+r_{1}right|}=frac{v_{2}-v_{1}}{left|v_{2}+v_{1}right|} )
11
132948. A block attached to a spring, pulled by a constant
horizontal force, is kept on a smooth surface as shown
in Fig. 8.240. Initially, the spring is in the natural length
state. Then the maximum positive work that the applied
force F can do is (given that string does not break)
Fig. 8.240
I
a. F²
b. 25²
c.
c.
oo
d. F
11
13303. A bob of mass m, suspended by a string of length 1, is
given a minimum velocity required to complete a full
circle in the vertical plane. At the highest point, it collides
elastically with another bob of mass m suspended by a
string of length 12, which is initially at rest. Both the
strings are mass-less and inextensible. If the second bob.
after collision acquires the minimum speed required to
complete a full circle in the vertical plane, the ratio 11/l, is
11
1331Assertion
In a two-body collision, the momenta of
the particles are equal and opposite to one another, before as well as after the
collision when measured in the centre
of mass frame.
Reason
The momentum of the system is zero from the centre of mass frame.
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
energy.
I. The electrical energy can be stored in
a capacitor to be recovered on its
discharge.
Il. It is stored in the electromagnetic radiations in electric and magnetic
fields.
III. In a closed system, the total energy is variable.
IV. Potential energy is stored in a body when it changes its configuration.
( A cdot ) ।, III and ( 1 V )
B. I, II and IV
C. I, II and III
D. II, III and IV
11
1333A neutron travelling with a velocity ( v ) and kinetic energy E collides perfectly elastically head on with the nucleus of an atom of mass number ( A ) at rest. The
fraction of total energy retained by the neutron is:
( ^{A} cdotleft(frac{A-1}{A+1}right)^{2} )
( ^{text {B. }}left(frac{A+1}{A-1}right)^{2} )
( ^{c}left(frac{A-1}{A}right)^{2} )
( ^{mathrm{D}}left(frac{A+1}{A}right)^{2} )
11
1334A man raises a box of mass ( 50 k g ) to a
height of ( 2 m ) in 2 minutes, while
another man raises the same box to the
same height in 5 minutes. Compare the work done by them.
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1
11
1335A ( 3000 mathrm{Kg} ) meteorite has a speed of ( 300 m s^{-1} ) just before colliding head on
with the energy that is the recoil speed of the earth? Mass of the earth ( =6 times )
( 10^{24} K g )
11
1336An object of mass ( m ) sliding along a frictionless surface collides with the
stationary object of mass ( m ). The two
bodies stick together. If the kinetic
energy of the two-body system is ( boldsymbol{E} ) Calculate the initial velocity of the first object before impact?
A ( cdot sqrt{E / 2 m} )
B. ( sqrt{2 E / 2 m} )
c. ( sqrt{2 E / m} )
D. ( sqrt{E / m} )
E ( .2 sqrt{E / m} )
11
1337A bullet of mass ( m ) is being fired from a
stationary gun of mass ( M . ) If the
velocity of the bullet is ( v, ) the velocity of
the gun is
A ( cdot frac{M v}{m+M} )
B. ( frac{m v}{M} )
c. ( frac{(M+m) v}{M} )
D. ( frac{M+m}{M v} )
11
1338Consider a gravity- free hall in which an experimenter of mass ( 50 mathrm{kg} ) is resting
on a ( 5 k g ) pillow, ( 8 f t ) above the floor of
the hall. He pushes the pillow down so that it starts falling at a speed of ( 8 f t / s )
The pillow makes a perfectly elastic
collision with the floor, rebounds and
reaches the experimenter’s head. Find the time elapsed in the process.
11
1339A ball falls from a height of ( 10 mathrm{m} ) on to a horizontal plane. if the coefficient 0
restitution is 0.6. the height to which it
rebounds after 2 collision is
approximate.
( mathbf{A} cdot 2.24 m )
B. ( 0.47 m )
( mathrm{c} .0 .3 mathrm{m} )
D. ( 1.296 mathrm{m} )
11
1340A body of mass ( 3 mathrm{kg} ) collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body?
( A cdot 1 mathrm{kg} )
B. 2.5 ( mathrm{kg} )
( c cdot 2 k g )
( D .5 mathrm{kg} )
11
1341A body of mass ( 3 mathrm{kg} ) is under a force, which causes a displacement in it given by ( S=frac{t^{3}}{3}left(text { in }^{prime} m^{prime}right) . ) Find the work
done by the force in first 2 seconds.
11
1342An ideal spring with spring constant ( k ) is hung from the ceiling and a block of mass ( M ) is attached to its lower end.
The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (Given acceleration due to gravity ( =g) )
A ( cdot frac{4 M g}{k} )
в. ( frac{2 M g}{k} )
c. ( frac{M g}{k} )
D. ( frac{M g}{2 k} )
11
1343A particle is projected at ( 60^{00} ) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is-
( A cdot K )
B. zero
( c cdot k / 4 )
D. K /2
11
1344The coefficient of restitution e for a
perfectly inelastic collision is:
( mathbf{A} cdot mathbf{1} )
B.
( c cdot alpha )
( D )
11
1345A body of mass 5 kg rests on a rough horizontal surface of friction coefficient
0.2. The is pulled through a distance 10
( mathrm{m} ) by a horizontal force of ( 25 N . ) The kinetic energy acquired by it is
A . ( 200 J )
в. ( 150 J )
( c cdot 100 J )
D. ( 50 J )
11
1346A ball of mass m approaches a wall of ( operatorname{mass} M(>>m) ) with the speed ( 4 mathrm{m} / mathrm{s} )
along normal to the wall. The speed of wall is ( 1 mathrm{m} / mathrm{s} ) towards the ball. The speed of the ball after an elastic collision with
the wall is-
A. ( 5 mathrm{m} / mathrm{s} ) away from the wall
B. 3 m/s away from the wall
c. ( 9 mathrm{m} / mathrm{s} ) away from the wall
D. ( 6 mathrm{m} / mathrm{s} ) away from the wall
11
13473. Two blocks A and B, each of mass m, are connected by a
massless spring of natural length L and spring constant
k. The blocks are initially resting on a smooth horizontal
floor with the spring at its natural length as shown in
Fig. 8.314. A third identical block C, also of mass m moves
on the floor with a speed v along the line joining A and B
and collides with A, then
L
Fig. 8.314
(IIT JEE, 1993)
a. The KE of the AB system at maximum compression
of the spring is zero.
b. The KE of the AB system at maximum compression
of the spring is (1/4)mv.
c. The maximum compression of the spring is v.
m
d. The maximum compression of the spring is
V2k
Descanina Tune
11
1348A massive ball moving with a speed ( boldsymbol{v} )
collide with a tiny ball having a very small mass, immediately after the impact the second ball will move at
speed approximately equal to :
( A cdot infty )
B. ( frac{v}{2} )
( c )
D. ( 2 v )
11
1349The co-efficient of restitution for a
perfectly elastic collision is:
A .
B. 0
c. lies in between 0 and 1
D. infinity
11
1350A spring of force constant ( 800 mathrm{N} / mathrm{m} ) has
an extension of ( 5 mathrm{cm} ). Find work done in
extending it from ( 5 mathrm{cm} ) to ( 15 mathrm{cm} )
11
1351A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is
( A cdot h e^{2 n} )
В. ( h e^{n} )
c. ( frac{2^{e n}}{h} )
D. ( frac{h}{2^{e n}} )
11
1352Set the angles made by following vectors with ( x ) -axis in increasing order:
a) ( 3 hat{i}+4 hat{j} )
b) ( 4 hat{i}+3 hat{j} )
c) ( hat{boldsymbol{i}}+hat{boldsymbol{j}} )
( A cdot a, b, c )
B. ( c, b, a )
( c cdot b, c, a )
D. a, c, b
11
1353Consider the situation shown if figure
Initially the string is unstretched when
the system is released from rest

Assuming no friction in the pulley, what is the maximum elongation of the
spring?

11
1354The type of collision is:
A . perfectly elastic
B. elastic
C . inelastic
D. perfectly inelastic
11
1355( operatorname{Let} vec{A}=hat{i} A cos theta+hat{j} A sin theta, ) be any
vector. Another vector ( vec{B} ) which is normal to ( vec{A} ) is :
A ( . hat{i} B cos theta+hat{j} B sin theta )
B. i ( B ) sin ( theta+hat{j} B cos theta )
c. ( hat{i} B sin theta-hat{j} B cos theta )
D. ( hat{i} B cos theta-hat{j} B sin theta )
11
1356If both the objects have the same PE
curve as shown in the figure, then
A . For objects having total energy ( E_{2} ), all values of r are possible
B. For the object having total energy ( E_{2} ), values of ( r<r_{0} )
are only possible
C. For the object having total energy ( E_{1} ), all values of rare possible
D. None of the above
11
1357A block of mass ( mathrm{m} ) is kept over another
block of mass ( 2 mathrm{m} ) and the system rests
on a smooth horizontal surface. The
coefficient of friction between the
blocks is ( 0.50 . ) Find the work done by the
force of friction on the smaller block by the bigger block during a displacement
d the system, when a force mg is applied to the lower block.
( mathbf{A} cdot frac{m g d}{3} )
B. mgd
c. ( frac{m F d}{2(M+m)} )
D. Zero
11
1358As a builder lifts a ( 3.0 mathrm{kg} ) brick at a steady speed from the ground to a platform 2.0 meters high. How much work is done on the brick by the builder and by the earth while it is being lifted, and what is the net work done on the
brick by all forces while it is being lifted?
A. ( 60 mathrm{N},-60 mathrm{N}, mathrm{O} )
в. – -60 N, 60 N, 0
c. ( 60 mathrm{N}, 60 mathrm{N}, 0 )
D. – -60 N,-60 N, 0
E. 60 N, 60 N, -60 N
11
1359One of the two forces is double and the
other resultant is equal to the greater force. The angle between then is
( mathbf{A} cdot cos ^{-1}(1 / 2) )
B . ( cos ^{-1}(-1 / 2) )
c. ( cos ^{-1}(1 / 4) )
D. ( cos ^{-1}(-1 / 4) )
11
1360If vector ( 2 hat{i}+3 hat{j}+8 hat{k} ) is perpendicular to the vector ( 4 hat{j}-4 hat{i}+alpha hat{k}, ) then the
value of ( alpha ) is :
A . -1
в. ( frac{1}{2} )
( c cdot-frac{1}{2} )
D.
11
13612. Two masses of 1 g and 4 g are moving with equal ki
energies. The ratio of the magnitudes of their momenta is
(IIT JEE, 1980)
a. 4:1 b. √2:1 c. 1:2 d. 1:16
11
1362Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of
( 3 m s^{-1} ) and ( 2 m s^{-1} ) respectively. They collide with each other. After collision,
glass sphere of mass 10 g moves with a velocity of ( 2.5 m s^{-1} . ) Find the velocity of the second ball after collision.
A ( .2 .25 m s^{-1} )
B. ( 5.5 m s^{-1} )
( mathbf{c} cdot 2.75 m s^{-1} )
D. ( 7.5 m s^{-1} )
11
1363A uniform rod of mass ( m ) and length ( l ) is resting on a smooth horizontal surface.
A particle of mass ( m / 2 ) travelling with a
speed ( v_{0} ) hits the rod normally and
elastically. Then,
This question has multiple correct options
A ( cdot ) final velocity of the particle is ( -frac{2}{15} v_{0} )
B. final velocity of the particle is ( -frac{1}{15} v_{0} )
c. angular velocity of the rod ( frac{8 v_{0}}{5 e} )
D. angular velocity of the rod ( frac{6 v_{0}}{5 ell} )
11
1364Ball A of mass m, after sliding from an inclined plane,
strikes elastically another ball B of same mass at rest.
Find the minimum height h so that ball B just completes
the circular motion of the surface at C. (All surfaces are
smooth.)
Fig. 8.268
b. h = 2R
a. h=2R
d. h = 3R
11
1365A body of weight 1 newton has a potential energy of 1 joule relative to the ground when it is at a height of:
A . ( 1 mathrm{m} )
B. 9.8 m
( mathrm{c} cdot 1 / 9.8 mathrm{m} )
D. o m
11
1366Potential energy is classified into which
two energy?
A. Gravitational and Elastic Potential Energy
B. Kinetic and Elastic Potential Energy
c. Mechanical and Elastic Potential Energy
D. None
11
1367The gravitational potential energy of a body is ( _{-}–_{-}-_{-}- ) to its height above
the surface of the Earth.
A. directly proportional
B. indirectly proportional
c. independent
D. none
11
1368A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic
energy, ( boldsymbol{E}_{mathbf{0}} ). The minimum energy of
explosion will be
( mathbf{A} cdot 6 E_{0} )
в. ( frac{4 E_{0}}{3} )
c. ( 4 E_{0} )
D. ( 8 E_{0} )
11
1369Consider the following statements
A) Linear momentum of a system of
particles is zero
B) Kinetic energy of a system of particles is zero Then
A. A does not imply B & B does not imply A
B. A implies B and B does not imply A
c. A does not imply B but B implies A
D. A implies B and B implies A
11
1370A block of mass 2 kg slides on a rough surface at ( t=0, ) if speed is ( 2 mathrm{m} / mathrm{s} ). It stops after covering a distance of ( 20 mathrm{cm} ) because of friction. Find work done by
the friction.
11
1371Energy required to accelerate a car from
( 10 m s^{-1} ) to ( 20 m s^{-1} ) compared with
that required to acceleration it from 0 to ( 10 m s^{-1} ) is
( A ). twice
B. three times
c. four times
D. same
11
1372A wound-up watch spring possesses
A. kinetic energy
B. elastic potential energy
c. nuclear energy
D. sound energy
11
1373Tlus
ration 8.35 A plate of mass m, length b, and breadth
a is initially lying on a horizontal floor with length parallel
to the floor and breadth perpendicular to the floor. Find the
work done to erect it on its breadth.
BOLA
Fig. 8.74
11
137433. In the above question, the average power delivered by
gravity is
a. -mg u cos a
b. -mgu sina
c.
mgucosa
d.
mgu sina
11
1375If the kinetic energy of a body increases
b ( 4 % ) the momentum:
A. increases by 2%
B. increases by 4%
c. increases by ( 8 % )
D. increases by 16%
11
1376Find the speed of ( C ) after collision of ( B )
and ( C ) for first time.
A ( cdot frac{V}{4} )
в. ( frac{2 V}{4} )
c. ( frac{3 V}{4} )
( D )
11
1377A truck weighing 1000 kgf changes its
speed from ( 36 k m h^{-1} ) to ( 72 k m h^{-1} ) in 2
minutes. ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) . ) Calculate the
work done by the engine
A ( cdot 1.5 times 10^{4} J )
В. ( 1 times 10^{5} J )
c. ( 7.2 times 10^{5} J )
D. ( 0 . J )
11
1378Find the fraction of kinetic energy lost when the body of mass ( M ) is jerked into
motion
A ( cdot frac{M}{M+m} )
В. ( frac{M}{M-m} )
c. ( frac{2 M}{M+m} )
D. ( frac{M}{2(M+m)} )
11
1379A simple pendulum is vibrating with an
angular amplitude of ( frac{r}{2} . ) The value of ( alpha )
for which the resultant acceleration has
a direction along the horizontal is :
( mathbf{A} )
( frac{pi}{2} )
B. ( 180^{circ} )
c. ( cos ^{-1}left(frac{1}{sqrt{3}}right) )
D. ( cos ^{-1}left(frac{1}{sqrt{2}}right) )
11
1380At which depth, we get the necessary temperature for OTEC in the ocean?
( A cdot O m ) to ( 20 m )
B. 100 m to 300 m
c. ( 400 mathrm{m} ) to ( 600 mathrm{m} )
D. 700 ( mathrm{m} ) to ( 900 mathrm{m} )
11
1381A cricket ball of mass 250 g collides with a bat with velocity ( 10 mathrm{m} / mathrm{s} ) and returns with the same velocity within
0.01 second. The force acted on bat is:
A. 25
B. 50 N
c. 250 N
D. 500 N
11
1382The potential energy function associated with the force ( overrightarrow{boldsymbol{F}}=mathbf{4 x y} hat{mathbf{i}}+ )
( 2 x^{2} hat{j} ) is
A ( cdot U=-x^{2} y )
B . ( U=-2 x^{2} y+ ) constant
C. ( U=2 x^{2} y+ ) constant
D. Not defined
11
1383A constant force ( boldsymbol{F}=(hat{boldsymbol{i}}+boldsymbol{3} hat{boldsymbol{j}}+boldsymbol{4} hat{boldsymbol{k}}) boldsymbol{N} )
acts on a particle and displace it from ( (-1 m, 2 m, 1 m) ) to ( (2 m,-3 m, 1 m) )
Then the work done by the force is:
( mathbf{A} cdot 12 J )
в. ( -10 J )
c. ( -12 J )
D. ( 15 J )
11
1384An object with mass ( 2 mathrm{kg} ) moves with a velocity of ( 10 mathrm{m} / mathrm{s} ). What is the net force
on the body?
A. 20
B. on
( c cdot 5 N )
D. 25 N
11
1385In Fig. Force ( F ) is gradually increased from zero. Draw the graph between applied force ( F ) and tension ( T ) in the
string. The coefficient of static friction
between the block and the ground is ( mu_{s} )
11
1386A stone is tied to the middle of a string
and suspended from one end as shown
in the figure. Here ( mathrm{S} ) is the stone and 0 is the pint of suspension
(ii) if we increase the pull at ( mathrm{P} )
A. Below the stone
B. At the point P itself
c. Above the stone
D. Nothing can be decided
11
1387A boy pulls a ( 5 k g ) block along a ( 20 m ) long horizontal surface at a constant
velocity by applying a horizontal force ( boldsymbol{F} )
If the coefficient of kinetic friction is 0.2
how much work does the boy do on
the block? ( left(g=10 m s^{-2}right) )
( mathbf{A} cdot 100 J )
B. ( 300 J )
c. ( 200 J )
D. ( 400 J )
11
1388What is the angular velocity of rotation of this rigid body?
A ( cdot frac{V_{0}}{5 d} )
B. ( frac{V_{0}}{d} )
c. ( frac{V_{0}}{3 d} )
D.
11
1389A weight of ( 5 mathrm{N} ) is moved upon a frictionless inclined plane from ( R ) to ( Q )
as shown. What is the work done in
joule?
A ( cdot 15 )
B. 20
( c cdot 25 )
D. 35
11
1390Compute the work which must be performed (in ( K g f-m ) ) to slowly
pump water out of a hemispherical reservoir of radius ( boldsymbol{R}=mathbf{0 . 6 m} )
11
1391The work done by the tension T in the
above process is
A . ( Z ) ero
B . ( T(L-L cos theta) )
c. ( -T L )
D. ( -T L sin theta )
11
1392A man has a strange ability to jump from any height to another with ease. The manjumps to P then to Q, R, S, T and then into water. For which jump will he require the highest energy?
A. Land to P
в. s to ( T )
( c cdot Q ) to ( R )
D. R to
11
1393Which of the following quantity is different from others?
A. work
B. Kinetic energy
c. Force
D. Potential energy
11
1394A girl in a swing is ( 2.5 m ) above ground
at the maximum height and at ( 1.5 m )
above the ground at the lowest point. Her maximum velocity in the swing is
( left(g=10 m s^{-2}right) )
В. ( 2 sqrt{5} mathrm{ms}^{-1} )
D. ( 3 sqrt{2} mathrm{ms}^{-1} )
E ( cdot 4 sqrt{2} m s^{-1} )
11
1395A spring is kept compressed by a toy car of mass ( 150 g . ) On releasing the car it moves with a speed of ( 0.2 m s^{-1} . ) So, the elastic potential energy of the spring is
( A .3 m J )
B. ( 3 J )
c. ( 1.5 m J )
D. ( 4 m J )
11
1396A force acts on a ( 3 g ) particle in such a way that the position of the particle as a function of time is given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}- )
( 4 t^{2}+t^{3}, ) where ( x ) is in meters and ( t ) is in
second. The work done during the first 4 second is:
A. ( 490 m J )
J
в. ( 450 m J )
( mathrm{c} .528 mathrm{mJ} )
D. ( 530 m J )
11
13975. Find average power transferred to the body in first 2 s.
a. 50W b. 100 W c. 150 W d. 200 W
To Problems 68
11
1398Assertion
In an inelastic collision between two
bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system 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
1399A block of mass ( m ) has initial velocity ( u ) having direction ( +x ) axis. The block stops after covering distance ( S ) causing
an extension in the spring of spring
constant ( K ) holding it. If ( mu ) is the kinetic
friction between the block and the
surface on which it was moving, the distances ( boldsymbol{S} ) is :
A ( cdot frac{1}{K} mu^{2} m^{2} g^{2} )
B. ( frac{1}{K}left(m K u^{2}-mu^{2} m^{2} g^{2}right)^{frac{1}{2}} )
c. ( frac{1}{K}(sqrt{mu^{2} m^{2} g^{2}+m K u^{2}}-mu m g) )
D ( cdot frac{1}{K}left(mu^{2} m^{2} g^{2}-m K u^{2}+mu m gright)^{frac{1}{2}} )
11
1400When a body moves in a circular path,
no work is done by the force since:
A. force and displacement are perpendicular to each other.
B. the force is always away from the centre.
C. there is no displacement.
D. there is no net force.
11
1401If the potential energy of two molecules is given by, ( U=frac{A}{r^{12}}-frac{B}{r^{6}} ) then at
equilibrium position, its potential energy is equal to:
A ( cdot frac{A^{2}}{4 B} )
B. ( -frac{B^{2}}{4 A} )
c. ( frac{2 B}{A} )
D. 3A
11
1402A spring block system is placed on a horizontal surface so as to just fit within two vertical walls. The spring is initially unstretched. The coefficient of restitution for collison is ( e=frac{1}{2} . ) The block is pulled to the left by a distance ( x=1 c m ) and released from rest. The
time between second and third collision
of the block with the
wall is
A ( cdot 2 pi sqrt{frac{m}{k}} )
В. ( pi sqrt{frac{m}{k}} )
c. ( frac{pi}{2} sqrt{frac{m}{k}} )
D. ( frac{pi}{4} sqrt{frac{m}{k}} )
11
1403A bullet of mass ( A ) and velocity ( B ) is fired
into a block of wood of mass ( C . ) If loss of
any mass and friction be neglected, the velocity of the system will be
( ^{text {A }} cdot frac{A B}{A+C} )
в. ( frac{A+C}{B+C} )
c. ( frac{A C}{B+C} )
D. ( frac{A+B}{A C} )
11
1404A electron at rest is accelerated by
applying a ( P . D . ) of ( 250 mathrm{V} ). What is its
( K . E . ) in electron volt ?
A ( .250 e V )
B. 225 eV
c. 200 eV
D. 150 eV
11
1405Two identical ( 5 mathrm{kg} ) blocks are moving
with same speed of ( 2 m s^{-1} ) towards
each other along a frictionless
horizontal surface. The two blocks
collide, stick together, and come to rest. Consider the two blocks as a system
The work done by external and internal forces are respectively,
( A cdot 0,0 )
B. 0, 20J
c. 0,-20
D. 20J, -20J
11
1406ilustration 8.15 An inclined plane is
moving up with constant velocity v. A block
pt on incline is at rest. Calculate the work
Mone by gravity, friction force, and normal
reaction on block in time interval of
Fig. 8.28
11
1407A force of 5 N acts on a 15 kg particle initially at rest. What will be
instantaneous power due to the force at
the end of ( 6^{t h} ) second.
A. 10 watt
B. 5 watt
c. 20 watt
D. 25 watt
11
14088. Select the correct option(s).
a. A single external force acting on a particle necessarily
changes its momentum and kinetic energy.
b. A single external force acting on a particle necessarily
changes its momentum.
c. The work-energy theorem is valid for all types of
forces: internal, external, conservative as well as non-
conservative.
d. The kinetic energy of the system can be increased
without applying any external force on the system.
11
1409When a body slides down from an inclined plane, Work is said to be done because of gravity. State whether given statement is True/
False?
A. True
B. False
11
1410Give an example for each of the following energy conversion: (1) electrical energy to kinetic energy. chemical energy to electrical energy (3) sound energy to electrical energy11
1411Two bodies of equal weights are kept at
heights ( h ) and 1.5 respectively. The ratio of their potential energy is
A .3: 2
B. 1: 1
( c cdot 2: 3 )
D. 3: 4
11
1412When ( 1 g ) of water ( operatorname{at} 0^{circ} C ) and ( 1 times ) ( 10^{5} N / m^{2} ) pressure is converted into
ice of volume ( 1.091 mathrm{cm}^{3} ), the external
work done will be:
A. 0.0091 joule
B. 0.0182 joule
c. -0.0091 joule
D. – 0.0182 joule
11
1413For the system shown in the figure, the cylinder on the left at L has a mass of
( 600 mathrm{kg} ) and a cross sectional area of
( 800 c m^{2}, ) the piston on the right, at ( S )
has cross sectional area ( 25 c m^{2} ) and
negligible weight. If the appartus is
filled with oil. ( left(rho=0.75 g m / c m^{3}right) ) Find
the force ( F ) requird to hold the system in equilibrium.
A . 50 N
В. 33 n
D. 22.5
11
1414An object of mass ( mathrm{m} ) is allowed to fall from rest along a rough inclined plane. The speed of the object on reaching the bottom of the plane is proportional to?
( mathbf{A} cdot m^{0} )
B. ( m )
( c cdot m^{2} )
D. ( m^{-1} )
11
1415i.e., potom
estration 8.37 A conservative force held function is given
hy F = k/r’, where k is a constant.
Determine the potential energy function U(r) assuming
zero potential energy at r= ro.
h. Also, determine the potential energy at r=o.
11
1416What is the recoil velocity of the gun of mass ( 8 mathrm{kg} ) when a bullet of mass ( 10 mathrm{g} ) is fired from it with a velocity of ( 400 mathrm{m} / mathrm{s} ? )
( mathbf{A} cdot 5 mathrm{m} / mathrm{s} )
B. ( 2 mathrm{m} / mathrm{s} )
c. ( 50 mathrm{m} / mathrm{s} )
D. ( 0.5 mathrm{m} / mathrm{s} )
11
1417A wedge of mass ( M ) is kept at rest on
smooth surface, a particle of mass ( boldsymbol{m} )
hits the wedge normally. Find the velocity of wedge and particle just after collision. Take coefficient of restitution
as ( e )
11
1418A proton in motion makes head on collision with an unknown particle at rest. If the collision is perfectly elastic and proton rebounds back with ( frac{4}{9} ) of its initial kinetic energy after collision, the mass of unknown particle is
A. Equal to mass of proton
B. Twice the mass of proton
c. 3 times the mass of proton
D. 5 times the mass of proton
11
1419A particle of mass ( m_{1} ) moving with a velocity of ( 5 m / s ) collides head on with a
stationary particle of mass ( m_{2} . ) After collision both the particle move with a
common velocity of ( 4 m / s, ) then the
value ( boldsymbol{m}_{1} / boldsymbol{m}_{2} ) is:
A .4:
B. 2:
( c cdot 1: 8 )
D. 1:
11
1420A rod of length 1 m and mass 0.5 kg
hinged at one end, is initially hanging vertical. The other end is now raised
slowly until it makes an angle ( 60^{circ} ) with the vertical. The required work is (use
( left.boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) )
A ( cdot frac{5}{2} J )
в. ( frac{5}{4} J )<