Motion In A Plane Questions

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

List of motion in a plane Questions

Question No Questions Class
1 The velocity of projection of a projectile is given by : ( vec{u}=5 hat{i}+10 hat{j} . ) Range is:
A ( .2 m )
в. ( 4 m )
( c .6 m )
D. ( 10 m )
11
2 A particle is projected upwards from the roof of a tower ( 60 m ) high with velocity
( 20 m / s . ) Find the average speed.
11
3 When a man stands on a moving escalator he goes up in ( 40 s ) and when
he walked up the moving escalator he goes up in 20 s. The man walk up the
stationary escalator in a time of:
( mathbf{A} cdot 60 )
B. ( 40 s )
( c cdot 20 s )
D. ( 50 s )
11
4 A man running on a horizontal road at
( 8 k m p h ) find that rain is falling vertically. He increases the speed to
( 12 k m p h ) and find the drops make an
angle ( 30^{circ} ) with the vertical
A. The speed of rain is ( 8 sqrt{3} k m p h )
B. The speed of rain is ( 8 sqrt{112} k m p h )
c. speed of rain wrt man is ( 8 k m p h )
D. Speed of rain wrt man is ( 8 sqrt{3} k m p h )
11
5 подоtапу.
9. A particle is moving in a circle of radius R with constant
speed. The time period of the particle is T = 1. In a time
t = T/6, if the difference between average speed and
average velocity of the particle is 2 ms’, find the radius
R of the circle (in meters).
11
6 A particle is moving in a horizontal circle with constant speed. It has
constant
A. Velocity
B. Acceleration
c. Kinetic energy
D. Displacement
11
7 A plank fitted with a gun is moving on a horizontal surface with speed of ( 4 mathrm{m} / mathrm{s} ) along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the mass of the gun is 50 kg. When the plank reaches the origin, a shell of
mass ( 10 mathrm{kg} ) is fired at an angle of ( 60^{circ} ) with the positive x-axis with a speed of ( mathbf{v}=20 mathrm{m} / mathrm{s} ) with respect to the gun ( mathrm{n} mathbf{x}-mathrm{z} )
plane. Find the position vector of the shell at ( t=2 ) s after firing it. Take ( g= ) ( 9.8 m / s^{2} )
A. ( [15 hat{i}-24 hat{k}] m )
в. ( [28 hat{i}+15 hat{k}] m )
c. ( [15 hat{i}-18 hat{k}] m )
D. ( [14 hat{i}-15 hat{k}] m )
11
8 2. The time after which they are closest to each other
a. 1/3 s b. 8/3 s c. 1/5 s d. 8/5 s
11
9 A vertical wall of height ( a ) running from south to north has the height. A policeman of height ( b>a ) is standing
in front of the wall at a distance ( c ) from
it on the eastern side. What should be
the maximum distance of a crawling theif from the wall so that the thief can hide from the view of the policeman if the thief is on the other side of the wall
in the west of the policeman?
A ( cdot frac{a c}{b-a} )
в. ( frac{b c}{b-a} )
c. ( frac{a+b}{b-a} cdot c )
D. ( frac{a c}{a+b} )
11
10 A vector having magnitude 30 unit
makes equal angles with each of ( boldsymbol{x}, boldsymbol{y} )
and ( z ) axes. The component along each
of ( x, y ) and ( z ) -axis are
A ( cdot 10 sqrt{3} )
is
в. ( 20 sqrt{3} )
c. ( 30 sqrt{3} )
is
D. ( 18 sqrt{3} )
11
11 15. The horizontal range of particle is
3 u* sin 20
(0) “”sin 26
4
g
(b) usin 20 (1+ +
(a) u? sin 20 (2++)
2g
11
12 A particle is acted upon by a force of
constant magnitude which is always perpendicular to the velocity of the
particle. The motion of the particle takes place in a plane. It follows
A. its velocity is constant
B. its K.E. is constant
c. its acceleration is constant
D. it moves in a straight line
11
13 Two forces acting in opposite directions
have a resultant of ( 10 mathrm{N} 10 mathrm{N} ). What are the
magnitudes of the two forces?
( mathbf{A} cdot F_{1}=40 N, F_{2}=30 N )
B. ( F_{1}=30 N, F_{2}=40 N )
C . ( F_{1}=50 N, F_{2}=40 N )
D. ( F_{1}=100 N, F_{2}=60 N )
11
14 The position vector of a particle is ( r= )
( a sin omega t hat{i}+a cos omega t hat{j} )
The velocity of the particle is
A. Parallel to position vector
B. Perpendicular to position vector
c. Directed towards origin
D. Directed away from the origin
11
15 A boy playing on the roof of a ( 10 mathrm{m} ) high building throws a ball with a speed of ( 10 m s^{-1} ) at an angle of ( 30^{circ} ) with the horizontal. How far from the throwing point with the ball be at the height of 10 ( mathrm{m} ) from the ground? ( (boldsymbol{g}= ) ( 10 m s^{-2}, sin 30^{circ}=1 / 2, cos 30^{circ}= ) 11
16 In the arrangement shown in the figure,
the ends ( P ) and ( Q ) of an un-stretchable
string move downwards with uniform
speed ( U ). Pulleys ( A ) and ( B ) are fixed. The
mass ( M ) moves upwards with a speed:
( mathbf{A} cdot 2 U cos theta )
B. ( frac{U}{cos theta} )
c. ( frac{2 U}{cos theta} )
( D . U cos theta )
11
17 A vector of magnitude 100 units is
inclined at ( 30^{0} ) to another vector of
magnitude 80 units. Then vector
product is:
A. 4000
B. ( 4000 sqrt{3} )
c. 8000
D. ( 8000 sqrt{3} )
11
18 C.
lall
(14)
23. A shot is fired from a point at a distance of 200 m from
the foot of a tower 100 m high so that it just passes over
it horizontally. The direction of shot with horizontal is
a. 30° b. 45° c. 60° d. 70°
……. 1:
11
19 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 ( delta, ) then
A ( cdot frac{F}{k}frac{2 F}{k} )
B . ( delta frac{2 F}{k} )
c. work done by force F is equal to ( F delta )
D. Increase in energy stored in the spring is ( frac{1}{2} k delta^{2} )
11
20 A horizontal wind is blowing with a velocity ( v ) towards north-east. A man starts running towards north with
acceleration ( a ). The time after which
man will feel the wind blowing towards east is
A ( cdot frac{v}{a} )
B. ( frac{sqrt{2} v}{a} )
c. ( frac{v}{sqrt{2} a} )
D. ( frac{2 v}{a} )
11
21 T
y
m
00
-12.
9 IV
Illustration 3.10 A person in a
wheelchair is moving up a ramp at
constant speed. Their total weight
is 900 N. The ramp makes an angle
of 37° with the horizontal. Calculate
the component of its weight parallel
and perpendicular to the ramp.
370
Fig. 3.26
11
22 Rain is falling vertically with a speed of
( 30 mathrm{m} s^{-1} . ) A woman rides a bicycle with a
speed of ( 10 mathrm{m} s^{-1} ) in the north to south
direction. What is the direction in which
she should hold her umbrella?
11
23 On applying brakes the angular velocity of a flywheel reduces from 900
cycles/min to 720 cycles/min in 6 seconds. Its angular retardation in rad
( / s^{2} ) will be?
A . ( pi / 3 )
в. ( pi )
c. ( 2 pi / 3 )
D. ( 2 pi )
11
24 In going from one city to another, a car travels ( 75 k m ) north, ( 60 k m ) north-west and ( 20 k m ) east. The magnitude of
displacement between the two cities is (take ( sqrt{mathbf{2}}=mathbf{0 . 7}) )
A. ( 170 k m )
в. ( 137 k m )
c. ( 119 k m )
D. ( 140 k m )
11
25 Point ( ^{prime} A^{prime} ) moves uniformly with speed
( v_{1}(=20 m / text {sec}) ) so that vector ( vec{v}_{1} ) is
continuously ‘aimed’ at point ‘ ( B^{prime} ) which in turn moves rectilinearly and uniformly with velocity ( v_{2}(=10 m / s e c) )
along the path ( P rightarrow Q ) as shown in the
figure. If the time (in sec)when the
points ( A ) and ( B ) converge is ( frac{3 k}{7} . ) Then
find the value of ( k ? )
11
26 In a uniform circular motion, the
magnitude and direction of velocity at different points remain the same.
A. True
B. False
11
27 3. Cannon A is located on a plain a distance L from a wall of
height H. On top of this wall is an identical cannon (cannon
B). Ignore air resistance throughout this problem.
KL-
Fig. 5.185
Also ignore the size of the cannons relative to L and H.
The two groups of gunners aim the cannons directly at
each other. They fire at each other simultaneously, with
equal muzzle speed Vo.
What is the value of v, for which the two cannon balls
collide just as they hit the ground?
11
28 A particle moves along a circle of radius ( 2 m ) with a constant speed of ( 8 m / s . ) It
covers the quarter of circle in sec?
A ( cdot frac{pi}{16} )
в.
( c cdot frac{pi}{4} )
D.
11
29 1. Two forces, each of magnitude F have a resultant of the
same magnitude F. The angle between the two forces is
(a) 45° (b) 120° (c) 150° (d) 60°
1.
10
11
30 In reaching her destination, a backpacker walks with an average velocity of ( 1 m / s, ) due west. This average
velocity results, because she hikes for
( 6 k m ) with an average velocity of ( 3 m / s ) due west, turns around, and hikes with
an average velocity of ( 0.3 m / s ) due east.How far to east did she walk (in
kilometers)?
A. 1.714
в. 2
( c .6 )
D
11
31 An uniform circular motion is an
uniform velocity motion
A. True
B. False
11
32 A wheel rotating at 12 rev/s is brought
to rest in ( 6 s . ) The average angular
deceleration in ( r a d / s^{2} ) of the wheel during this process is?
A . ( 4 pi )
в. 4
( c cdot 72 )
D. ( frac{1}{pi} )
( E . pi )
11
33 8. A particle is projected up an inclined plane of inclination
B at an elevation a to the horizontal. Find the ratio
between tan a and tan B, if the particle strikes the plane
horizontally.
11
34 Two tall buildings are ( 80 m ) apart. The velocity with which a ball should be thrown horizontally from a window ( 95 m ) above the ground in one building so that it will enter a window 15 m above the
ground in the second building is : ( (g= )
( left.10 m / s^{2}right) )
A. ( 15 mathrm{m} / mathrm{s} )
B. ( 5 m / s )
c. ( 10 mathrm{m} / mathrm{s} )
D. 20 ( m / s )
11
35 Illustration 5.55 A man is coming down an incline of angle
30°. When he walks with speed 2/3 ms’ he has to keep
his umbrella vertical to protect himself from rain. The actua
speed of rain is 5 ms. At what angle with vertical should
he keep his umbrella when he is at rest so that he does not
get drenched?
30°
Fig. 5.109
11
36 45. In a two-dimensional motion of a particle, the particle
moves from point A, with position y
vector , to point B, with po-
sition vector 72. If the magnitudes
of these vectors are, respectively,
r = 3 and r2 = 4 and the angles
they make with the x-axis are 0,
=75° and e2 =15°, respectively,
then find the magnitude of the Fig. 3.80
displacement vector.
a. 15 b. 813 c. 17 d. /15
We
11
37 When a body is projected from a level
ground, the ratio of it’s speed in the
vertical and horizontal direction is 4: 3
If the velocity of projection is ( u, ) the time
after which the ratio of the velocities
in the vertical and horizontal directions
is reversed is
A. ( frac{7 u}{20 g} )
B. ( frac{35 u}{10 g} )
c. ( frac{9 u}{g} )
D. ( frac{10 u}{g} )
11
38 hollis projected from the ground with velocity v such
that its range is maximum.
Column I
Column II
Velocity at half of the maximum
height
i
Velocity at the maximum
height
Change in its velocity when it
returns to the ground
tc.
iv.
Average velocity when it reaches
the maximum height
11
39 The position of a body moving along ( x- )
axis at time ( t ) is given by ( boldsymbol{x}=left(boldsymbol{t}^{2}-boldsymbol{4} boldsymbol{t}+right. )
6) ( m . ) The distance travelled by body in
time interval ( t=0 ) to ( t=3 ) s is
( mathbf{A} cdot 5 m )
B. ( 7 m )
c. ( 4 m )
D. ( 3 m )
11
40 Ay
1. Which of the following statements
is/are correct (Fig. 3.81)?
a. The sign of the x-component
of d, is positive and that of
d2 is negative.
b. The signs of the y-com-
ponents of d, and d2 are
Fig. 3.81
positive and negative, re-
spectively.
c. The signs of the x- and y-components of d. + d, are
positive.
d. None of these.
11
41 All straight wires are very long. Both ( boldsymbol{A B} )
and ( C D ) are arcs of the same circle,
both subtending right angles at the
centre ( O . ) Then the magnetic field at 0
is-
A ( cdot frac{mu text { is }}{4 pi R R R} )
B・ ( frac{mu_{text {Di }}}{4 pi} sqrt{2} )
c. ( frac{mu text { li }}{2 pi R_{R}} )
D. ( frac{mu_{0} i}{2 pi R}(pi+1) )
11
42 Fill in the blanks.
At any point in a circular motion the
direction of linear velocity of the
particle is
11
43 39. Two forces Ē = 500 N due east and F = 250 N due
north have their common initial point. F2 – F is
a. 250 V5 N, tan-‘(2) W of N
b. 250 N, tan-|(2) W of N
c. Zero
d. 750 N, tan-‘(3/4) N of W
11
44 For given vectors, ( vec{a}=2 hat{i}-hat{j}+2 hat{k} ) and ( vec{b}=-hat{i}+hat{j}-hat{k}, ) find the unit vector in the direction of the vector ( vec{a}+vec{b} ) 11
45 A projectile is thrown into space so as to have the maximum possible
horizontal range equal to ( 400 m ). Taking
the point of projection as the origin, the coordinates of the point where the
velocity of the projectile is minimum
are:
( mathbf{A} cdot(400,100) )
в. (200,100)
c. (400,200)
D. (200,200)
11
46 22. A spy plane is being tracked by a radar. Att=0, its position
is reported as (100 m, 200 m, 1000 m). 130 s later, its
position is reported to be (2500 m, 1200 m, 1000 m).
Find a unit vector in the direction of plane velocity and
the magnitude of its average velocity.
11
47 An ice cream truck travels around many circular curves at constant speeds.
Each table represents the speed of the truck and radii for some of these curves
During which curve is the magnitude of the truck’s acceleration the greatest??
A. Radius of curve – Speed of Truck, ( 30 mathrm{m}-5 mathrm{m} / mathrm{s} )
B. Radius of curve – Speed of Truck, ( 60 mathrm{m}-10 mathrm{m} / mathrm{s} )
c. Radius of curve – Speed of Truck, ( 90 mathrm{m}-15 mathrm{m} / mathrm{s} )
D. Radius of curve – speed of Truck, ( 120 mathrm{m}-20 mathrm{m} / mathrm{s} )
E. The magnitude of the acceleration for the ice cream truck on all these curves is the same
11
48 A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the
ratio ( frac{mid text {displacement} mid}{text {distance}} ) is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot frac{2}{7} )
D. ( frac{7}{11} )
11
49 A bomb is dropped from a flying
aeroplane. Its path will be
A. an arc of a circle
B. a parabola
c. a zig-zag path
D. a straight vertical path in the do rection
11
50 In a projectile motion from a point of horizontal surface to another point on
the same surface (Take ( overrightarrow{boldsymbol{a}}= )
acceleration and ( vec{v}= ) instantaneous
velocity) This question has multiple correct options
A. ( vec{a} cdot vec{v}=0 ) at maximum height
B . ( vec{a} cdot vec{v}=0 ) only if angle of projection is ( 90^{circ} )
c. ( vec{a} times vec{v}= ) constant every where in air
D. None of these
11
51 If ( vec{p} & vec{s} ) are not perpendicular to each other and ( vec{r} times vec{p}=vec{q} times vec{p} & vec{r} . vec{s}=0 )
( operatorname{then} vec{r}= )
A ( cdot vec{p} . vec{s} )
В ( cdot vec{q}+left(frac{vec{q} . vec{s}}{vec{p} . vec{s}}right) vec{p} )
c. ( vec{q}-left(frac{vec{q} . vec{s}}{vec{p} . vec{s}}right) vec{p} )
D. ( vec{q}+mu vec{p} ) for all scalars ( mu )
11
52 A boats man finds that he can save 6
( sec ) in crossing a river by quicker path, then by shortest path if the velocity of boat and river be respectively ( 17 mathrm{m} / mathrm{s} ) and ( 8 mathrm{m} / mathrm{s} ), then river width is?
( mathbf{A} cdot 675 mathrm{m} )
B. ( 765 mathrm{m} )
( c .567 mathrm{m} )
D. 657 m
11
53 U
2.11
. J NIC
. 1.J110
41. A ball rolls off the top of a staircase with a horizontal
velocity u ms. If the steps are h metre high and b metre
wide, the ball will hit the edge of the nth step, if
2 2hu
2hu²
a. n=
b. n=
gb
862
d. n=
c. n=2hu?
8b2
. n. hu2
11
54 A body moves in a plane so that the displacements along the ( x ) and ( y ) axes are given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}^{3} ) and ( boldsymbol{y}=mathbf{4} boldsymbol{t}^{3} . ) The
velocity of the body is :
A ( .10 t )
B . 15
( c cdot 15 t^{2} )
D. ( 25 t^{2} )
11
55 Given that ( vec{A} ) and ( vec{B} ) are greater than one, then the magnitude of ( (vec{A} times vec{B}) ) can not be
A . equal to ( overrightarrow{A B} )
B. less than ( vec{B} )
c. more than ( |vec{A}||vec{B}| )
D. equal to ( vec{A} / vec{B} )
11
56 Ship A is located ( 4 k m ) north and ( 3 k m )
east of ship B. Ship A has a velocity of
( 20 mathrm{kmh}^{-1} ) towards the south and ship ( mathrm{E} )
is moving at ( 40 mathrm{kmh}^{-1} ) in a direction
( 37^{circ} ) north of east. ( X ) and ( Y ) axes are along east and north directions, respectively. This question has multiple correct options
A. Velocity of A relative to B is ( -32 hat{i}-44 hat{j} )
B. Position of A relative to B as a function of time is given by ( vec{r}_{A B}=(3-32 t) hat{i}+(4-44 t) hat{j} )
c. Velocity of A relative to B is ( 32 hat{i}-44 hat{j} )
D. Position of A relative to B as a function of time is given by ( (32 t hat{i}-44 t hat{j}) )
11
57 10. A sail boat sails 2 km due east, 5 km 37° south of east, and
finally an unknown displacement. If the final displacement
of the boat from the starting point is 6 km due east,
determine the third displacement.
11
58 At the maximum height of a projectile, the velocity and acceleration are
A. parallel to each other
B. antiparallel to each other
c. perpendicular to each other
D. inclined to each other at ( 45^{circ} )
11
59 You throw a ball which a launch velocity of ( overrightarrow{boldsymbol{v}}=(mathbf{3} hat{boldsymbol{i}}+mathbf{4} hat{boldsymbol{j}}) boldsymbol{m} / boldsymbol{s} ) the maximum
height attaind by the body is?
A. ( 0.8 m )
в. ( 0.2 m )
( mathrm{c} .2 .3 mathrm{m} )
D. ( 5.3 mathrm{m} )
11
60 29
Two tall buildings are 30 m apart. The speed with which
a ball must be thrown horizontally from a window 150 m
above the ground in one building so that it enters a window
27.5 m from the ground in the other building is
a. 2 ms-1 b. 6 ms c. 4 ms 1 d. 8 ms-1
11
61 A particle is travelling in a circular path of radius 4 m. At certain instant the
particle is moving at ( 20 mathrm{m} / mathrm{s} ) and its
acceleration is at an angle of ( 37^{circ} ) from the direction to the centre of the circle
as seen from the particle.
(i) At what rate is the speed of the particle increasing?
(ii) What is the magnitude of the acceleration?
11
62 Find the average velocity of a projectile
between the instants it crosses half the
maximum height. It is projected with a
speed ( u ) at an angle ( theta ) with the horizontal.
11
63 A particle is moving around a circular
path with uniform angular speed ( ( omega ) ) The radius of the circular path is ( (r) )
The acceleration of the particle is:
A ( cdot frac{omega^{2}}{r} )
в. ( frac{omega}{r} )
c. ( v )
D. ( v r )
11
64 10.
10. A particle is projected with a velocity v such that its range
on the horizontal plane is twice the greatest height attained
by it. The range of the projectile is (where g is acceleration
due to gravity)
11
65 Wind is blowing from west to east along two parallel tracks. A train is moving on each track in opposite directions. They have same speed when no wind is blowing. Now, one train has
speed double that of the other. The speed of each train is
A. Equal to that of wind
B. Double that of wind
c. Three times that of wind
D. Half of that of wind
11
66 a. TUJU
ody is projected at an angle of 30° with the horizontal
od with a speed of 30 ms. What is the angle
horizontal after 1.5 s? (g = 10 ms-2)
200 b. 30° c. 60° d. 900
11
67 A wheel, starting from rest, rotates with a uniform angular acceleration of
2rads ( ^{-2} ). The number of rotations it
performs in the tenth second is
( A cdot 3 )
B. 6
( c cdot 9 )
D. 12
11
68 A large rectangular box falls vertically with an acceleration a. A toy gun fixed
at ( A ) and aimed towards 0 fires a
particle P. Which of the following is
false
A. P will hit ( mathrm{C} ) if ( mathrm{a}=mathrm{g} )
B. P will hit the roof BC if a ( >g )
c. P will hit the wall cD if ( a<g )
D. may be either
( (a),(b) ) or
(c), depending on the projection speed of
11
69 Consider an expanding sphere of instantaneous radius ( R ) whose total
mass remains constant. The expansion is such that the instantaneous density
( rho ) remains uniform throughout the
volume. The rate of fractional change in density ( left(frac{1}{rho} frac{d p}{d t}right) ) is constant. The
velocity ( v ) of any point on the surface of
the expanding sphere is proportional to
A ( cdot R^{2 / 3} )
в. ( R )
c. ( R^{3} )
D. ( frac{1}{R} )
11
70 A particle is moving along a circular
path of radius ( 5 m ) with a uniform speed
( 5 m s^{-1} . ) What is the magnitude of average acceleration during the interval in which particle completes half revolution?
11
71 L.
V SM
70
18. A particle is projected with a velocity v so that its
on a horizontal plane is twice the greatest height att
If g is acceleration due to gravity, then its range is
4,2
h
4v
5g-
11
72 The circular motion of a particle with
constant speed is
A. periodic and simple harmonic
B. simple harmonic but not periodic.
c. neither periodic nor simple harmonic.
D. periodic but not simple harmonic.
11
73 A particle moves along a straight line such that its displacement at any time is given by ( s=left(t^{3}-6 t^{2}+3 t+4right) m )
Find the velocity when the acceleration
is zero.
11
74 A ball is thrown upwards. It returns to ground describing a parabolic path.Which of the following remains constant.
A. Speed of the ball
B. Kinetic energy of the ball
c. vertical component of velocity
D. Horizontal component of velocity
11
75 Consider the following two statements A and B and identify the correct option:
A) When a rigid body is rotating about its own axis at a given instant, all particles of body possess same angular velocity
B) When a rigid body is rotating about its own axis, the linear velocity of a particle is directly proportional to its perpendicular distance from axis.
A . A is true but B is false
B. A is false but B is true
c. Both A and B are true
D. Both A and B are false
11
76 A circular disc is rotating about its own
axis at constant angular acceleration. If its angular velocity increases from
210 rpm to 420 rpm during 21 rotations then the angular acceleration of disc is :
A. ( 5.5 mathrm{rad} / mathrm{s}^{2} )
B. 11 rad / ( s^{2} )
c. ( 16.5 mathrm{rad} / mathrm{s}^{2} )
D. 22 rad / ( s^{2} )
11
77 Illustration 4.3 A particle moves from position A to position
B in a path as shown in Fig 4.5. If the position vectors ,
and i, making an angle between them are given, find the
magnitude of displacement.
Fig. 4.5
11
78 A wheel has angular acceleration of ( 3.0 mathrm{rad} / mathrm{s}^{2} ) and an intial angular speed
of 2.00 rad/s. In a time of ( 2 s ) it has rotated through an angle (in radians) of
( mathbf{A} cdot mathbf{6} )
B. 10
c. 12
D.
11
79 U. Noe u ulls
37. A platform is moving upwards with an acceleration of
5 ms. At the moment when its velocity is u=3 ms,
a ball is thrown from it with a speed of 30 ms w.r.l.
platform at an angle of O= 30° with horizontal. The time
taken by the ball to return to the platform is
a. 2s b. 3. c. 15 d. 2.5s us
1
11
80 Associate law of vector addition is
A. The sum of vectors remains same irrespective of their order or grouping in which they are arranged.
B. The sum of vectors is different irrespective of their order or grouping in which they are arranged.
C. The sum of vectors changes with the change of their order or grouping in which they are arranged
D. None of the above
11
81 When a man is standing, rain drops appear to him falling at ( 60^{circ} ) from the
horizontal from his front side. When he
is travelling at ( 5 k m / h ) on a horizontal
road they appear to him falling at ( 30^{circ} ) from the horizontal from his front side.
The actual speed of the rain is ( ( ) in
( boldsymbol{k m} / boldsymbol{h}) )
A . 3
B. 4
c. 5
D. 6
11
82 6. Five equal forces of 10 N each are applied at one point and
all are lying in one plane. If the angles between them are
equal, the resultant force will be
(a) Zero
(b) 10 N
(c) 20 N
(d) 10/2N
11
83 An astronaut, orbiting in a spaceship round the earth, has a centripetal
acceleration of ( 6.67 m / s^{2} . ) Find the
height of the spaceship above the surface of the earth.
( left(G=6.67 times 10^{11} N m^{2} / k g^{2}, ) radius of right.
the earth ( =6400 mathrm{km} )
11
84 u ULUIT OLICI, ull wey Will Conde.
Illustration 5.62 Two particles A and B are moving with
constant velocities y, and vs. At t=0, v, makes an angle 8
with the line joining A and B and v, makes an angle e2 with
the line joining A and B.
10,
Fig. 5.127
a. Find the condition for A and B to collide.
b. Find the time after which A and B will collide if separation
between them is dat t = 0
11
85 State whether the given statement is True or False :

The earth moves around the sun with a
uniform velocity.
A. True
B. False

11
86 22. In the above problem, what is the angle of projection was
horizontal?
a. tan-(1/4).
b. tan-‘(4/3)
c. tan-+(3/4)
d. tan-(1/2)
11
87 From point ( A ) located on a highway, one
has to get by a car as soon as possible to point ( B ) located in the field at a
distance ( l ) from point ( D . ) If the car
moves ( n ) times slower in the field, at
what distance ( x ) from ( D ) one must turn
off the highway.
A ( cdot x=frac{l}{sqrt{n^{3}-1}} )
B. ( x=frac{l}{sqrt{n^{2}-1}} )
c. ( _{x}=frac{l}{sqrt{n^{3}-2}} )
D. ( x=frac{l}{sqrt{n^{2}-2}} )
11
88 Position vector of a particle is given by ( vec{r}=a cos omega t hat{i}+a sin omega t hat{j} . ) Which of the
following is/are true? This question has multiple correct options
A. velocity vector is parallel to position vector
B. velocity vector is perpendicular to position vector
c. acceleration vector is directed towards the origin
D. acceleration vector is directed away from the origin
11
89 Q Type your question
a wall. The jeep has to take a sharp
perpendicular turn along the wall. A rocket flying at uniform speed of 100kmh ( ^{-1} ) starts from the wall towards
the jeep which is ( 30 k m ) away. The
rocket reaches the windscreen and
returns to wall. Total distance covered
by the rocket is
A . ( 100 k m )
( mathbf{B} .50 k m )
( c .37 k m )
D. ( 75 k )
11
90 A particle is projected with a velocity
making an angle ( theta ) with the horizontal.
What is the radius of curvature of the
parabola where the particle makes an angle ( theta ) /2 with the horizontal?
11
91 A block is moving in a circular path at constant speed. Which of the following statements is/are true?
I. The velocity is constant.
II. The direction of motion is constant.
III. The magnitude of velocity is constant.
A. II only
B. I and III only
c. ॥ and III only
D. I and II only
E. III only
11
92 An object ( A ) is kept fixed at the point ( x=3 m ) and ( y=1.25 m ) on a plank ( P )
raised above the ground. At time ( t= ) the plank starts moving along the positive ( x ) -direction with an acceleration
( 1.5 m / s^{2} . ) At the same instant a stone is projected from the origin with a velocity
( vec{u} ) as shown in the figure. A stationary person on the ground observes the
stone hitting the object during which it makes a downwards motion at the
angle of ( 45^{circ} ) to the horizontal. All the
motions are in ( x ) -y plane. Find ( vec{u} ) and the time after which the stone hits the
object (Take ( boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2} mathbf{)} )
11
93 Consider the motion of a particle
described by ( x=a cos t, y=a sin t ) and
( z=t . ) The trajectory traced by the
particle as a function of time is
A. Helix
B. Circular
c. Elliptical
D. Straight line
11
94 Three bodies are projected in three different ways: a) vertically up b) vertically down c) horizontally, with same speed from top of a tower. The time taken by the bodies to reach the ground in increasing order would be:
( mathbf{A} cdot t_{b}<t_{a}<t_{c} )
в. ( t_{c}<t_{a}<t_{b} )
c. ( t_{b}<t_{c}<t_{a} )
D ( cdot t_{a}<t_{b}<t_{c} )
11
95 Resultant of two vectors ( vec{P} ) and ( vec{Q} ) is
inclined at ( 45^{circ} ) to either of them. What
is the magnitude of the resultant?
( mathbf{A} cdot sqrt{P^{2}+Q^{2}} )
B . ( sqrt{P^{2}-Q^{2}} )
( c cdot P+Q )
D. ( P-Q )
11
96 A particle is projected up with an initial velocity of 80 the ball will be at a height of 96 from the ground after 11
97 A body moving in circular motion with constant speed has:
A. constant velocity
B. constant acceleration
c. constant kinetic energy
D. constant displacement
11
98 Example 5.7 A moves with constant velocity u along then
x-axis. B always has velocity towards A. After how much
time will B meet A if B moves with constant speed V? What
distance will be travelled by A and B?
JAU
Fig. 5.183
11
99 A person standing near the edge of the top of a building throws two balls ( A ) and
B. The ball ( A ) is thrown vertically
upward and ( B ) is thrown vertically downward with the same speed. The ball
( A ) hits the ground with a speed ( v_{A} ) and
the ball ( B ) hits the ground with a speed
( boldsymbol{v}_{B} . ) We have:
В . ( v_{A}<v_{B} )
c. ( v_{A}=v_{B} )
D. the relation between ( v_{a} ) and ( v_{b} ) depends on height of the building above the ground
11
100 Propeller blades in aeroplane are ( 2 mathrm{m} )
long. When propeller is rotating at 1800 rev/min, compute the tangential velocity of tip of the blade.
11
101 6. The speed of rain with respect to the moving man is
a. 0.5 ms
b. 1.0 ms?
c. 0.5 13 ms -1 d. 0.45 ms-1
11
102 Illustration 3.22 A bird moves with velocity 20 ms in a
direction making an angle of 60° with the eastern line and
60° with vertical upward. Represent the velocity vector in
rectangular form.
11
103 Uniform linear motion is a/an
motion while uniform
circular motion is a/an
motion.
A . accelerated, non accelerated
B. non accelerated, accelerated
c. deviated, retarded
D. uniform, retarded
11
104 9. The time taken for the displacement vectors of two bodies
to be come perpendicular to each other is
a. 0.1s b. 0.2 s c. 0.8 s d. 0.6 s
11
105 A particle of mass ( 1 mathrm{gm} ) and charge ( 1 mu C ) is held at rest on a frictionless horizontal surface at distance ( 1 mathrm{m} ) from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of
( 10 mathrm{m} ) from the fixed charge
A ( cdot 60 m s^{-1} )
B. ( 100 mathrm{ms}^{-1} )
c. ( 90 m s^{-1} )
D. ( 180 mathrm{ms}^{-1} )
11
106 The resultant of two forces which
are equal in magnitude is equal to either of two vectors in magnitude. Find
the angle between the forces.
A .60
B . 45
( c cdot 90 )
D. ( 120^{circ} )
11
107 An object is thrown between two tall
buildings ( 180 mathrm{m} ) from each other. The
object thrown horizontally from a
window ( 55 mathrm{m} ) above the ground from one
building strikes a window ( 10 mathrm{m} ) above the tom ground in another building.
Find out the speed of projection.
A. 60
B. 80
( c .70 )
D. 90
11
108 A particle of mass ( mathrm{m} ) is moving in a
circular path of constant radius r such
that its centripetal acceleration ( a_{c} ) is
varying with time ( t ) as ( a_{c}=k^{2} r t^{2} ) where
( k ) is a constant. The power delivered to the particle by the forces acting on it, is?
A. zero
B. ( m k^{2} r^{2} t^{2} )
( mathbf{c} cdot m k^{2} r^{2} t )
( mathbf{D} cdot m k^{2} r t )
11
109 3. Statement I: If the string of an oscillating simple
pendulum is cut, when the bob is at the mean position,
the bob falls along a parabolic path.
Statement II: The bob possesses horizontal velocity at
the mean position.
11
110 9. A stone is projected from the ground with velocity 50 m
at an angle of 30°. It crosses a wall after 3 sec. How far
beyond the wall the stone will strike the ground (g = 10
m/sec)?
(a) 90.2 m
(b) 89.6 m
(c) 86.6 m
(d) 70.2 m
10 portiola in
woh that its range
11
111 2.
00
0.
00
*
15. If the helicopter flies at constant velocity, find the x
y coordinates of the location of the helicopter when the
package lands.
a. 160 m, 320 m b. 100 m, 200 m
c. 200 m, 400 m
d. 50 m, 100 m
11
112 A particle moves with constant speed ( v ) along a regular hexagon ABCDEF in the same order. Then the magnitude of the velocity for its motion from A to This question has multiple correct options
( mathbf{A} cdot_{F} ) is ( frac{v}{5} )
B ( cdot ) D is ( frac{v}{3} )
c. ( quad mathrm{c} ) is ( frac{v sqrt{3}}{2} )
D. B is ( v )
11
113 6. A particle is moving in xy-plane with y = x/2 and
v=4-2t. Choose the correct options.
a. Initial velocities in x and y directions are negative
b. Initial velocities in x and y directions are positive
c. Motion is first retarded, then accelerated.
d. Motion is first accelerated, then retarded.
11
114 If the length of second’s hand of a clock
is ( 10 mathrm{cm}, ) the speed of its tip ( left(text { in } mathrm{cm} mathrm{s}^{-1}right) )
is nearly
( A cdot 2 )
в. 0.5
c. 1.5
D.
11
115 Illustration 5.45
stion 5.45 A man can swim at the rate of 5 kmh in
ater. A 1-km wide river flows at the rate of 3 kmh.
e man wishes to swim across the river directly opposite to
the starting point.
Along what direction must the man swim?
b. What should be his resultant velocity?
How much time will he take to cross the river?
11
116 Illustration 3.4 Two forces whose magnitudes are in the ratio
3: 5 give a resultant of 28 N. If the angle of their inclination
is 60°, find the magnitude of each force.
11
117 A particle of mass ( 5 g ) is moving in a
circle of radius ( 0.5 m ) with an angular
velocity of 6 rad( / )s. Find
(i) the change
in linear momentum in half a revolution
(ii) the magnitude of the acceleration of the particle.
11
118 JUL, 2011)
2. Airplanes A and B are flying with constant velocity in the
same vertical plane at angles 30° and 60° with respect to
the horizontal respectively as shown in the figure. The
speed of A is 1003 ms. At time t = 0 s, an observer
in A finds B at a distance of 500 m. This observer sees B
moving with a constant velocity perpendicular to the line
of motion of A. If a t = to, A just escapes being hit by B,
to in seconds is
130°
60°
Fig. A.55
(JEE Advanced, 2014)
11
119 Illustration 3.27 A bob of weight 3 N is in equilibrium under
the action of two strings 1 and 2 (Fig. 3.52). Find the tension
forces in the strings.
LLLLLLL
30.12
ITTI7777
3N
Fig. 3.52
11
120 Three force ( overrightarrow{boldsymbol{p}}, overrightarrow{boldsymbol{Q}} ) and ( quad overrightarrow{boldsymbol{R}} ) acting
with TA,IB,IC where I is the incentance of
( triangle A B C ) are in equim ( vec{P}_{Q}, quad_{R} )
is
11
121 the two balls will collide at time ( t= )
( A cdot 2 s )
В. 5 s
( c .10 s )
( 0.3 s )
11
122 How long does it stay in the air (in s)?
A . 37
в. 37.1
( c .36 )
D. 35 5
11
123 A ball is moving uniformly in a circular path of radius ( 1 m ) with a time period of
1.5 ( s ). If the ball is suddenly stopped at
( t=8.3 s, ) the magnitude of the
displacement of the ball with respect to
its position at ( t=0 s ) is closest to:
( mathbf{A} cdot 1 m )
в. 33 т
( c .3 m )
D. ( 2 m )
11
124 For the displacement-time graph shown
in the figure above, find the velocity at
point ( mathbf{A} )
A. ( 4 mathrm{m} mathrm{s}^{-1} )
B. 3 ( mathrm{m} ) s ( ^{-1} )
( c cdot 5 m s^{-} )
D. ( 6 mathrm{m} ) s ( ^{-1} )
11
125 Ring of radius ( R ) rotating about axis of ring such that angular velocity is given as omega ( =5 t . ) Find acceleration of a
point ( boldsymbol{P} ) on rim after ( mathbf{5} ) sec?
( mathbf{A} cdot 5 R )
в. 25 В
c. ( sqrt{650} R )
D. None of these
11
126 A merry go round has a radius of ( 4 m )
and completes a revolution in 2 s. Then
acceleration of a point on its rim will be:
( mathbf{A} cdot 4 pi^{2} )
В . ( 2 pi^{2} )
( mathbf{c} cdot pi^{2} )
D. zero
11
127 If a boat can travel with a speed of ( v ) in
still water, which of the following trips will take the least amount of time?
A. travelling a distance of ( 2 d ) in still water.
B. travelling a distance of ( 2 d ) across (perpendicular to) the current w.r.t. in a stream
C. travelling a distance ( d ) downstream and returning a distance ( d ) upstream
D. travelling a distance ( d ) upstream and returning a distance ( d ) downstream
11
128 The distance between the point ( P(x, y, z) ) and plane ( x z ) is :
A . ( x )
B. ( y )
( c )
D. ( x y )
11
129 A policeman on duty detects a drop of ( 10 % ) in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is ( 330 m / s, ) the speed of the car
will be
( mathbf{A} cdot 36.7 m / )sec
в. ( 17.3 mathrm{m} / mathrm{sec} )
( mathbf{c} .25 mathrm{m} / mathrm{sec} )
D. ( 27 mathrm{m} / mathrm{sec} )
11
130 In the absence of air resistance, a ball
thrown horizontally from a tower with velocity v, will land after time T seconds.
If, however, air resistance is taken into account, which statement is correct?
A. The ball lands with a horizontal velocity less than v after more than T seconds
B. The ball lands with a horizontal velocity less than v after T seconds
c. The ball lands with a horizontal velocity v after more than ( T ) seconds
D. The ball lands with a horizontal velocity v after seconds
11
131 Assertion
In circular motion work done by all the
forces acting on the body is zero.
Reason

Centripetal force and velocity are
mutually perpendicular.
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
132 ( sum_{k}^{i} ) 11
133 U sllele on IS POSiuve.
8. A small ball is projected along the surface of a smooth
inclined plane with speed 10 ms’ along the direction
shown at t = 0. The point of projection is origin, z-axis
is along vertical. The acceleration due to gravity is
10 ms?
Az-axis
10,
379
x-axis
Fig. A.41
Column I lists the values of certain parameters related to
motion of ball and Column II lists different time instants.
Match appropriately.
Column I
Column II
i. Distance from x-axis is a. 0,5 s
2.25 m
Speed is minimum b. 1.0 s
iii. Velocity makes angle c. 1.5 s
37° with x-axis
d. 2.0s
11
134 Illustration 3.23 A particle is initially at point A(2, 4, 6) m
moves finally to the point B(3, 2, -3) m. Write the initial
position vector, final position vector, and displacement vector
of the particle.
11
135 In the given figure, velocity of the body
at ( A ) is
A. Zero
B. Unity
c. Maximum
D. Infinite
11
136 Illustration 5.11 Figure 5.11 shows two positions A and B at
the same height h above the ground. If the maximum height of
the projectile is H, then determine the time t elapsed between
the positions A and B in terms of H.
|(H-h)
Fig. 5.11
11
137 A body moves in a circle covers equal distance in equal intervals of time.
Which of the following remains
constant
A. Velocity
B. Acceleration
c. speed
D. Displacement
11
138 Starting from rest the fly wheel of a motor attains an angular velocity of ( 60 r a d / s ) in ( 5 s, ) the angular acceleration of the fly wheel is:
A ( cdot 6 ) rad/s( ^{2} )
B. 12 rad / ( s^{2} )
C ( .300 mathrm{rad} / mathrm{s}^{2} )
D. 150 rad/s( ^{2} )
11
139 Sol. When the stone is released, it moves down executing a
circular motion. At any instant, the stone accelerates towards
(w.r.t.) the center of its revolution 0, that is, centripetal
acceleration a, and simultaneously accelerates down with an
acceleration, that is, gravitational acceleration g; ā, = 0ʻr.
Resolving ä, and along the tangent, we obtain the tangential
acceleration of the stone as a,=g cos e.
(tangent)
g cos e
Fig. 5.151
Angular acceleration, a=“,
8 cos e
=
a=
(since r = 1)
w do
do
-, we obtain @do_8 cos
Putting a= 0
der
= @do=(g/l) cos e do.
Integrating both the sides, we obtain
jo do 4 jcose do
* = sine or o = V1 sin e
Putting 1 = 1 m and 6 = 30°, we obtain
2(10) sin 30°
-= V10 = @=3.1 rads-1
V
W
=
11
140



5. All the particles thrown with same initial velocity would
strike the ground.
By 1,
a. with same speed
b. simultaneously
c. time would be least for the
particle thrown with velocity v
downward i.e., particle 1
d. time would be maximum for the F
11
141 A jet of water is projected at an angle
( theta=45^{circ} ) with horizontal from point ( A )
which is situated at a distance ( x=O A )
( =(a) 1 / 2 m,(b) 2 m ) from a vertical wall.
If the speed of projection is ( v_{0}= )
( sqrt{10} m s^{-1}, ) find point ( P ) of striking of
the water jet with the vertical wall.
11
142 How many minimum number of
coplanar vectors which represent same physical quantity having different magnitudes can be added to give zero
resultant.
A . (A) 2
в. (В) 3
( c cdot(c) 4 )
D. (D) 5
11
143 If a body is projected with certain
velocity making an angle ( 30^{circ} ) with the horizontal, then
A. its horizontal velocity remains constant
B. its vertical velocity changes
c. on falling to the ground its vertical displacement is zero
D. All of the above
11
144 A car traveled the total distance of ( x ) in three equal intervals, first at a speed of ( 10 mathrm{km} / mathrm{h} . ) The second at a speed of 20 ( mathrm{km} / mathrm{h} ) and the last third at a speed of 60 km/h. Determine the average speed of the car over the entire distance ( x ) 11
145 A point moves along a circle with a velocity ( boldsymbol{v}=boldsymbol{a} boldsymbol{t}, ) where ( boldsymbol{a}=mathbf{0 . 5 0} boldsymbol{m} / boldsymbol{s}^{2} )
The total acceleration of the point at the moment when it covered the ( n^{t h}(n= )
0.10) fraction of the circle after the
beginning of motion in ( m / s^{2} ) is ( frac{x}{10} . ) Find
( mathcal{L} )
11
146 A body of mass ( 5 k g ) under the action of constant force ( overrightarrow{boldsymbol{F}}=boldsymbol{F}_{boldsymbol{x}} hat{boldsymbol{i}}+boldsymbol{F}_{boldsymbol{y}} hat{boldsymbol{j}} ) has
velocity at ( t=0 s ) as ( vec{v}=(6 hat{i}-2 hat{j}) m / s ) and ( operatorname{at} t=10 s ) as ( vec{v}=+6 hat{j} m / s . ) The
force ( overrightarrow{boldsymbol{F}} ) is:
A ( cdot(-3 hat{i}+4 hat{j}) N )
В ( cdotleft(-frac{3}{5} hat{i}+frac{4}{5} hat{j}right) N )
c. ( (3 hat{i}-4 hat{j}) N )
D ( cdotleft(frac{3}{5} hat{i}-frac{4}{5} hat{j}right) N )
11
147 OABC is a current carrying square loop
an electron is projected from the centre
of loop along its diagonal ( A C ) as shown.
Unit vector in the direction of initial
acceleration will be
( A cdot hat{k} )
B. ( -left(frac{hat{i}+hat{j}}{sqrt{2}}right) )
( c .-hat{k} )
( frac{hat{i}+hat{j}}{sqrt{2}} )
11
148 Hence, digIC VIWA
UNU D-70
T
-luv
Illustration 3.6 Two forces of unequal magnitude
simultaneously act on a particle making an angle e(=120°)
with each other. If one of them is reversed, the acceleration
of the particle is becomes 13 times. Calculate the ratio of
the magnitude of the forces.
11
149 A uniform sphere of mass ( M ) and radius ( R ) is placed on a smooth horizontal ground. The angular acceleration of sphere if force ( boldsymbol{F} ) is
applied on it at a distance ( 7 frac{R}{5} ) from
ground level is
( ^{mathrm{A}} cdot frac{F}{2 M R} )
в. ( frac{F}{M R} )
c. ( frac{F R}{M} )
D. ( frac{2 F}{M R} )
11
150 If a particle moves with an acceleration, then which of the following can remains
constant
A. Both speed and velocity
B. Neither speed nor velocity
c. only the velocity
D. Only the speed
11
151 14. A river flows with a speed more than the maximum spec
with which a person can swim in still water. He intends to
cross the river by the shortest possible path (i.e., he wants
to reach the point on the opposite bank which directly
opposite to the starting point). Which of the following is
correct?
a. He should start normal to the river bank.
b. He should start in such a way that he moves normal
to the bank, relative to the bank.
c. He should start in a particular (calculated) direction
making an obtuse angle with the direction of water
current.
d. The man cannot cross the river in that way.
n. 11 .-
1
.11.
1
11
152 How far will the car have traveled in the
time? (in km)
( mathbf{A} cdot mathbf{6} )
B. 6.75
c. 7.75
D. 8.75
11
153 A man running along a straight road with uniform velocity ( vec{u}=u hat{i} ) feels that
the rain is falling vertically down along ( -hat{boldsymbol{j}} ). If he doubles his speed,he finds that
the rain is coming at an angle ( theta ) with the vertical. The velocity of the rain with respect to the ground is :
A ( . u i-u tan theta hat{j} )
B. ( u i-frac{u}{tan theta} )
c. ( u tan theta-u vec{j} )
D. ( frac{u}{tan theta} vec{i}-u vec{j} )
11
154 An aeroplane moving horizontally at 20
( mathrm{ms}^{-1} ) drops a bag. What is the displacement of the bag after 5 seconds ? Give
( left(g=10 mathrm{ms}^{-2}right) )
11
155 Example 2.3 Two particles, 1 and 2
move with constant velocities v, and V2
along two mutually perpendicular straight
lines towards the intersection point 0. At
the moment t=0 the particles were located
at the distance l, and l from the point O.
How soon will the distance between the
particles become the smallest? What is it
equal to?
Fig. 2.42
11
156 Height of the cliff is
( A cdot 20 m )
B. 10 ( m )
( c cdot 15 m )
D. 30 ( m )
11
157 11. An aircraft moving with a speed of 1000 km/h is at a
height of 6000 m, just overhead of an anti-aircraft gun. If
the muzzle velocity of the gun is 540 m/s, the firing angle
for the bullet to hit the aircraft should be
972 km/h
Vo = 540 m/s
6000 m
TITUTI
(a) 730
(6) 30°
(c) 60°
(d) 45°
11
158 A man standing on the road has to ho!d his umbrella at ( 30^{circ} ) with the vertical to
keep the rain away. He throws the umbrella and starts running at 10 k ( m / h r . ) He find that rain drops are
hitting his head vertically, then the speed of the rain drops with respect to moving man.
A. ( 20 k m / h r )
в. ( 10 sqrt{3} k m / h r )
c. ( frac{10}{sqrt{3}} k m / h r )
D. ( 10 k m / h r )
11
159 a. 41J
cal plane is
distances of the
59. The trajectory of a projectile in a vertical pl
y = ax – bx”, where a and b are constants and
are, respectively, horizontal and vertical distances
projectile from the point of projection. The maxim
height attained by the particle and the angle of project
from the horizontal are
62
a.
-, tan (b)
b.
, tan- (26)
a tan- (a)
do 2a tan(a)
11
160 A projectile is fired horizontally with a speed of ( 98 m s^{-1} ) from the top of a hill
( 490 m ) high. Find the magnitude of
vertical velocity with which the projectile hits the ground. (Take ( boldsymbol{g}= )
( left.9.8 m / s^{2}right) )
A ( cdot 98 m s^{-1} )
B. ( 40 mathrm{ms}^{-1} )
c. ( 116 mathrm{ms}^{-1} )
D. ( 196 mathrm{ms}^{-1} )
11
161 *
VE WCSc.
2. Given two vectors Ā== 3î + 4ſ and B == i + j. O is
the angle between A and B. Which of the following
statements is/are correct?
i tj
is the component of Ā along B.
is the component of A perpendicular
b. |ālsino (2 is the component of Ă perpendicular
c. alcoso ( 2 ) is the component of à along B.
to
B
1
+
d. Ä sin
is the component of Ā perpendicular
to B.
11
162 n
Illustration 5.8 Two particles A and B are proie
ome point in different directions in such a manner
hot vertical components of their initial velocities are same
(Fig. 5.8). Find the ratio of range.
YA
Fig. 5.8
11
163 illustration 5.74 Find the angular velocity of A with respect
to B in Fig. 5.156.
Fig. 5.156
11
164 A car ( A ) is going north-east at ( 80 mathrm{km} / mathrm{h} ) and another car ( B ) is going south-east at
( 60 mathrm{km} / mathrm{h} . ) Then the direction of the velocity
of ( A ) relative to ( B ) makes with the north
an ( alpha ) angle such that ( tan alpha ) is :
A ( cdot frac{1}{7} )
B. ( frac{3}{4} )
( c cdot frac{4}{3} )
D. ( frac{3}{5} )
11
165 Illustration 5.7 A bullet with muzzle velocity 100 m 1.
to be shot at a target 30 m away in the same horizontal li
How high above the target must the rifle be aimed so that
bullet will hit the target?
30 m
Target
Fig. 5.7
11
166 Which of the following motions is different from the rest?
A. a ball thrown horizontally in air
B. a bomb released from a flying aeroplane
c. a javelin thrown by an athlete
D. a bird flying in the air
11
167 17. To a man going with a speed of 5 ms, rain appears to
be falling vertically. If the actual speed of rain is 10 ms,
then what is the angle made by rain with the vertical?

1
11
168 A mass m rotates in a vertical circle of
radius, ( R ) and has a circular speed ( v_{c} ) at the top.- If the radius of the circle is increased by a factor of ( 4, ) circular speed at the top will be
A. decreased by a factor of 2
B. decreased by a factor of 4.
c. increased by a factor of 2
D. increased by a factor of 4
11
169 Consider the diagram of the trajectory
of a thrown tomato. At what point is the
kinetic energy least?
11
170 A gun fires a bullet. the barrel of the gun
is inclined at an angle of ( 45^{circ} ) with horizontal. when the bullet leaves the
barrel it will be travelling at an angle greater than ( 45^{circ} ) with horizontal.
A. True
B. False
11
171 If y denotes the displacement and t denote the time and the displacement is given by ( y=a sin t, ) the velocity of the particle is- 11
172 Illustration 5.43 A truck is moving with a constant velocity
of 54 kmh. In what direction should a stone be projected
up with a velocity of 20 ms, from the floor of the truck, so
as to appear at right angles to the truck, for a person standing
on earth?
v = 20 ms?
u= 15 ms
Fig. 5.83
11
173 An old man and a boy are walking
towards
each other and a bird is flying over them as shown in the figure. Find the
velocity of bird as seen by the boy.
A ( .12 hat{j} )
B. ( 16 hat{j} )
( c .-12 hat{j} )
D. ( -16 hat{j} )
11
174 The resultant of two forces, one double
the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:
A ( cdot 120^{circ} )
B . 135
( c .90^{circ} )
D. ( 150^{circ} )
11
175 In a uniform circular motion, the angle
between the velocity and acceleration is
( mathbf{A} cdot mathbf{0} )
B . ( 45^{circ} )
( c cdot 60^{circ} )
D. ( 75^{circ} )
E ( .90^{circ} )
11
176 If the sum of two unit vector is a unit
vector, then the magnitude of their difference is:
A. ( sqrt{3} )
B. ( sqrt{2} )
c. ( sqrt{5} )
D. ( frac{1}{sqrt{2}} )
11
177 Two uniform solid cylinders A and B each of mass 1 kg
are connected by a spring of constant 200 Nm at their
axles and are placed on a fixed wedge as shown in the Fig.
6.325. There is no friction between cylinders and wedge.
The angle made by the line AB with the horizontal, in
equilibrium, is
A Moto B
160°
30°
a. 0°
c. 30°
Fig. 6.325
b. 15°
d. None of these
11
178 The velocity of a particle is ( boldsymbol{v}=boldsymbol{v}_{0}+ )
( g t+f t^{2} . ) If its position is ( x=0 ) at ( t=0 )
then its displacement after unit time ( (t=1) ) is
A ( cdot v_{0}+2 g+3 f )
в. ( v_{0}+frac{g}{2}+frac{f}{3} )
( mathbf{c} cdot v_{0}+g+f )
D. ( v_{0}+frac{g}{2}+f )
11
179 tilustration 5.70 The tangential acceleration of a particle
moving in a circular path of radius 5 cm is 2 ms. The angular
velocity of the particle increases from 10 rad s-to 20 rads-
during some time. Find
a. this duration of time and
b. the number of revolutions completed during this time.
11
180 If ( boldsymbol{v}_{1} sin boldsymbol{theta}_{1}=boldsymbol{v}_{2} sin theta_{2}, ) then choose the
incorrect statement
A. The time of flight of both the particles will be same
B. The maximum height attained by the particles will be same
C. The trajectory of one with respect to another will be a horizontal straight line
D. None of these
11
181 Tu possible in this case
Two particles are projected simultaneously from the same
pint with the same speed, in the same vertical plane,
and at different angles with the horizontal in a uniform
gravitational field acting vertically downwards. A frame
of reference is fixed to one particle. The position vector
of the other particle, as observed from this frame, is 7.
Which of the following statements is correct?
a. r is a constant vector.
b. ř changes in magnitude as well as direction with
time.
c. The magnitude of r increases linearly with time; its
direction does not change.
d. The direction of r changes with time; its magnitude
may or may not change, depending on the angles of
projection.
11
182 CLIOL O NUUSUTIS WILT WU sono
26. A particle is projected from point A to hit an apple as
shown in Fig. 5.195. The particle is directly aimed at
the apple. Show that particle will not hit the apple. Now
show that if the string with which the apple is hung is cut
at the time of firing the particle, then the particle will hit
the apple.
Apple
Fig. 5.195
11
183 A person reaches a point directly opposite on the other bank of a river. The velocity of the water in the river is ( 4 m s^{-1} ) and the velocity of the person in
still water is ( 5 m s^{-1} ). If the width of the
river is ( 84.6 ~ m, ) time taken to cross the
river in seconds is:
A . 9.4
B. 2
c. 84.6
D. 28.2
11
184 The moment of the force, ( overrightarrow{boldsymbol{F}}=mathbf{4} hat{mathbf{i}}+ )
( 5 hat{j}-6 hat{k} ) at (2,0,-3) about the point
( (2,-2,-2), ) is given by
( mathbf{A} cdot-8 hat{i}-4 hat{j}-7 hat{k} )
B . ( -4 hat{i}-hat{j}-8 hat{k} )
( mathbf{c} .-7 hat{i}-8 hat{j}-4 hat{k} )
D. ( -7 hat{i}-4 hat{j}-8 hat{k} )
11
185 A ship moves at ( 40 mathrm{kmph} ) due north and
suddenly moves towards east through
( 90^{0} ) and continues to move with the
same speed. Then the change in velocity
is
A. zero
B. 40 kmph North East
c. ( 40 mathrm{kmph} ) south west
D. ( 40 sqrt{2} ) kmph south East
11
186 Two boys enter a running escalator on the ground floor in a shopping mall and they do some fun on it. The first boy
repeatedly follows ( p_{1}=1 ) step up and
then ( q_{1}=2 ) steps down whereas the
second boy repeatedly follows ( p_{2}=2 )
steps up and then ( q_{2}=1 ) step down.
Both of them move relative to escalator
with speed ( v_{r}=50 c m s^{-1} . ) If the first
boy takes ( t_{1}=250 s ) and the second boy
( operatorname{takes} t_{2}=50 s ) to reach the first floor
how fast is the escalator running?
11
187 A particle is revolving in a circular path
of radius ( 200 m ) at a speed of ( 20 m / s . ) lts speed is increasing at the rate of ( sqrt{5} m / s^{2} . ) Its acceleration is
( mathbf{A} cdot 2 m / s^{2} )
В. ( sqrt{7} m / s^{2} )
c. ( 3 m / s^{2} )
D. ( sqrt{5} m / s^{2} )
11
188 A particle at ( x=0 ) and ( t=0 ) starts
moving along +ve X-direction with velocity v then x varies with time as?
( mathbf{A} cdot mathbf{t} )
в. ( t^{3} )
( c cdot t^{2} )
D. ( t^{1 / 2} )
11
189 Snow is falling vertically at a constant speed of ( 8.0 mathrm{m} / mathrm{s} . ) At what angle from the
vertical do the snowflakes appear to be
falling as viewed by the driver of a car travelling on a straight, level road with a speed of ( 50 mathrm{km} / mathrm{h} ) ?
11
190 A gun fires two bullets at ( 60^{circ} ) and ( 30^{circ} )
with the horizontal the bullets strike att
same horizontal distance. The
maximum heights for the two bullets are in the ratio
A .2: 1
B. 3: 1
c. 4: 1
D. 1: 1
11
191 Out of the following set of forces, the resultant of which
cannot be zero?
a. 10, 10, 10
b. 10, 10, 20
c. 10, 20, 20
d. 10, 20, 40
11
192 If position vector of a point varies with time ” ( boldsymbol{t}^{prime prime} ) as ( overrightarrow{boldsymbol{r}}=left(boldsymbol{t}+boldsymbol{t}^{2}right)(hat{boldsymbol{i}}+hat{boldsymbol{j}}) ) meter
then velocity at time ( t=4 s ) will be
A ( cdot(6 hat{i}+6 hat{j}) m / s )
B . ( (6 hat{i}+9 hat{j}) m / s )
c. ( (9 hat{i}+6 hat{j}) m / s )
D. ( (9 hat{i}+9 hat{j}) m / s )
11
193 Magnitude of vector ( hat{boldsymbol{i}}-hat{boldsymbol{j}} )
( mathbf{A} cdot mathbf{0} )
B. ( sqrt{2} )
c. 1
D. 2
11
194 22. A body A is thrown vertically upwards with such a velocity
that it reaches a maximum height of h. Simultaneously,
another body B is dropped from height h. It strikes the
ground and does not rebound. The velocity of A relative
to B versus time graph is best represented by (upward
direction is positive)
a.
VABN
VAB
VAB
11
195 A car travels 1000 meters north and the
1000 meters south. The entire trip takes
200 seconds. What is the car’s average velocity for the trip?
A. ( 10 mathrm{m} / mathrm{s} )
в. ( 20 mathrm{m} / mathrm{s} )
c. ( 100 m / s )
D. ( 200,000 mathrm{m} / mathrm{s} )
E . ( 0 m / s )
11
196 11. An object has velocity v w.r.t. ground. An observer
moving with constant velocity vo W.r.t.ground measures
the velocity of the object as 72. The magnitudes of three
velocities are related by
a. Vo ? 1 + v2
b. V SV2 + Vo
c. 12 2 11+ Vo
d. All of the above
11
197 31. Shortest distance between them subsequently is
a. 18 m b. 15 m c. 25 m d. 8m
11
198 nan wants to swim in a river from A to
ack from B to A always following line AB (Fig. 5.94).
n points A and B is S. The velocity of the
nt v is constant over the entire width of the river.
AB makes an angle a with the direction of current.
man moves with velocity u at angle B to the line AB. Ine
man swim to cover distance AB and back, find the time
to complete the journey.
Illustration 5.50 A man wants to swim in
B and back from B to A always foll
The distance between points A and B is S. The vel
river current v is constant over the
The line AB makes an angle
Fig. 5.94
11
199 A ball is thrown from a point on ground at some angle of projection. At the time a bird starts from a point directly above
this point of projection at a height ( h ) horizontally with speed ( u ). Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes:
( sqrt[4]{2 u} sqrt{frac{h}{g}} )
в. ( u sqrt{frac{2 h}{g}} )
c. ( 2 u sqrt{frac{2 h}{g}} )
( u sqrt{frac{h}{g}} )
11
200 A man can swim with a speed of 4.0 ( k m / h r ) in still water. How long does
he take to cross a river ( 1.0 mathrm{km} ) wide, if
the river flows steadily at ( 3.0 mathrm{km} / mathrm{hr} ) and he makes his strokes normal to the
river current? How far down the river
does he go, when he reaches the other bank?
11
201 I
SOUVvE ou CIVIL
8. A person goes 10 km north and 20 km east. What will be
displacement from initial point?
(a) 22.36 km
(b) 2 km
(c) 5 km
(d) 20 km
11
202 If ( vec{a}=hat{i}+2 hat{j}+2 hat{k} ) and ( vec{b}=3 hat{i}+6 hat{j}+ )
( 2 hat{k}, ) then a vector in the direction of ( vec{a} )
and having magnitude as ( |vec{b}| ) is
A ( cdot 7(hat{i}+hat{j}+hat{k}) )
B ( cdot frac{7}{3}(hat{i}+2 hat{j}+2 hat{k}) )
c. ( frac{7}{9}(hat{i}+2 hat{j}+2 hat{k}) )
D. none of these
11
203 It is possible for a body to move in a circular path with uniform speed as
long as it is travelling
A. equal distances in equal interval of time
B. unequal distances in unequal interval of time
c. equal distances in unequal interval of time
D. unequal distances in equal interval of time
11
204 46. The sum of the magnitudes of two forces acting at a point
is 16 N. The resultant of these forces is perpendicular to
the smaller force and has a magnitude of 8 N. If the smaller
force is of magnitude x, then the value of x is
a. 2N b. 4N C. 6N d. 7 N
11
205 A body moving in a circular path with constant speed is an accelerated
motion. Why?
11
206 Define uniform circular motion. A
particle is travelling in a circle of diameter ( 15 m ). Calculate the distance
covered and the displacement when it completes two rounds.
11
207 Mark the following statement is true or
false.

A ball thrown vertically up takes more
time to go up than to come down.

11
208 Which of the following quantity remains constant in a uniform circular motion?
A. velocity
B. speedd
c. both velocity and speed
D. none of these
11
209 Wind is blowing west to east along two parallel tracks. Two trains moving with same speed in opposite directions have the relative velocity with respect to wind in the ratio ( 1: 2 . ) The speed of each train
is
A. equal to that of wind
B. double that of wind
c. three times that of wind
D. half that of wind
11
210 7. The maximum height reached by the ball as measured
from the ground would be
a. 52 m b. 31.25 m c. 83.25 m d. 63.25 m
11
211 An aeroplane flying at a constant speed
releases a bomb. As the bomb moves
away from the aeroplane, it will
A. always be vertically below the aeroplane only if the aeroplane was flying horizontally
B. always be vertically below the aeroplane only if the aeroplane was flying at an angle of ( 45^{circ} ) to the horizontal
c. always be vertically below the aeroplane
D. gradually fall behind the aeroplane if the aeroplane was flying horizontally
11
212 The velocity of a particle is ( boldsymbol{v}=boldsymbol{v}_{0}+ )
( g t+f t^{2} . ) If its position is ( x=0 ) at ( t=0 )
then its displacement after unit time ( (t=1) ) is:
A ( cdot v_{0}+2 g+3 f )
B . ( v_{0}+g / 2+f / 3 )
( mathbf{c} cdot v_{0}+g+f )
D . ( v_{0}+g / 2+f )
11
213 Two particles ( A ) and ( B ) are moving in a
horizontal place anticlockwise on two different concentric circles with
different constant angular velocities ( 2 omega )
and ( omega ) respectively. Find the relative
velocity (in ( m s ) ) of ( B ) w.r.t ( A ) after time
( boldsymbol{t}=boldsymbol{pi} / omega . ) They both start at the position
as shown in figure (Take ( omega= )
3 radsec, ( r=2 m )
11
214 Illustration 3.3 Two equal forces have their resultant equal
to either. At what angle are they inclined?
11
215 Compare the motion of a body dropped to that of a horizontal projectile, both
falling from the same height.
11
216 A body is projected horizontally from a point above the ground and motion of the body is described by the equation
( boldsymbol{x}=mathbf{2} boldsymbol{t}, boldsymbol{y}=mathbf{5} boldsymbol{t}^{2} ) where ( boldsymbol{x}, ) and ( boldsymbol{y} ) are
horizontal and vertical coordinates in
meter after time ( t . ) The initial velocity of the body will be
A. ( sqrt{29} mathrm{m} / mathrm{s} ) horizontal
B . ( 5 mathrm{m} / mathrm{s} ) horizontal
c. ( 2 m / s ) vertical
D. ( 2 m / s ) horizontal
11
217 A shell is fired from a cannon with a
speed of ( 100 mathrm{m} / mathrm{s} ) at an angle ( 30^{circ} ) with the horizontal (positive ( y- ) direction). At the highest point of its trajectory, the
shell explodes into two equal fragments
of masses in the ratio ( 1: 2 . ) The lighter
fragment moves vertically upwards with an initial speed of ( 200 mathrm{m} / mathrm{s} ). What is the
speed of the other fragment at the time of explosion?
11
218 Find the ( x- ) coordinate of the particle at
the moment of time ( t=20 s )
A. ( -4.0 m )
в. ( -3.0 m )
c. ( 4.0 m )
D. ( -2.0 m )
11
219 Jo
10. 200 . JOM
N
32. A cannon fires a projectile as shown
in Fig. A.14. The dashed line shows
the trajectory in the absence of
gravity. The points M, N, O, and P
correspond to time at t= 0,1 s, 2 s M
and 3 s, respectively. The lengths of Fig. A.14
X, Y, and Z are, respectively,
a. 5 m, 10 m, 15 m b. 10 m, 40 m, 90 m
c. 5 m, 20 m, 45 m d. 10 m, 20 m, 30 m
SM-
11
220 If the speed of body moving in circle is doubled and the radius is halved, its
centripetal acceleration becomes
A. Eight times
B. Four times
c. Two times
D. Sixteen times
11
221 The radius of the Earth is approximately
( 6.4 times 10^{6} m . ) The instantaneous velocity
of a point on the surface of the Earth at
the equator is ( 4.672 times 10^{x} ). Find the
value of ( mathbf{x}: )
11
222 At the highest point of a projectile its velocity i half the initial velocity in magnitude The angle of projection from ground is
A ( .30^{circ} )
В . ( 45^{circ} )
( c cdot 60^{circ} )
D. ( 90^{circ} )
11
223 The velocity of a particle is zero at time
( t=2, ) then
A. displacement must be zero in the interval ( t=0 ) to ( t= ) 2
B. acceleration may be zero at ( t=2 )
c. velocity must be zero for ( t>2 )
D. acceleration must be zero at ( t=2 )
11
224 A particle moves from ( A ) to ( B ) such that
( boldsymbol{x}=boldsymbol{t}^{2}+boldsymbol{t}-mathbf{3} . ) Its average velocity from
( t=2 s ) to ( t=5 s ) is
( A cdot 6 m s^{-1} )
3. ( 8 m s^{-1} )
( c cdot 8.5 m s^{-1} )
D. ( 7 mathrm{ms}^{-1} )
11
225 A circular platform is mounted on a
frictionless vertical axle. Its radius ( mathrm{R}=2 mathrm{m} )
and its moment of inertia about the axle
is ( 200 k g m^{2} ). It is initially at rest. A ( 50 mathrm{kg} )
man stands on the edge of the platform and begins to walk along the edge at the speed of ( 1 mathrm{ms}^{-1} ) relative to the ground.
Time taken by the man to compete one
revolution with respect to disc is:
( mathbf{A} cdot pi s )
B . ( frac{3 pi}{2} s )
( mathbf{c} cdot 2 pi s )
D. ( frac{pi}{2} s )
11
226 If ( |bar{A}+bar{B}|=|bar{A}|+|bar{B}| ) then the angle
between ( bar{A} ) and ( bar{B} ) is:
( A cdot 0^{0} )
B . ( 90^{circ} )
( c cdot 180^{circ} )
D. ( 60^{circ} )
11
227 4. The drift of the man along the direction of flow, when he
arrives at the opposite bank is
a.
b. 673 cm
a.
1 km
673 km
c. 3/3 km
km
11
228 A solid sphere is rolling on a rough surface, whose centre of mass is at ( C ) at
a certain instant. Find at that instant it
has angular velocity ( omega ) Its radius is ( mathrm{R} ). Find the angular acceleration at that instant mass of sphere is ( mathrm{m} )
A ( frac{5}{2} frac{g d}{R^{2}} )
В ( frac{5}{7} frac{g d}{R^{2}} )
c. ( frac{5}{2} frac{dleft(g+omega^{2} Rright)}{R^{2}} )
( D )
11
229 6. Two guns are mounted (fixed) on two vertical cliffs that are
very high from the ground as shown in figure. The muzzle
velocity of the shell from G, is u, and that from G, is uz
The guns aim exactly towards each other The ratio u, :u
such that the shells collide with each other in air is (Assume
that there is no resistance of air)
Gaui
(a) 1:2
(b) 1:4
(c) will not collide for any ratio
(d) will collide for any ratio
11
230 In the above problem, the angular acceleration
of the particle at ( t=2 sec ) is
rads( ^{-2} )
A ( cdot 14 )
B. 16
( c cdot 18 )
D. 24
11
231 Consider the two vectors ( vec{A}=3 hat{i}-2 hat{j} ) and ( vec{B}=-hat{i}-4 hat{j} . ) Calculate ( (a) vec{A}+ )
( overrightarrow{boldsymbol{B}} cdot(boldsymbol{b}) overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}} )
( (c)|overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}}| cdot(boldsymbol{d})|overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}}| )
and ( (e) ) the directions of ( vec{A}+vec{B} ) and ( overrightarrow{boldsymbol{A}}-overrightarrow{boldsymbol{B}} )
11
232 A particle is going in a spiral path as
shown in Fig. with constant speed. Then
A. its velocity is constant
B. its acceleration is constant
C. magnitude of its acceleration is constant
D. The magnitude of acceleration decreases continuously
11
233 A triangle has sides of length 13,30 and
( 37 . ) If the radius of the inscribed circle is
( frac{p}{q}(text { where } p text { and } q text { are coprime }) ),then the value of ( boldsymbol{q}^{boldsymbol{p}+mathbf{3}} ) is
A . 2048
в. 4096
c. 1024
D. 512
11
234 Mark the correct statement(s):
A. The magnitude of the velocity of particle is equal to its speed
B. The magnitude of average velocity in an interval is equal to its average speed in that interval.
C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not
zero.
D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.
11
235 An aeroplane is flying in a horizontal direction with a velocity ( 600 mathrm{km} / mathrm{h} ) at
height of 1960 m. When it is vertically above the point ( A ) on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB.
11
236 In circular motion of a particle,
This question has multiple correct options
A. particle cannot have uniform motion
B. particle cannot have uniformly accelerated motion
C . particle cannot have net force equal to zero
D. particle cannot have any force in tangential direction
11
237 An object is thrown into space horizontally under the action of earth’s gravity. Then the object is said to be a :
A. projectile
B. trajectory
c. spaceship
D. none of these
11
238 top
Q Type your question
Ball ( X ) has an initial velocity of
( 3.0 m s^{-1} ) in a direction along line ( A B )
Ball ( Y ) has a mass of ( 2.5 k g ) and an
initial velocity of ( 9.6 m s^{-1} ) in a
direction at an angle of ( 60^{circ} ) to line ( A B )
The two balls collide at point ( B ). The
balls stick together and then trave along the horizontal surface in a
direction at right-angles to the line ( boldsymbol{A B} ) as shown in Fig.

Determine the difference between the
initial kinetic energy of ball ( X ) and the initial kinetic energy of ball ( Y ). difference in kinetic energy ( = )
( boldsymbol{J} )

11
239 body is projected with a velocity of 60 ms at 30° to
horizontal
Column I
Column II
Initial velocity vector a.
60/3 + 40ĵ
Velocity after 3 s
30/3ỉ +10j
Displacement after c. 30.3 + 30
2 s
iv.
iv. Velocity after 2
s d. 3053
11
240 A boat crossing a river moves with a velocity v relative to still water. The river
is flowing with a velocity v/2 with
respect to the bank. The angle with respectively the slow direction with which the boat should move to
minimize the drift is
A ( .30^{circ} )
B. ( 60^{circ} )
( c cdot 180^{circ} )
D. ( 120^{circ} )
11
241 The wind appears to blow from north to
a man moving in the north-east
direction. When he doubles his velocity,
the wind appears to move in the
direction cot ( ^{-1} )
(2) east of north. If the
actual magnitude of velocity of the wind
is ( V=frac{1}{sqrt{x}} times ) magnitude of velocity of
man and direction along east. Find ( x )
11
242 Statement 1: The magnitude of velocity of two boats relative to river is same.
Both starts simultaneously from same point on one bank and they may reach opposite bank simultaneously moving along different paths.
Statement 2: For boats to cross the
river in same time.The component of their velocity relative to river in direction normal to flow should be
same.
A. Statement-1 is false, Statement- 2 is true
B. Statement-1 is true, Statement-2 is true, Statementis a correct explanation for statement- –
c. statement-1 is true, statement- 2 is true; statementis not a correct explanation for statement-
D. Statement-1 is true, Statement-2 is false.
11
243 The positive vector of a particle is
determined by the expression ( vec{r}= ) ( 3 t^{2} hat{i}+4 t^{2} hat{j}+7 hat{k} . ) The distance
traversed in first 10 sec is:
A. ( 500 mathrm{m} )
B. 300 ( m )
c. ( 150 mathrm{m} )
D. ( 100 mathrm{m} )
11
244 A stone is projected from the ground
with a velocity of ( 14 mathrm{ms}^{-1} . ) One second
later it clears a wall ( 2 m ) high. The angle
of projection is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) )
A ( cdot 45^{circ} )
B. ( 30^{circ} )
( c cdot 60^{circ} )
D. ( 15^{circ} )
11
245 Illustration 3.25 An insect crawls from A to B where B is
the center of the rectangular slant face. Find the (a) initial
and final position vector of the insect and (b) displacement
vector of the insect.
(0,2,0)
(0,2,0)
3 1
BI 2″ 2)
(0, 2, 1)
(3.0,0)
(3,0,0)
z/ (0,0,1)
z (0,0,1)
Fig. 3.49
(3,0,1)
11
246 4. In 1.0 s, a particle goes from point A to point a
B, moving in a semicircle of radius 1.0 m (Fig.
A.48). The magnitude of the average velocity
1.0 m
is
a. 3.14 ms-
c. 1.0 ms-1
b. 2.0 ms
d. Zero
Fig. A.51
(IIT JEE, 1999)
11
1
doboro the
11
247 A projectile is fired with a velocity ( u ) at
angle ( theta ) with the ground surface. During
the motion at any time it is making an
angle ( alpha ) with the ground surface. The speed of particle at this time will be
A . ucostheta( theta )seca
B. ucostheta.tana
c. ( u^{2} cos ^{2} alpha sin ^{2} alpha )
D. usintheta.sina
11
248 Same force acts on two bodies of
different masses ( 2 k g ) and ( 4 k g ) initially at rest. The ratio of times required to acquire same final velocity is:-
A .2: 1
B. 1: 2
( c cdot 1: 1 )
D. 4: 16
11
249 A large number of particles are moving towards each other with velocity ( V )
having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs?
A. ( 4 V / pi )
в. ( 4 pi V )
( c cdot V )
D. ( pi V / 4 )
11
250 A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of ( 2.0 mathrm{m} ) from the
goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is ( 19.6 mathrm{cm} ) from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationary goli without falling on the ground earlier?
11
251 An object starts from rest, and moves under the acceleration ( overrightarrow{boldsymbol{a}}=mathbf{4} hat{mathbf{i}} ). Its
position after ( 3 s ) is given by ( vec{r}= ) ( (7 hat{i}+4 hat{j}) . ) What is its initial position?
11
252 A swimmer swims in still water at a
speed ( =5 k m / h . ) He enters a ( 200 m )
wide river, having river flow speed ( = )
( 4 k m / h r ) at point ( A ) and proceeds to
swim at an angle of ( 127^{circ} ) with the river flow direction. Another point B is located
directly across ( A ) on the other side. The
swimmer lands on the other bank at a
point ( C, ) from which he walks the
distance ( mathrm{CB} ) with a speed ( =3 k m / h r )
The total time in which he reaches from
( A ) to ( B ) is
A . 5 minutes
B. 4 minutes
c. 3 minutes
D. none
11
253 A spaceship rotating around earth with a constant speed experiences
acceleration towards
A. against the instantaneous direction of velocity of spaceship
B. in the instantaneous direction of velocity of spaceship
c. center of the earth
D. away from the center of the earth
11
254 List
List II
A) Constant
I) At highest point speed and varying ( quad ) of body velocity ( quad ) projected vertically up
B) Zero
II) Uniform displacement and ( quad ) circular motion finite distance
III) At any
C) Zero velocity ( quad ) intermediate point of and finite acceleration ( quad ) freely falling body
D) Non-zero
IV) Body on reaching point of velocity and nonzero acceleration
The correct match is:
( A cdot A-|V, B-| I, C-|I|, D-1 )
B. ( A-11, B-1 V, C-1, D-11 )
( mathbf{C} cdot A-|I, B-I, C-I V, D-| )
D. ( A-1, B-111, C-11, D-1 V )
11
255 A car is traveling with linear velocity
on a circular road of radius ( r ). If it is
increasing its speed at the rate of ‘a’
( m s^{-2}, ) then the resultant acceleration
will be
A ( cdot sqrt{frac{v^{4}}{r^{2}}+a^{2}} )
B. ( sqrt{frac{v^{4}}{r^{2}}-a^{2}} )
c. ( sqrt{frac{v^{2}}{r^{2}}+a^{2}} )
D. ( sqrt{frac{v^{2}}{r^{2}}-a^{2}} )
11
256 The horizontal distance between two
bodies, when their velocity are
perpendicular to each other, is
A. ( 1 m )
B. ( 0.5 mathrm{m} )
( c .2 m )
D. ( 4 m )
11
257 Two particles of masses ( m ) and ( 2 m ) are kept at a distance a. Find their relative
velocity of approach when separation becomes ( a / 2 )
( mathbf{1} )
2
A ( cdot 2 sqrt{frac{3 a}{2 G M}} )
B. ( sqrt{frac{a}{2 G M}} )
( ^{mathbf{C}} cdot 2 sqrt{frac{2 G M}{3 a}} )
D. ( sqrt{frac{6 G M}{a}} )
11
258 A vector perpendicular to ( hat{i}+hat{j}+hat{k} ) is
( mathbf{A} cdot hat{i}-hat{j}+hat{k} )
B. ( hat{i}-hat{j}-hat{k} )
c. ( -hat{i}-hat{j}-hat{k} )
D. ( 3 hat{i}+2 hat{j}-5 hat{k} )
11
259 A body is moving down into a well through a rope passing over a fixed pulley of radius ( 10 mathrm{cm} . ) Assume that
there is no slipping between rope ( & ) pulley, calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of ( 20 mathrm{cm} / mathrm{s} ) and has an
acceleration of ( 4.0 m / s^{2} )
11
260 47. A ball is projected from the ground at angle o w
horizontal. After 1 s, it is moving at angle 45
horizontal and after 2 s it is moving horizontally. What
the velocity of projection of the ball?
a. 10/3 ms-1 b. 20/3 ms-1
c. 1075 ms -1 d. 202 ms-1
11
261 A small sphere is projected with a velocity of 3 ms-‘ in
a direction 60° from the horizontal y-axis, on the smooth
inclined plane (Fig. 5.197). The motion of sphere takes
place in the x-y plane. Calculate the magnitude v of its
velocity after 2 s.
R
$60º – Y
30°7
Fig. 5.197
11
262 The velocity with which particle strikes the plane ( boldsymbol{O B} )
A ( cdot 15 mathrm{ms}^{-1} )
B. ( 30 m s^{-1} )
( c cdot 20 m s^{-1} )
D. ( 10 mathrm{ms}^{-1} )
11
263 19. The velocity with which particle strikes the plane OB,
a. 15 ms- b. 30 ms c. 20 ms- d. 10 ms-
ca:
11
11
264 In the projectile motion shown is figure,
( operatorname{given} t_{A B}=2 s ) then which of the
folowing is correct ( :left(g=10 m s^{-2}right) )
his question has multiple correct options
A. particle is at point B at 3 s
B. maximum height of projectile is 20 m
c. initial vertical component of velocity is ( 20 mathrm{ms} )
D. horizontal component of velocity is ( 20 mathrm{ms} )
11
265 1. Statement I: The projectile has only vertical component
of velocity at the highest point of its trajectory.
Statement II: At the highest point, only one component
of velocity is present.
11
266 When a man is standing, rain drops
appear to him falling at ( 60^{circ} ) from the horizontal from his front side. When he
is travelling at ( 5 k m / h ) on a horizontal
road, they appear to him falling at ( 30^{circ} )
from the horizontal from his front side.
The actual speed of the rain in ( k m / h ) is.
A . 3
B. 4
( c .5 )
D. 6
11
267 The time in which a force of ( 2 N )
produces a change in momentum of ( 0.4 k g m s^{-1} ) in the body is
A . ( 0.2 s )
в. 0.02
c. ( 0.5 s )
D. ( 0.05 s )
11
268 The length of hour hand of a wrist watch
is ( 1.5 mathrm{cm} . ) Find magnitude of angular acceleration?
A. ( 0 r a d / s e c^{2} )
B. ( 2 pi r a d / s e c^{2} )
C ( .2 mathrm{rad} / mathrm{sec}^{2} )
D. ( 1 r a d / s e c^{2} )
11
269 14. The sum of the magnitudes of two forces acting at point is
18 and the magnitude of their resultant is 12. If the resultant
is at 90° with the force of smaller magnitude, what are the
magnitudes of forces?
(a) 12,5 (b) 14,4 (c) 5,13 (d) 10,8
11
270 A person standing on a road has to hold
his umbrella at ( 60^{circ} ) with the vertical to
keep the rain away. He throws the
umbrella and starts running at ( 20 m s^{-1} )
He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to (a) the road
and
(b) the moving person.
11
271 The positions of a particle moving along a straight line are ( x_{1}=50 mathrm{m} ) at 10.30
a.m. and ( x_{2}=55 mathrm{m} ) at 10.35 a.m.
respectively. What is the displacement of the particle between 10.30 a.m. and
10.35 a.m.?
( A cdot 2 m )
B. ( 5 mathrm{m} )
( c cdot 7 m )
D. ( 9 mathrm{m} )
11
272 A stone tied to the end of a string which is ( 80 mathrm{cm} ) long is whirled in a horizontal
circle with a constant speed. If the stone makes 14 revolutions in ( 25 s ), what is
the magnitude of
centripetal acceleration? ( left(operatorname{in} boldsymbol{m} / boldsymbol{s}^{2}right) )
A . 9.91
B . 2.36
c. 10.36
D. 12.69
11
273 The sun revolves around galaxy with speed of ( 250 k m / s ) around the center of
milky way and its radius is ( 3 times 10^{4} )
light year. The mass of milky way in ( k g )
is
A ( cdot 6 times 10^{4} )
В ( .5 times 10^{4} )
( c cdot 4 times 10^{4} )
D. ( 3 times 10^{4} )
11
274 Which of the following is an example of
uniform circular motion?
A. The planet Pluto in its wandering about the sun
B. The swing of a pendulum between the turning points
C. A bug sitting still at the centre of a playing 50 rpm record
D. The weights on the rim of a car tire as the car slowly accelerates
11
275 A car goes around uniform circular track of radius ( R ) at a uniform speed ( v )
once in every ( T ) seconds. The
magnitude of the centripetal
acceleration is ( a_{C} ). If the car now goes uniformly around a larger circular track
of radius ( 2 R ) and experiences a
centripetal acceleration of magnitude
( 8 a_{c}, ) then its time period is
A . ( 2 T )
в. ( 3 T )
c. ( T / 2 )
D. 3 / 27
11
276 In circular motion if ( bar{v} ) is velocity vector,
( bar{a} ) is acceleration vector, ( bar{r} ) is
instantaneous position vector, ( bar{p} ) is momentum vector and ( bar{omega} ) is angular velocity of particle, then:
This question has multiple correct options
A ( . bar{v}, bar{omega}, bar{r} ) are mutually perpendicular
B . ( bar{p}, bar{v}, bar{omega} ) are mutually perpendicular
c. ( bar{r} times bar{v}=0 ) and ( bar{r} times bar{omega}=0 )
D. ( bar{r} . bar{v}=0 ) and ( bar{r} . bar{omega}=0 )
11
277 If the displacement of a particle varies
with time as ( sqrt{x}=t+7, ) which of the
following statements is(are) true?
This question has multiple correct options
A. Velocity of the particle is inversely proportional to ( t ).
B. Velocity of the particle is proportional to ( t )
C. Velocity of the particle is proportional to ( sqrt{t} )
D. The particle moves with a constant accelera
11
278 The position of a particle along along ( x ) axis is given by ( x=a+b t^{2}, ) where ( a= )
( 8.5 mathrm{m}, mathrm{b}=2.5 mathrm{m} ) and ( t ) is in seconds.
What is its average velocity at ( t=2.0 ) s? What will be its average velocity between ( t=2 s & t=4 s ? )
11
279 Two particles are simultaneously projected in the horizontal direction
from a point ( boldsymbol{P} ) at a certain height. The
initial velocities of the particles are
oppositely directed to each other and
have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point ( P ) ) are mutually perpendicular, is
( ^{mathrm{A}} cdot frac{v^{2}}{2 g g} )
В. ( frac{v^{2}}{g} )
c. ( frac{4 v^{2}}{g} )
D. ( frac{2 v^{2}}{g} )
11
280 Assertion
Time taken by the bomb to reach the ground from a moving aeroplane depends on height of aeroplane only.
Reason
Horizontal component of velocity of the bomb remains constant and vertical
component of bomb changes due to gravity.
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
C. Assertion is true, but the Reason is false
D. Assertion is false, but the Reason is true.
11
281 (0) 21 dl II
5. If vectors P, Q and R have magnitude 5, 12 and 13 units
and + + = Ã, the angle between Q and Ris
(a) cos
(b) cos
(c) cos112
(d) cos -1
131
11
282 Illustration 5.14 From a point on the ground at a distance
a from the foot of a pole, a ball is thrown at an angle of 45°,
which just touches the top of the pole and strikes the ground
at a distance of b, on the other side of it. Find the height of
the pole.
11
283 The relation between the time of flight of projectile ( T, ) and the time to reach the
maximum height ( t_{m} ) is
A ( cdot T_{f}=2 t_{m} )
B . ( T_{f}=t_{m} )
c. ( T_{f}=t_{m} / 2 )
( mathbf{D} cdot T_{f}=sqrt{2} t_{m} )
11
284 A swimmer wishes to cross a ( 500 mathrm{m} )
wide river flowing at ( 5 mathrm{km} / mathrm{h} ). His speed with respect to water is ( 3 mathrm{km} / mathrm{h} ). (a) If he
heads in a direction making an angle ( theta )
with the flow, find the time he takes to
cross the river.(b) Find the shortest
possible time to cross the river.
11
285 In a uniform circular motion, radial
acceleration is due to
A. Change in position of the particle along ( X ) axis
B. Change in position of the particle along Y axis
C. Change in direction of tangential velocity
D. Change in magnitude of tangential velocity
11
286 Illustration 5.17 A rubber ball escapes from the horizontal
roof with a velocity – 5 ms. The roof is situated at a height,
ha 20 m. If the length of each cnr is equal to X 4 m, with
which car will the ball hit?
Fig. 5.21
11
287 Position of a particle in a rectangular coordinate system is (3,2,5) . Then its position vector will be
A ( cdot 3 hat{i}+5 hat{j}+hat{k} )
B ( cdot 3 hat{i}+2 hat{j}+5 hat{k} )
c. ( 5 hat{i}+3 j+2 hat{k} )
D. None of tese
11
288 CE and DF are two walls of equal height
(20 meter) from which two particles ( A ) and ( mathrm{B} ) of same mass are projected as
shown in the figure.A is projected
horizontally towards left while B is
projected at an angle ( 37^{0} ) (with horizontal towards left) with
velocity ( 15 ~ m / s e c ). If ( A ) always sees ( B ) to
be moving perpendicular to EF, then the range of A on ground is
A ( .24 m )
в. ( 30 m )
( c .26 m )
D. ( 28 m )
11
289 A body moving along a circular path will
have :
A. a constant speed
B. a constant velocity
c. no tangential velocity
D. a radial acceleration
11
290 The smallest distance between the
planes and the time when this occurs are: (nearly)
( left(operatorname{given} tan ^{-1}left(frac{128}{252}right)=tan ^{-1}left(26.9^{0}right)right) )
A. ( 54 mathrm{km}, 98 mathrm{s} )
B. ( 98 mathrm{km}, 54 mathrm{s} )
( c .27 mathrm{km}, 189 mathrm{s} )
D. ( 189 mathrm{km}, 54 mathrm{s} )
11
291 8. Two forces, each equal to F, act as shown in Fig. 3.78.
Their resultant is
1600
Fig. 3.78
b. F
ن نه
d. 15F
.
.
11
292 A stationary wheel starts rotating about its own axis at a constant angular acceleration. If the wheel completes 50 rotations in the first ( 2 s, ) then the number of rotations made by it in the
next ( 2 s ) is:
A . 75
в. 100
c. 125
D. 150
11
293 U. MIVUUNI 15 M
lown over by
7. A particle is dropped from a tower in a unit
gravitational field at t = 0. The particle is blown ou
a horizontal wind with constant velocity. The slope om
the trajectory of the particle with horizontal and its kiner
energy vary according to curves. Here, x is the horizontal
displacement and h is the height of particle from ground
at time t.
a.
b. ſ
KE
11
294 16. A student throws soft balls out of the window at different
angles to the horizontal. All soft balls have the same
initial speed v= 10/3 ms. It turns out that all soft balls’
landing velocities make angles 30° or greater with the
horizontal. Find the height h (in m) of the window above
the ground.
11
295 A particle is projected with a speed u at
an angle ( theta ) with the horizontal. What is the radius of curvature of the parabola traced out by the projectile at a point where the particle velocity makes an ( boldsymbol{theta} )
angle ( frac{-}{2} ) with the horizontal
11
296 A particle of mass ‘m’ is projected with
a velocity ‘u’ at an angle ‘ ( boldsymbol{theta}^{prime} ) with the
horizontal. Work done by gravity during its descent from its highest point to a point which is at half the maximum height is?
A. none of these
B. ( frac{m u^{2} sin ^{2} theta}{4} )
c. ( frac{1}{2} m u^{2} sin ^{2} theta )
D ( cdot frac{1}{2} m u^{2} cos ^{2} theta )
11
297 A particle moves in the ( x ) -y plane with
velocity ( v_{x}=8 t-2 ) and ( v_{y}=2 . ) If it
passes through the point ( x=14 ) and
( boldsymbol{y}=mathbf{4} ) at ( boldsymbol{t}=mathbf{2 s}, ) the equation of the path
is?
A. ( x=y^{2}-y+2 )
В. ( x=y^{2}-2 )
c. ( x=y^{2}+y-6 )
D. None of these
11
298 Find the time dependence of the velocity of the particle.
A ( cdot v=frac{alpha t}{4} )
B. ( v=frac{alpha^{2} t}{2} )
( ^{mathrm{C}} cdot_{v}=frac{alpha^{2} t}{4} )
D. ( v=frac{alpha t}{2} )
11
299 NO
28. A target is fixed on the top of a tower 13 m high. A person
standing at a distance of 50 m from the pole is capable of
projecting a stone with a velocity 10/8 ms. If he wants
to strike the target in shortest possible time, at what angle
should he project the stone?
20
11
300 An athlete completes one round of a circular track of radius ( boldsymbol{R} ) in ( mathbf{4 0} boldsymbol{s} ). His
displacement at the end of 2 minutes will be
A ( .2 pi R )
в. ( 6 pi R )
( c .2 R )
D. Zero
11
301 Position of a particle moving along ( boldsymbol{x}- ) axis is given by ( boldsymbol{x}=mathbf{3}(mathbf{2} boldsymbol{t}-mathbf{3})+mathbf{4}(mathbf{2} boldsymbol{t}- )
3)( ^{2} )
Which of the following is correct about
the particle?
A. Initial speed is ( 21 mathrm{m} / mathrm{s} )
B. Initial speed is ( 18 mathrm{m} / mathrm{s} )
c. Initial speed is ( 42 mathrm{m} / mathrm{s} )
D. Acceleration is ( 8 mathrm{m} / mathrm{s} )
11
302 10. A swimmer wishes to cross a 500-m river flowing at
5 kmh. His speed with respect to water is 3 kmh. The
shortest possible time to cross the river is
a. 10 min b. 20 min c. 6 min d. 7.5 min
11
303 If ( |vec{A}+vec{B}|=|vec{A}-vec{B}|, ) then the angle between ( vec{A} ) and ( vec{B} ) will be
( A cdot 30^{circ} )
B . 45
( c cdot 60 )
D. 90
11
304 6. A projectile is fired with velocity vo from a gun adjusted
for a maximum range. It passes through two points P and
Q whose heights above the horizontal are h each. Show
that the separation of the two points is
11
305 A trolley is moving horizontally with a velocity of ( v ) m/s w.r.t. earth. A man
starts running in the direction of
motion of trolley from one end of trolley
with a velocity ( 1.5 v ) m/ ( s ) w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running
with a velocity of1.5 ( boldsymbol{v} boldsymbol{m} / boldsymbol{s} ) w.r.t. trolley
in the backward direction. If the length
of the trolley is ( mathrm{L} ), then the displacement
of the man with respect to earth,
measured as a function of time, will
attain a maximum value of
A ( cdot frac{4}{3} L )
B. ( frac{2}{3} L )
c. ( frac{5 L}{3} )
D. ( 1.5 L )
11
306 22
locities v, and
18. In Fig. 6.307, blocks A and B move with velocities
V2 along horizontal direction. Find the ratio of y.lv
W
Fig. 6.307
sine,
a
sin
cos 82
sin e
sine,
cose,
cos
cos
11
307 A coin is tossed with a velocity of ( 3 mathrm{m} / mathrm{s} )
at
A.
a) What happens to the velocity along
AB, along DE and at C?
b) What happens to the acceleration of the coin along ( A C ) and ( C E ? )
c) What is the distance and vertical
displacement covered by the coin between A and E.
11
308 49. A plane flying horizontally at 100 ms releases an object
which reaches the ground in 10 s. At what angle with
horizontal it hits the ground?
a. 550 b. 45o c. 60° d. 75°
11
309 13. A truck is moving with a constant velocity of 34 km
In which direction (angle with the direction of motion of
truck) should a stone be projected up with a velocity
20 ms, from the floor of the truck, so as to appear at right
angles to the truck, for a person standing on earth?
a. cos
b. Cos -1
a. cost ( 22
COS
d. cost (2)
11
310 Which of the following cannot be in equilibrium?
A. ( 10 N, 10 N, 5 N )
( N )
B. ( 5 N, 7 N, 9 N )
c. ( 8 N, 4 N, 13 N )
D. ( 9 N, 6 N, 5 N )
11
311 Two particles ( A ) and ( B ) are placed as
shown in figure. The particle A on the
top of a tower of height H is projected horizontally with a velocity u and the particle B is projected along the horizontal surface towards the foot of
the tower, simultaneously. When particle A reaches at ground, it simultaneously hits particle B. Then the speed of projected particle B is:(neglect any type of friction)
A ( cdot d sqrt{frac{g}{2 H}} )
B. ( d sqrt{frac{g}{2 H}}-u )
( c )
[
sqrt[d]{frac{g}{2 H}+u}
]
D.
11
312 Consider a plane flying due West at 200 MPH. The co-pilot is firing a gun in the opposite direction the plane is flying due East. If the co-pilot clocks the bullets at ( 500 mathrm{MPH} ), how fast would the
bullets be clocked from the ground?
A. 300 MPH East
в. 700 МРн Еазн
c. 500 MPH West
D. 200 MPH West
E. cannot determine with information provided
11
313 Ideal fluid flows along a flat tube of constant cross-section, located in a
horizontal plane and bent as shown in figure above (top view). The flow is steady. Are the velocities of the
fluid equal at points 1 and ( 2 ? )
A. Velocity at point 1 is less than velocity at point 2
B. Velocity at point 1 is more than velocity at point 2
c. velocity at point 1 is equal to velocity at point 2
D. can’t be determined
11
314 35. Maximum height attained from the point of projection
a. 1.25 m
b. 12.5 m
c. 2.25 m
d. None of these
11
315 A car accelerates on a horizontal road
due to the force exerted by
A. The engine of the car
B. The driver of the car
c. The car on earth
D. The road on the car
11
316 w
(0)
b
46′
ton
60. A projectile is given an initial velocity of i +2j. The
cartesian equation of its path is (g = 10 ms?).
a. y = 2x – 5.r
b. y = x – 5×2
c. 4y = 2x – 5×2
d. y = 2x – 25/?
11
317 The angle turned by a body undergoing circular motion depends on time as
( boldsymbol{theta}=boldsymbol{theta}_{0}+boldsymbol{theta}_{1} boldsymbol{t}+boldsymbol{theta}_{2} boldsymbol{t}^{2} . ) Then the angular
acceleration of the body is
( A cdot theta_{1} )
в. ( theta_{2} )
( c cdot 2 theta_{1} )
D. ( 2 theta_{2} )
11
318 A particle projected from 0 and moving
freely under gravity strikes
the horizontal plane passing through 0 at a distance ( R ) from the starting
point 0 as shown in the figure. Then
This question has multiple correct options
A. there will be two angles of projection if ( R g<u^{2} )
B. the two possible angles of projection are complementary
c. the product of the possible times of flight from 0 to ( A ) is ( frac{2 R}{g} )
D. there will be more than two angles of projection if ( R g=u^{2} )
11
319 Two particles having position vectors ( vec{r}_{1}=3 hat{i}+5 hat{j} mathrm{m} ) and ( vec{r}_{2}=-5 hat{i}+3 hat{j} mathrm{m} )
are moving with velocities ( vec{V}_{1}=4 hat{i}+ ) ( 3 hat{j} mathrm{m} / mathrm{s} ) and ( vec{V}_{2}=-a hat{i}+4 hat{j} mathrm{m} / mathrm{s} . ) If they
collide after 2 seconds, the value of ( a ) is:
A . -2
B. -4
( c .-6 )
D. -8
11
320 Two vectors ( overrightarrow{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+hat{boldsymbol{j}} ) and ( overrightarrow{boldsymbol{B}}=boldsymbol{a} hat{boldsymbol{i}}- )
( 2 hat{j} ) are perpendicular to each other. The value of a is
A.
B. 2
( c cdot 3 )
D. 4
11
321 A particle is projected from the ground
with an initial velocity of ( 20 mathrm{m} / mathrm{s} ) at an
angle of ( 30^{circ} ) with horizontal. The
magnitude of change in velocity in a time interval from ( t=0 ) to ( t=0.5 mathrm{s} ) is
( left(g=10 m / s^{2}right) )
( A cdot 5 mathrm{m} / mathrm{s} )
в. ( 2.5 mathrm{m} / mathrm{s} )
( c cdot 2 m / s )
D. ( 4 mathrm{m} / mathrm{s} )
11
322 The path of projectile is represented by
( boldsymbol{y}=boldsymbol{P} boldsymbol{x}-boldsymbol{Q} boldsymbol{x}^{2} )
begin{tabular}{|l|l|l|l|}
hline multicolumn{2}{|c|} { Column I } & multicolumn{2}{|c|} { Column II } \
hline i. & Range & a. & ( P / Q ) \
hline ii. & Maximum height & b. & ( P ) \
hline iii. & Time of flight & c. & ( P^{2} / 4 Q ) \
hline iv. & Tangent of angle of projection is & d. & ( sqrt{frac{2}{Q g}} ) P \
hline
end{tabular}
11
323 Their common speed ( mathbf{v} ) will be
( mathbf{A} cdot frac{q}{4} sqrt{frac{1}{m R pi varepsilon_{0}}} )
( mathbf{B} cdot q sqrt{frac{m R pi varepsilon_{0}}{4}} )
( mathbf{c} cdot 4 q sqrt{m R pi varepsilon_{0}} )
D. ( frac{4 q}{sqrt{m R pi varepsilon_{0}}} )
11
324 Assertion
It is possible to accelerate even if you are travelling at constant speed.
Reason
In the uniform circular motion, even if the particle has the constant speed, it
has an acceleration.
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
325 Write a vector in the direction of the vector ( hat{boldsymbol{i}}-boldsymbol{2} hat{boldsymbol{j}}+2 hat{boldsymbol{k}} ) that has magnitude
9 units.
11
326 The graph shows position as a function of time for two trains ( A ) and ( B ) running on parallel tracks. For times greater
than ( t=0, ) which of the following
statement is true?
A. At time ( t_{B} ), both trains have the same velocity
B. Both trains speed up all the time
( c . ) Both trains may have the same velocity at some time earlier than ( t_{B} )
D. Graph indicates that both trains have the same acceleration at a give
11
327 A car is travelling with an acceleration
of ( 2 m / s^{2} . ) If the diameter of the car
wheel is ( 50 mathrm{cm}, ) the angular acceleration of the wheel is:
A ( .2 .5 mathrm{rad} / mathrm{s}^{2} )
B. 8 rad/s( ^{2} )
C ( .5 mathrm{rad} / mathrm{s}^{2} )
D. 4 rad/s( ^{2} )
11
328 12. A stone is projected from level ground such that its
horizontal and vertical components of initial velocity are
u = 10 m/s and u, = 20 m/s respectively. Then the angle
between velocity vector of stone one second before and
one second after it attains maximum height is:
(a) 30° (b) 45° (c) 60° (d) 90°
11
329 A ferris wheel with a radius of ( 8.0 m )
makes 1 revolution every 10 s.When a
passenger is at the top essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land?
( mathbf{A} cdot mathbf{0} )
в. ( 1.0 mathrm{m} )
( c .8 .0 m )
D. ( 9.1 mathrm{m} )
11
330 58. The speed of a projectile at its maximum height
times its initial speed. If the range of the projectile is pl
times the maximum height attained by it, P is equal to
a. 4/3 b. 2√3 c. 4√3 d. 3/4
11
331 Two forces simultaneously act on a
particle making an angle ( 120^{circ} ) with
each other if one of them is reversed the
acceleration of the particle becomes ( sqrt{3} ) times its initial value. The ratio of the
magnitude of the forces is?
A . 1: 2
B. 1: 1
( c cdot 2: 1 )
D. 1: 3
11
332 A man throws a ball at height of ( 10 mathrm{m} ) at
an angle of ( 35^{circ} ) from horizontal. If mass
of ball is ( 0.5 mathrm{kg} ) and its initial speed is ( 30 mathrm{m} / mathrm{s} )
( boldsymbol{g}=-mathbf{9 . 8} frac{boldsymbol{m}}{s^{2}} )
How long is the ball in the air?
A . ( 2.26 s )
B. 4.02s
( c cdot 1.76 s )
D. 5.05s
E. 1.12 s
11
333 Uniform Circular Motion refers to a
motion of an object in a circle at a
constant
A. Velocity
B. Speed
c. Both
D. None
11
334 A particle is projected at an angle of ( 45^{circ} )
from ( 8 m ) before the foot of a wall,just
touches the top of the wall and falls on the ground on the opposite side at a distance ( 4 m ) from it. The height of wall is:
A ( frac{2}{3} m )
в. ( frac{4}{3} m )
c. ( frac{8}{3} m )
D. ( frac{3}{4} m )
11
335 Two particles are projected in air with
speed ( u ) at angles ( theta_{1} ) and ( theta_{2} ) (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then
which one of the following is correct?
(where ( T_{1} ) and ( T_{2} ) are the time of flight.)
A. ( theta_{1}>theta_{2} )
a
B ( cdot theta_{1}=theta_{2} )
c. ( T_{1}<T_{2} )
D. ( T_{1}=T_{2} )
11
336 The position vector of a particle changes with time according to the relation ( vec{r}(t)=15 t^{2} hat{i}+left(4-20 t^{2}right) hat{j} )
What is the magnitude of the acceleration at ( t=1 ? )
A . 40
в. 100
c. 25
D. 50
11
337 Ship A is travelling with a velocity of 5 kmh due east.
A second ship is heading 30° east of north. What should
be the speed of second ship if it is to remain always due
north with respect to the first ship?
10 km h-b. 9 km h c. 8 kmh d. 7 kmh
La
11
338 A bus is moving on a straight road towards North with a uniform speed of
( mathbf{5 0} mathrm{km} / mathrm{h} . ) If the speed remains
unchanged after turning through ( 90^{circ} )
the increase in the velocity of the bus in the turning process is?
11
339 12 13
63. In the arrangement show
of B is ā, then fin
ngement shown in Fig. 6.335, if the acceleration
is a. then find the acceleration of A.
Fixed
incline
Fig. 6.335
a. a sin a
b. a cote
c. a tan o
d. a(sin a cot 0 + cos a)
11
340 A particle moves along +x-axis with initial velocity ( 5 mathrm{m} / mathrm{s} ). If acceleration (a)
varies with time (t) as shown in a-tt
graph, then the velocity of the particle
just after 4 second is
A ( .2 .5 m / s )
B. ( 10 mathrm{m} / mathrm{s} )
c. ( -1.25 m / s )
D. ( -5 m / s )
11
341 5.3
20. A motor boat is to reach at a point 30°
upstream on the other side of a river
120
flowing with velocity 5 ms. The
velocity of motor boat with respect to
water is 5 1/3 ms. The driver should
Fig. A.10
steer the boat at an angle
a. 30° w.rt. the line of destination from the starting
point
b. 60° w.r.t. normal to the bank
c. 120°w.rt. stream direction
d. None of these
11
342 A police van moving on a highway with a speed of ( 30 mathrm{km} h^{-1} ) fires a bullet at a
thief’s car speeding away in the same
direction with a speed of ( 192 mathrm{km} h^{-1} . ) If
the muzzle speed of the bullet is 150
( mathrm{m} s^{-1}, ) with what speed does the bullet
hit the thief’s car?
( mathbf{A} cdot 95 mathrm{m} mathrm{s}^{-1} )
B . ( 105 mathrm{m} s^{-1} )
C. ( 115 mathrm{m} s^{-1} )
D. ( 125 mathrm{m} s^{-1} )
11
343 In uniform circular motion the particle moves with a
A. Constant speed
B. Variable speed
c. constant acceleration
D. Variable acceleration
11
344 30. A ball rolls off the top of a stairway horizontally with a
velocity of 4.5 ms. Each step is 0.2 m high and 0.3 m
wide. If g is 10 ms?, and the ball strikes the edge of nth
step, then n is equal to
a. 9 b. 10 c. 11 d. 12.
11
345 Minimum number of unequal vectors
which can give zero resultant are:
A . two
B. three
c. four
D. more than four
11
346 Tyres are made circular because:
A. they can be inflated
B. they require less materaial
C. they look beautiful
D. they face less friction
11
347 toppr
Q Type your question-
a. The angle between the edge along
the ( z ) -axis (line ab) and the diagonal
from the origin to the opposite corner
(line ad).
b. The angle between line ( a c ) (the
diagonal of a face) and line ( a d )
A ( cdot ) a. ( cos ^{-1} frac{1}{sqrt{2}} )
b. ( cos ^{-1} frac{sqrt{2}}{sqrt{3}} )
B. a. ( cos ^{-1} frac{1}{sqrt{3}} )
c. a ( cos ^{-1} frac{1}{sqrt{3}} )
b. ( cos ^{-1} frac{sqrt{3}}{sqrt{3}} )
D. a. ( cos ^{-1} frac{2}{sqrt{3}} )
11
348 A car traveling at a constant speed of ( 30 m / s ) passes a highway patrol car, which is at rest. The police officer
accelerates at a constant rate of ( 3 m / s^{2} )
and maintains this rate of acceleration
until he pulls next to the speeding car. Assume that the police car starts to
move at the moment the speeder passes the police car. What is the time required for the police officer to catch
the speeder?
( mathbf{A} cdot 20 s )
B. ( 30 s )
c. ( 40 s )
D. ( 50 s )
11
349 30. A hose lying on the ground shoots a stream of water
upward at an angle of 60° to the horizontal with the
velocity of 16 ms. The height at which the water strikes
the wall 8 m away is
a. 8.9 m b. 10.9 m c. 12.9 m d. 6.9 m
1.1 ppiootile is at
11
350 In Fig. the angle of inclination of the
inclined plane is ( 30^{0} . ) Find the horizonta
velocity ( V_{0} ) so that the particle hits the
inclined plane perpendicularly.
A ( cdot V_{0}=sqrt{frac{2 g H}{5}} )
B. ( V_{0}=sqrt{frac{2 g H}{7}} )
( mathbf{c} cdot_{V_{0}}=sqrt{frac{g H}{5}} )
D ( cdot V_{0}=sqrt{frac{g H}{7}} )
11
351 A body is revolving with a constant
speed along a circular path. If the
direction of its velocity is reserved,
keeping speed unchanged, then at that
instant.
A. centripetal force disappears
B. centripetal force will be doubled
C. the centripetal force does not suffer any change in magnitude and direction both
D. the centripetal force does not suffer any change in magnitude but its direction is reserved.
11
352 18. Minimum separation between A and B is
a. 3 m b. 6 m c. 12 m d. 9 m
11
353 Illustration 5.73 A stone tied to an inextensible string of
length 7 = 1 m is kept horizontal. If it is released, find the
angular speed of the stone when the string makes an angle
O= 30° with horizontal.
11
354 shows a rod of length I resting on a wall and the floor. Its lower end A is pulled
towards left with a constant velocity ( v ) Find the velocity of the other end ( B ) downward when the rod makes an angle
( theta ) with horizontal.
11
355 When a body moves in a circular motion
A. its direction constantly changes
B. its direction remains constant
C. its velocity vector is always perpendicular to the direction
D. all of the above
11
356 TUNC U UDU
14. Find the resultant of three vectors OA. OB and OC show
in the following figure. Radius of the circle is R.
C
450
45o
(a) 2R
(c) RZ
(b) R(1+2)
(d) R(12 – 1)
11
357 An open topped freight car of mass ( mathbf{1 0}, mathbf{0 0 0} boldsymbol{k g} ) is coasting without friction along a level track in heavy rains, falling vertically downwards. Initially the car is empty and is moving with a velocity of ( 0.88 m / s . ) What is the velocity of the car after it has collected 1000 kg of water? 11
358 The tire pictured below is rolling to the
left at a constant speed without
slipping on a horizontal roadway.
What is the direction of the acceleration
of the part of the tire that is in contact
with the road?
A. Left
B. Right
c. up
D. Down
E. The acceleration of this part of the tire is zero
11
359 Two particles move on a circular path (one just inside and the other just
outside) with angular velocities ( omega ) and
( 5 omega ) starting from the same point. Then:
This question has multiple correct options
A cdot they cross each other at regular intervals of time ( frac{pi}{2 omega} ) when their angular velocities are directed opposite to each other
B. they cross each other at points on the path subtending an angle of ( 60^{circ} ) at the centre if their angular velocities are directed opposite to each other
C . they cross at intervals of time ( frac{pi}{3 omega} ) if their angular velocities are directed opposite to each other
D. they cross each other at points on the path subtending ( 90^{circ} ) at the centre if their angular velocities are similar to each other
11
360 A man is ( 45 mathrm{m} ) behind the bus when the
bus start accelerating from rest with acceleration 2.5. With what minimum velocity should the man start running to catch the bus
A . 12
B . 14
c. 15
D. 16
11
361 A system is shown in the figure. A man
a standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is
( 2 m / s ) downwards. The velocity of the
block will be: [Assume that the block
does not rotate ( ] )
A. ( 3 m / s )
B. ( 2 m / s )
c. ( frac{1}{2} m / s )
D. ( 1 mathrm{m} / mathrm{s} )
11
362 2
8
Vo
V2 8
26. In Fig. A. 11, the angle of inclination of the
inclined plane is 30°. Find the horizontal
velocity Vo so that the particle hits the
inclined plane perpendicularly.
|2gH
7
9030°
Fig. A.11
/23H
a. V
b. Vo = 7
c. Vo = 1/3
d. Vo = 18H
11
363 42. At a height 0.4 m from the ground, the velocity of a
projectile in vector form is v = (6i +2j) ms. The angle
of projection is
a. 45° b. 60° c . 30° d. tan (3/4)
Amanin tile in than in the word direction making an
11
364 A fan is running at 3000 rpm. It is switched off. It comes to rest by
uniformly decreasing its angular speed in 10 seconds. The total number of
revolutions in this period.
A. 150
B. 250
c. 350
D. 300
11
365 If an object is thrown vertically up, with the initial speed ( u ) from the ground, then the time taken by the object to return back to the ground is
( ^{mathrm{A}} cdot frac{u^{2}}{2 g} )
в. ( frac{u^{2}}{g} )
c. ( frac{u}{2 g g} )
D. ( frac{2 u}{g} )
11
366 A force of ( 10 mathrm{N} ) is resolved into the
perpendicular components. If the first
component makes ( 30^{0} ) with the force
the magnitudes of the components are:
A . 5N, 5N
B . ( 5 sqrt{2} mathrm{N}, ) 5N
( mathbf{c} cdot 5 sqrt{3} mathbf{N}, 5 mathrm{N} )
D. ( 10 mathrm{N}, 1 sqrt{3} mathrm{N} )
11
367 When in going east at ( 10 mathrm{km} / mathrm{h} ) a train moving with constant velocity appears to be moving exactly north – east. when my velocity is increased to ( 30 mathrm{km} / mathrm{h} ) east it appears to be moving north What is the velocity of train along north (in ( mathrm{Kmph}) ) ?
( A cdot 30 mathrm{km} / mathrm{h} )
B. 20 km/h
( c cdot 50 mathrm{km} / mathrm{h} )
D. ( 10 mathrm{km} / mathrm{h} )
11
368 The velocity of the body at any instant is
A ( cdot frac{M+2 N t^{4}}{4} )
B. 2N
c. ( frac{M+2 N}{4} )
D. ( 2 N t^{3} )
11
369 6. The time in which the ball strikes the floor of elevator is
given by
a. 2.13s b. 4.26 S c. 1.0 s d. 2.0 s
L
L

ched by the ball am
11
370 A particle moves in a straight line and its speed depends on time as ( boldsymbol{v}=mid mathbf{2 t}- )
3). Find the displacement of the particle
in ( 5 s )
11
371 18-10
31. A machine gun is mounted on the top of a tower of heghe
h. At what angle should the gun be inclined to cover
a maximum range of firing on the ground below? The
muzzle speed of bullet is 150 ms. Take g = 10 ms?
11
372 acceleration
13. Measuring g
The figure shows a method for measuring the acceler
due to gravity. The ball is projected upward by a 4
The ball passes electronic “gates” 1 and 2 as it rises
again as it falls. Each gate is connected to a sep:
timer. The first passage of the ball through each gate
starts the corresponding timer, and the second passage
through the same gate stops the timer. The time intervals
At, and At, are thus measured. The vertical distance
between the two gates is d. If d = 5 m, At, = 3 s, At,=
2 s, find the measured value of acceleration due to gravity
(in ms).
Gate 2
B: 1:18
0000 0
Timer 2
Te
TEL:5:1:1:13
0000
Timer 1
Bal
Gun
Fig. A.49
14 A
lomotion of
11
373 Consider the following statements A and B given below and identity the
correct answer.
A) With the help of the relative velocity of rain with respect to man, the direction of the umbrella held by him to save from the rain is determined.
B) A parallelogram has sides represented by vectors ( vec{a} ) and ( overrightarrow{mathrm{b}} ). If ( overrightarrow{mathrm{d}}_{1} ) and
( overrightarrow{mathrm{d}}_{2} ) are the
diagonal vectors of the parallelogram then ( 2left(mathrm{a}^{2}+mathrm{b}^{2}right)=mathrm{d}_{1}^{2}+mathrm{d}_{2}^{2} )
A. Both A and B are true
B. A is true but B is false
c. ( B ) is true but ( A ) is false
D. Both A and B are false
11
374 Any vector in an arbitrary direction can always be replaced by two (or three):
A. Parallel vectors which have the original vector as their resultant
B. Mutually perpendicular vectors which have the original vector as their resultant
c. Arbitrary vectors which have the original vector as their resultant
D. It is not possible to resolve a vector
11
375 9. On a two-lane road, car A is travelling with a speed of
36 kmh. Two cars B and C approach car A in opposite
directions with a speed of 54 kmh each. At a certain
instant, when the distance AB is equal to AC, both being
1 km, B decides to overtake A before C does. What
minimum acceleration of car B is required to avoid an
accident?
11
376 d. non-zero
UUM
13. From the top of a tower of height 200 m, a ball A:
projected up with speed 10 ms and 2 s later, ano
ball B is projected vertically down with the same speed
Then
a. Both A and B will reach the ground simultaneously
b. Ball A will hit the ground 2 s later than B hitting the
ground
c. Both the balls will hit the ground with the same
velocity
d. Both will rebound to the same height from the ground.
if both have same coefficient of restitution.
nale – 200 with 1
11
377 A particles revolves along a circle with a
uniform speed. The motion of the
particle is
A. one dimensional
B. two dimensional.
c. translatory
D. oscillatory
11
378 If ( A ) is to the south of ( B ) and ( C ) is to the
east of ( mathrm{B} ), in what direction is ( mathrm{A} ) with
respect to C?
A. North-east
B. North-west
c. South-west
D. None of the above
11
379 A force ( overrightarrow{boldsymbol{F}}=2 hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{k}} ) acts on a particle
at ( vec{r}=0.5 hat{j}-2 hat{k} . ) The torque ( vec{Gamma} ) acting
on the particle relative to a point with co-ordinates ( (2.0 mathrm{m}, 0 ;-3.0 mathrm{m}) ) is?
11
380 Consider driving in a car at 65 MPH while drinking a cup of coffee. Which of the following would be traveling at the greatest speed?
A. The car, coffee and you are traveling at the same velocity
B. The coffee is traveling with the greatest velocity assuming it has the least mass
c. The car is the only object with velocity, as the other objects are within the car
D. None of the objects have velocity, as they are all traveling together
E. As velocity is a function of speed and direction, this question cannot be answered
11
381 In a situation, a board is moving with a
velocity ( v ) with respect to earth, while a
man A and man B are running with a
velocity ( 2 v ) with respect to earth and
both men are running from the opposite
ends of the board at the same time, as
shown. Length of the board is ( L ). If they
meet after time ( boldsymbol{T}, ) then
This question has multiple correct options
A. value of ( mathrm{T} ) is ( mathrm{L} / 4 mathrm{v} )
B. value of ( T ) is ( L / 2 v )
C. Displacement of man B with respect to board in time ( T ) is ( 3 L / 4 )
D. Displacement of man A with respect to board in time ( T ) is L/4
11
382 A particle starts travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment
when particle complete half the circular track, is:
( mathbf{A} cdot tan ^{-1}(2 pi) )
B. ( tan ^{-1}(pi) )
( mathbf{c} cdot tan ^{-1}(3 pi) )
D. ( tan ^{-1}(2) )
11
383 Two particle ( A ) and ( B ) are located in ( x-y ) plane at points (0,0) and ( (0,4 mathrm{m}) ). They simultaneously start moving with velocities. ( vec{V}_{A}=2 hat{j} m / s ) and ( vec{V}_{B}= )
2 ì ( m / s . ) Select the correct alternative(s).
This question has multiple correct options
A. The distance between them is constant
B. The distance between them first decreases and then increases
c. The shortest distance between them is ( 2 sqrt{2} m )
D. Time after which they are at minimum distance is 1 s
11
384 Find a vector in thedirection of ( 5 hat{i}-widehat{j}+ )
( 2 widehat{k} ) which has magnitude 8 units.
A ( cdot frac{8}{sqrt{30}} hat{i}-frac{40}{sqrt{30}} hat{j}+frac{16}{sqrt{30}} widehat{k} )
B. ( frac{16}{sqrt{30}} hat{i}+frac{8}{sqrt{30}} hat{j}-frac{40}{sqrt{30}} widehat{k} )
c. ( frac{40}{sqrt{30}} hat{i}-frac{8}{sqrt{30}} hat{j}+frac{16}{sqrt{30}} widehat{k} )
D. None
11
385 Illustration 5.1 At what point on a projectile’s trajectory, its
speed is minimum? If a stone is thrown with a speed vo at an
angle @ with horizontal, find the velocity of the stone when
its line of motion makes an angle with horizontal.
11
386 Which of the following statement is
correct
A. The motion of earth around the sun is vibratory
B. The motion of a mosquito in a room is in a straight line
C. The motion of moon around the earth is periodic
D. None of these
11
387 le 0 above
55. A projectile is fired from level ground at an angle o
the horizontal. The elevation angle Pof the higher
seen from the launch point is related to O by the
a. tan o = 2 tano
b. tano = tano
highest pointas
e by the relation
c.
tan
d. tan o = -tan
= -tan e
11
388 Air resistance is proportional to
This question has multiple correct options
A ( . v )
B ( cdot v^{2} )
( c cdot v^{-2} )
( mathbf{D} cdot v^{3} )
11
389 A swimmer swims in still water at a
speed ( =5 k m / h r . ) He enters a ( 200 m ) wide
river, having river flow speed ( =4 k m / h r ) at a point ( A ) and proceeds to swim at an
angle of ( 127^{0}left(sin 37^{*}-0.6right) ) with the
river flow direction. Another point B is located directly across ( A ) on the other side. The swimmer lands on the river
bank at a point C. from which he walks the distance ( mathrm{CB} ) with a speed ( =3 k m / h r ) The total time in which he reach from ( mathbf{A} )
to B is
( mathbf{A} cdot 5 min )
B. 4 min
c. 3 min
D. None
11
390 The displacement ( (x) ) of a particle
starting from rest is given by ( boldsymbol{x}=mathbf{6} boldsymbol{t}^{2}- )
( t^{3} . ) The time at which the particle will
attain zero velocity again is
A . 2
B. 4
( c .6 )
D.
11
391 36. A ball is thrown at different angles with the same speed
u and from the same point and it has the same range in
both the cases. If y, and y2 are the heights attained in the
two cases, then yı + y2 is equal to
– 2u²
a. – D. 8 c. 28 . 48
02
b.
11
392 A particle ( A ) moves along a circle of
radius ( R=50 mathrm{cm} ) so that its radius
vector ( r ) relative to the point ( O ) (figure)
rotates with the constant angular
velocity ( omega=0.40 ) rad ( / ) s. Then
magnitude of the velocity of the
particle, and the magnitude of its total acceleration will be
A ( cdot v=0.4 mathrm{m} / mathrm{s}, a=0.4 mathrm{m} / mathrm{s}^{2} )
B . ( v=0.32 mathrm{m} / mathrm{s}, a=0.32 mathrm{m} / mathrm{s}^{2} )
C ( cdot v=0.32 mathrm{m} / mathrm{s}, a=0.4 mathrm{m} / mathrm{s}^{2} )
D. ( v=0.4 mathrm{m} / mathrm{s}, a=0.32 mathrm{m} / mathrm{s}^{2} )
11
393 The angle turned by a body undergoing circular motion depends on time as
( boldsymbol{theta}=sqrt{mathbf{2}} boldsymbol{theta}_{0}+mathbf{3} boldsymbol{theta}_{1} boldsymbol{t}+boldsymbol{theta}_{2} boldsymbol{t}^{2} ) Then the
angular acceleration of the body is
A. ( sqrt{theta_{1}} )
в. ( sqrt{3} theta_{2} )
( c cdot 2 theta_{1} )
D. ( 2 theta_{2} )
11
394 21. The point from where a ball is projected is taken as the
origin of the coordinate axes. The x and y components of
its displacement are given by x = 6t and y = 8t -57. Wha
is the velocity of projection?
a. 6 ms-1 b. 8 ms -1 c. 10 ms- d. 14 ms -1
11
395 9. An airplane is observed by two observers traveling
60 kmh ‘ in two vehicles moving in opposite direction
on a straight road. To an observer in one vehicle, the plane
appears to cross the road track at right angles while to
the other appears to be 45º. At what angle does the plane
actually cross the road track and what is its speed relative
to ground?
11
396 A ball (solid sphere) of mass ( m ) is
rolling on a smooth horizontal surface
as shown in figure. At an instant the
magnitude of the velocity of the centre
of mass is ( v_{0} ) and its angular velocity is ( omega frac{v_{0}}{2 R}, ) where ( R ) is the radius of the ball.
The total kinetic energy of the rolling
ball at this instant is:-
( mathbf{A} cdot frac{7}{5} m R^{2} omega_{0}^{2} )
B. ( frac{11}{5} m R^{2} omega_{0}^{2} )
( c )
D.
11
397 A girl riding a bicycle with a speed of 5
( m s^{-1} ) towards north direction, observes
rain falling vertically down. If she
increases her speed to ( 10 mathrm{ms}^{-1}, ) rain
appears to meet her at ( 45^{circ} ) to the
vertical. What is the speed of the rain?
A ( cdot 5 sqrt{2} mathrm{ms}^{-1} )
B. ( 5 m s^{-1} )
D. ( 10 m s^{-1} )
11
398 In the given figure, ( a=15 mathrm{m} / mathrm{s}^{2} )
represents the total acceleration of a particle moving in the clockwise direction in a circle of radius ( boldsymbol{R}=mathbf{2 . 5 m} )
at a given instant of time. The speed of
the particle is:
( mathbf{A} cdot 6.2 m / s )
B. ( 4.5 m / s )
( c .5 .0 m / s )
D. ( 5.7 m / s )
11
399 56. A projectile has initially the same horizontal veloci
as it would acquire if it had moved from rest with unif
acceleration of 3 ms for 0.5 min. If the maximum heich
reached by it is 80 m, then the angle of projection i
(8 = 10 ms2)
a. tan-3
b. tan-‘(3/2)
c. tan-(4/9)
d. sin-(4/9)
11
400 Two wheels are constructed, as shown in Figure, with four spokes. The wheels are mounted one behind the
other so that an observer normally sees a total of eight spokes but only four spokes are seen when they happen to align with one another. If one wheel spins at 6 rev/min, while other spins at
8 rev/min in same sense, how often
does the observer see only four spokes?
A. 4 times a minute
B. 6 times a minute
c. 8 times a minute
D. Once in a minute
11
401 Assertion
To move a body uniformly in a circular
path, an external agent has to apply a force.
Reason
To more a body uniformly in a circular path, an external agent has to do work.
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 is correct
11
402 If you are traveling on a spaceship close to the speed of light (pick a number e.g.
0.95c), With or without constant acceleration whichever works for the
question. Time will slow down relative to earth
and you will be able to travel a greater distance than you would be able to without relativistic effects. You would
also be able to return to earth with
significant time passed relative to your experience. My question is, what would it feel like on the spaceship…I know the standard answer is you wouldn’t feel anything, but logically, if you were traveling through galaxy after galaxy in a relativistic time of human life then
intuition says everything would look like it whizzing past. Basically, what is the human experience of being able to trave interstellar distances?
11
403 The adjacent sides of a paralleleogram ( operatorname{are} vec{A}=2 hat{i}-3 hat{j}+hat{k} quad ) and ( quad vec{B}= )
( -2 hat{i}+4 hat{j}-hat{k} ) What is the area of the
parallelogram?
A. 4 units
B. 7units
c. ( sqrt{5} ) units
D. ( sqrt{8} ) units
11
404 single Correct Answer Type
f a stone has to hit at a point which is
at a distance ( d ) away and at a height ( h )
above the point from where the stone starts, then what is the value of initial
speed ( u ) if the stone is thrown at an
angle ( theta ? )
A ( cdot frac{g}{cos theta} sqrt{frac{d}{(2(d tan theta-h)}} )
в. ( frac{d}{cos theta} sqrt{frac{g}{(2(d tan theta-h)}} )
c. ( sqrt{frac{g d^{2}}{h cos ^{2} theta}} )
D. ( sqrt{frac{g d^{2}}{(d-h)}} )
11
405 A particle starts moving from point ( (2, )
10,1)( . ) Displacement for the particle is 8 ( hat{mathbf{i}}-2 hat{mathbf{j}}+hat{boldsymbol{k}} . ) The final coordinates of the
particle is
A. (10,8,2)
)
в. (8,10,2)
( c cdot(2,10,8) )
D. (8,2,10)
11
406 When the particle reaches its maximum height, which of the following MUST be true about the particle?
A. It has the same horizontal speed it had initially
B. It has the same vertical speed it had initially
C. Its net acceleration is momentarily zero
D. It is momentarily at rest
E. All of the above
11
407 How can you say circular motion of an object is said to be an accelerated
motion.
11
408 4. A ladder is resting with the wall at an angle of 30°. A man
is ascending the ladder at the rate of 3 ft/sec. His rate of
approaching the wall is
(a) 3 ft/sec
(b) ft/sec
(d) ft/sec
ft sec
11
409 MAPOCIUIU MULUI VOL
From the top of tower of height 80 m, two stones are
projected horizontally with velocities 20 ms and
30 ms” in opposite directions. Find the distance between
both the stones on reaching the ground in 10 m).
11
410 A steamer plies between two stations ( boldsymbol{A} )
and ( B ) on opposite banks of a river, always following the path ( A B ). The
distance between stations ( A ) and ( B ) is
1200 ( m ). The velocity of the current is ( sqrt{17} m s^{-1} ) and is constant over the
maim width of the river. The line ( A B )
makes an angle ( 60^{circ} ) with the direction
of the flow. The steamer takes 5 min to
cover the distance ( A B ) and back.
a. Find the velocity of steamer with
respect to water.
b In what direction should the steamer
move with respect to line ( boldsymbol{A B} ) ?
11
411 O 0510 COOL
11. A ball is fired from point P, with an initial speed of
50 ms at an angle of 53°, with the horizontal. At the same
time, a long wall AB at 200 m from point P starts moving
toward P with a constant speed of 10 ms. Find
50 ms-1
S
P53°
200 m
Fig. 5.190
a. the time when the ball collides with wall AB.
b. the coordinate of point C, where the ball collides,
taking point P as origin.
11
412 particle is projected with a certain velocity at an angle a
hove the horizontal from the foot of an inclined plane of
inclination 30°. If the particle strikes the plane normally,
then a is equal to
a. 30° + tan-1
b. 45°
c. 60°
d. 30° + tan-|(273)
11
413 Given that ( overrightarrow{boldsymbol{A}}+overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{C}} ). If ( |overrightarrow{boldsymbol{A}}|=4,|overrightarrow{boldsymbol{B}}|= )
( mathbf{5} ) and ( |overrightarrow{boldsymbol{C}}|=sqrt{mathbf{6 1}}, ) the angle between ( boldsymbol{A} )
and ( B ) is
A ( .30^{circ} )
B. ( 60^{circ} )
( c .90^{circ} )
D. ( 120^{circ} )
11
414 44. Two guns on a battleship
simultaneously fire two shells
with same speed at enemy ships.
ie Battleship
If the shells follow the parabolic
A
trajectories as shown in Fig. A.22, Fig. A.22
which ship will get hit first?
a. A
b. B
c. both at same time d. need more information
11
415 43. A projectile is thrown in the upward direction making an
angle of 60° with the horizontal direction with a velocity
of 150 ms. Then the time after which its inclination with
the horizontal is 45° is
a. 15(13 – 1)s b. 15673 +1) s
c. 7.56√3-1)s d. 7.56√3+1)s
c
ania
11
416 A car is moving with speed 30 m/sec on
a circular path of radius 500 m. Its
speed is increasing at the rate of ( 2 m / s e c^{2} . ) What is the acceleration of
the car at that moment?
11
417 To get from one office to another, one travels as follows (with all angles
measured clockwise from the West) ( 2 m )
at ( 180^{circ}, 0.5 m ) at ( 150^{circ}, ) and ( 1 m ) at ( 30^{circ} ) How far will a person be from his starting point? ( (text { in } m) )
A . 1.5
B. 1.43
( c .1 )
D. 1.96
11
418 A body is moving with a constant speed
( v ) in a circle of radius ( r . ) Its angular acceleration is:
A . ( v r )
B. ( frac{v}{r} )
c. zero
D. ( v r^{2} )
11
419 Illustration 5.6 The horizontal range of a projectile is 23
times its maximum height. Find the angle of projection.
friention and
11
420 The co-ordinates of a moving particle at
any time ( t ) are given by ( alpha t^{3} ) and ( y=beta t^{3} )
The speed of the particle at time is given by
A ( cdot 3 t sqrt{alpha^{2}+beta^{2}} )
B . ( 3 t^{2} sqrt{alpha^{2}+beta^{2}} )
c. ( 3 t sqrt{alpha^{2}+beta^{2}} )
D. ( sqrt{alpha^{2}+beta^{2}} )
11
421 In the figure shown ( mathrm{S} ) is the source of
white light kept at a distance ( x_{0} ) from
the plane of the slits. The source moves with a constant speed u towards the slits on the line perpendicular to the plane of the slits and passing through the slit ( S_{1} ). Find the instantaneous velocity (magnitude and direction) of the central maxima at time t having range ( 0 leq t<>d )
11
422 The parameters for a particle that describe a uniform circular motion and
a uniform velocity motion in a straight line are given below. Which one of them will you use to distinguish their motions
A. Speed of both the particles
B. Distance traveled by both the particles
C. Average velocity of both the particles
D. None of these
11
423 31. What displacement at an angle 60° to the x-axis has an
x-component of 5 m? i and j are unit vectors in x and y
directions, respectively.
a. 5î
b. 5i +5 bar
c. 5i +531 d . All of the above
atamant
11
424 The relative velocity of ( B ) as seen from
( A ) is
( mathbf{A} cdot-8 sqrt{2} hat{i}+6 sqrt{2} hat{j} )
B. ( 4 sqrt{2} hat{imath}+3 sqrt{3} hat{j} )
c. ( 3 sqrt{5 hat{imath}}+2 sqrt{3} hat{jmath} )
D. ( 3 sqrt{2 hat{i}}+4 sqrt{3} hat{j} )
11
425 Why do the passengers fall forward when a fast moving bus stops suddenly? 11
426 0.5 m
AA30
30.
71. A ball is projected from a point
A with some velocity at an angle
30° with the horizontal as shown
in Fig. 5.204. Consider a target
at point B. The ball will hit the
Fig. 5.204
target if it is thrown with a
velocity vo equal to
a. 5 ms-1
c. 7 ms-1
d. None of these
b. 6 ms-1
11
427 52. A golfer standing on level ground hits a ball with a velocity
of u = 52 ms at an angle a above the horizontal. If tan
a = 5/12, then the time for which the ball is at least 15 m
above the ground will be (take g = 10 ms)
a. Is b. 2s c. 35 d. 4s
11
428 If the angle between the vectors ( vec{A} ) and
( vec{B} ) is ( theta, ) then the value of the product ( (vec{B} times vec{A}) cdot vec{A} ) equals
A. ( B A^{2} sin theta )
B. ( B A^{2} cos theta sin theta )
c. ( B A^{2} cos theta )
D. zero
11
429 ( P ) is a point moving with constant speed ( 10 m / s ) such that its velocity
vector always maintains an angle ( 60^{circ} )
with line ( O P ) as shown in figure ( (O ) is a fixed point in space). The initial distance between ( O ) and ( P ) is ( 100 m ).
After what time shall ( P ) reach ( O )
A . ( 10 s )
B. ( 15 s )
c. ( 20 s )
D. ( 20 sqrt{3} s )
11
430 A projectile is fired with a speed ( u ) at an angle ( theta ) with horizontal. Its speed when
its direction of motion makes an angle
( alpha^{prime} ) with the horizontal is
A . u ( sec theta cos alpha )
B. u ( sec theta sin alpha )
( c cdot u cos theta sec alpha )
D. u ( sin theta sec alpha )
11
431 15. A particle moves along positive branch of the curve
y=-, where x== , X and y are measured in meters
and t in seconds, then
a. The velocity of particle at t = 1 s is î+-j
b. The velocity of particle at t= 1 sis
1 / 1 + .
c. The acceleration of particle at t = 2 s
d. The acceleration of particle at t = 2 s is î+2î .
Ti 11
ca: 11.
11
432 A carom board ( (4 f t times 4 f t text { square }) ) has
the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen
(i) from the centre to the front edge
( (i i) ) from the front edge to the hole and
(iiii) from the centre of the hole.
A.
( (i) frac{2}{3} sqrt{10} f t(i i) frac{4}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t )
в.
(i) ( frac{4}{3} sqrt{10} f t(i i) frac{4}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t )
( c )
(i) ( frac{4}{3} sqrt{10} f t(i i) frac{2}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t )
( D )
( (i) frac{2}{3} sqrt{10} f t(i i) frac{2}{3} sqrt{10} f t(i i i) 2 sqrt{2} f t )
11
433 If ( vec{A}+vec{B} ) is a unit vector along ( x ) -axis and ( vec{A}=hat{i}-hat{j}+hat{k} ) then what is ( vec{B} ? )
( mathbf{A} cdot hat{j}+hat{k} )
B. ( hat{j}-hat{k} )
( mathbf{c} cdot hat{i}+hat{j}+hat{k} )
D. ( hat{i}+hat{j}-hat{k} )
11
434 In Fig. 5.201, the time taken by the
projectile to reach from A to B ist. Then
the distance AB is equal to
ance ARCh from se taken 1
609
ut
A
30°
a.
b. V3ut
Fig. 5.201
3
c. √ut
d. 2ut
11
435 Two identical balls ( P ) and ( Q ) are
projected with same speeds in vertical
plane from same point ( boldsymbol{O} ) with making
projection angles with horizontal ( 30^{circ} )
and ( 60^{circ}, ) respectively and they fall
directly on plane ( A B ) at points ( P^{prime} ) and
( Q^{prime} ) respectively. Which of the following
statement is true about distance as
given in options?
A ( cdot A P^{prime}>A Q^{prime} )
B. ( A P^{prime}<A Q^{prime} )
c. ( A P^{prime} leq A Q^{prime} )
D. As there are complimentary projection angles
11
436 Q Type your question
illustrated in Fig.
Ball ( X ) has an initial velocity of
( 3.0 m s^{-1} ) in a direction along line ( A B )
Ball ( Y ) has a mass of ( 2.5 k g ) and an
initial velocity of ( 9.6 m s^{-1} ) in a
direction at an angle of ( 60^{circ} ) to line ( A B )
The two balls collide at point ( B ). The
balls stick together and then trave along the horizontal surface in a
direction at right-angles to the line ( boldsymbol{A B} )
as shown in Fig.

Calculate the common speed ( V ) of the
two balls after the collision

11
437 7. The resultant of P and Ở is perpendicular to P. What
is the angle between P and 2 ?
(a) cos-1 (PIQ) (b) cos-l(-PIQ)
(c) sin-‘ (PIQ)
(d) sin-‘(-PIQ)
11
438 46. Two identical balls are set into motion
simultaneously from equal heights h.
While the ball A is thrown horizontally
with velocity v, the ball B is just
Ground
released to fall by itself. Choose the
alternative that best represents the motion of A and B with
respect to an observer who moves with velocity v/2 with
respect to the ground as shown in Fig A.24.
А В
A B
2.
f
11
439 To how much angel does the earth revolve around sun in 2 days? 11
440 18. A particle travels with speed 50 m s from the point
(3, -7) in a direction Tử – 24j. Find its position vector
after 3 s.
11
441 The physical quantity corresponding to the rate of change of displacement is
A. speed
B. velocity
c. acceleration
D. retardation
11
442 A balloon initially at rest, starts rising from the ground with an acceleration of
( 2 m / s^{2} . ) After ( 4 s, ) a stone is dropped
from a balloon. In one second of time
after the drop, the stone will cover a
distance of ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
A. ( 3.0 mathrm{m} )
в. 3.4 m
( mathbf{c} .3 .8 mathrm{m} )
D. ( 2.6 mathrm{m} )
11
443 10. A bullet is fired from horizontal ground at some angle
passes through the point, where ‘R’ is the range of the
bullet. Assume point of the fire to be origin and the bullet
moves in x-y plane with x-axis horizontal and y-axis
vertically upwards. Then angle of projection is
(a) 30° (b) 37° (c) 53° (d) none
+00
11
444 0
(0)
3
(0)
2
ed at an angle of 60° from the ground level
9. A stone projected at an angle of 60° from the 8
strikes at an angle of 30° on the roof of a building of height
‘h’. Then the speed of projection of the stone is.
30°C
260°
(a) v2gh
(b) Vogh
(d) Vgh
(c) /3gh
11
445 Two billiard balls are rolling on a flat table. One has velocity components ( boldsymbol{V}_{boldsymbol{x}}=mathbf{1} boldsymbol{m} / boldsymbol{s}, boldsymbol{V}_{boldsymbol{y}}=sqrt{mathbf{3}} boldsymbol{m} / boldsymbol{s} ) and the
other has component ( V_{x}=2 m / s ) and
( V_{y}=2 m / s . ) If both the balls start moving from the same point the angle between their path is:
A ( .60^{circ} )
B . 45
( c cdot 22.5 )
D. ( 15^{circ} )
11
446 The resultant of two forces ( P ) and ( q ) is
right angle to ( P ), the resultant of ( P ) and
( Q ) acting at the same angle is at right
angle to ( Q ). Prove that ( P ) is the
geometric mean of ( Q ) and ( Q ) (i.e. ( P= )
( sqrt{boldsymbol{Q} boldsymbol{q}} ? )
11
447 A fly wheel rotating at 600 rev/min is
brought under uniform deceleration and
stopped after 2 minutes, then what is
angular deceleration in ( r a d / s e c^{2} ? )
A ( cdot frac{pi}{6} )
в. ( 10 pi )
( c cdot frac{1}{12} )
D. 300
11
448 14. A buoy is attached to three tugboats by three ropes. The
tugboats are engaged in a tug-of-war. One tugboat pulls
west on the buoy with a force Ē, of magnitude 1000 N.
The second tugboat pulls south on the buoy with a force
F of magnitude 2000 N. The third tugboat pulls northeast
(that is, half way between north and east), with a force Fz
of magnitude 2000 N.
a. Express each force in unit vector form (î, j).
b. Calculate the magnitude of the resultant force.
11
449 28. Find the equation of trajectory of the boat.
1/3
C1=1=-(3)”
c.
x=l=u
d. None of these
d. None of these
11
450 Statement 1: If dot product and cross product of ( vec{A} ) and ( vec{B} ) are zero, it implies that one of the vector ( vec{A} ) and ( vec{B} ) must be
a null vector.

Statement 2: Null vector is a vector with
zero magnitude.
A ( . ) 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
451 7. Hailstones falling vertically with a speed of 10 mshi
the wind screen (wind screen makes an angle 30° with the
horizontal) of a moving car and rebound elastically. Find
the velocity of the car if the driver finds the hailstone
rebound vertically after striking.
30°
Fig. 5.187
11
452 A man walks ( 8 mathrm{m} ) towards East and then
( 6 mathrm{m} ) towards North. His magnitude of displacement is equal to:
A . ( 10 mathrm{m} )
B. 14 ( m )
( c cdot 2 m )
D. zero
11
453 A boy sitting on the top most berth in the compartment of a train which is
just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about ( 2 mathrm{m} )
The apple will fall
A. In the hand of his brother
B. Slightly away from the hands of his brother in the direction of motion of the train
c. Slightly away from the hands of his brother in the direction opposite to the direction of motion of the train
D. None of these
11
454 What is a projectile? Give example. 11
455 A wheel has moment of inertia
( 10^{-2} k g-m^{2} ) and is making 10 rps. The
torque required to stop it in 5 secs is
A. 12.56
B. 9.42
( c cdot 6.28 )
D. 3.14
11
456 A man is walking on a road with a velocity ( 3 k m / h . ) Suddenly rain starts falling. Velocity of rain is ( 10 mathrm{km} / mathrm{h} ) in vertically downward direction. The relative velocity of the rain with respect to man is
A ( cdot sqrt{13} k m / h r )
B. ( sqrt{7} mathrm{km} / mathrm{hr} )
c. ( sqrt{109} mathrm{km} / mathrm{hr} )
D. ( 13 mathrm{km} / mathrm{hr} )
11
457 Speed of the current. 11
458 A car travels along a circular path of radius ( left(frac{50}{pi}right) mathrm{m} ) with a speed of ( 10 mathrm{m} / mathrm{s} )
Then what is its displacement after 17.5 seconds.
( A cdot frac{50 sqrt{2}}{pi} )
B. ( frac{50 sqrt{3}}{pi} )
c. ( frac{100 sqrt{2}}{pi} )
D. 175
11
459 1/2 MIIS
luwalus 101
d.
2. A river is flowing from west to east at a speed of 5 m per
min. A man on the south bank of the river, capable of
swimming at 10 m per min in still water, wants to swim
across the river in the shortest time. He should swim in a
direction
(IIT JEE, 1983)
a. Due north
b. 30° east of north
c. 30° west of north d. 60° east of north
worth
11
460 The position of a particle as a function
of time is described by relation ( boldsymbol{x}= )
( 3 t-3 t^{2}+t^{3} ) where the quantities are
expressed in S.I. units. If mass of the particle be ( 10 mathrm{kg} ), the work done in first
three seconds is
A . 10
B. 30 J
c. ( 300 J )
D. 675 J
11
461 A train ( 100 mathrm{m} ) long travelling at ( 40 mathrm{m} / mathrm{s} ) starts overtaking another train ( 200 mathrm{m} ) long travelling at ( 30 mathrm{m} / mathrm{s} ). The time taken by the first train to pass the second train completely is:
A. 30
B. 40
( c .50 mathrm{s} )
D. 60 s
11
462 A helicopter is to reach a point ( 200000 m ) east of his existing place. Its velocity relative to wind blowing at ( 30 k m h^{-1} ) from northwest taking
scheduled arrival time duration as
40minute is
B. ( 279 hat{i}+21 hat{j} )
c. ( 729 hat{i}+12 hat{j} )
D. ( 12 hat{i}+729 hat{j} )
11
463 Prove that the vectors ( 2 hat{i}-3 hat{j}-hat{k} ) and ( -6 hat{i}+9 hat{j}+3 hat{k} ) are parallel. 11
464 9. A particle is projected from a stationary
Fig. A.46
trolley. After projection, the trolley
moves with a velocity 2/15 m/s. For an observer on the
trolley, the direction of the particle is as shown in the
figure while for the observer on the ground, the ball rises
vertically. The maximum height reached by the ball from
the trolley is h meter. The value of h will be
(W.r.t. Trolley)
60
0
10 m/s
Fig. A.47
11
465 The position vector of a particle is ( vec{r}= ) ( (a cos omega t) hat{i}+(a sin omega t) hat{j} . ) The velocity of
the particle is
A. Parallel to position vector
B. Perpendicular to position vector
c. Directed towards the origin
D. Directed from away from the origin
11
466 Velocity of particle moving along a
straight line at any time ( t ) is given by ( v=cos left(frac{pi}{3} tright) . ) The distance travelled by the particle in the first two seconds is equal to
A ( cdot frac{sqrt{3}}{2 pi} )
B. ( frac{3 sqrt{3}}{2 pi} )
( c cdot frac{3 sqrt{3}}{pi} )
D. zero
11
467 What is a projectile? Derive an equation of the path of a projectile 11
468 39. An electric fan has blades of length 30 cm as measured
from the axis of rotation. If the fan is rotating at 1200 rpm,
find the acceleration of a point on the tip of a blade.
11
469 SIP-
Illustration 5.25 A particle is projected with relocity
angle with horizontal. Calculate the time when it is movin
perpendicular to initial direction. Also calculate the velo
at this position.
Initial
direction
Fig. 5.42
11
470 If a body placed at the origin is acted upon by a force ( overline{boldsymbol{F}}=(hat{boldsymbol{i}}+hat{boldsymbol{j}}+sqrt{mathbf{2}} hat{boldsymbol{k}}) )
then which of the following statements are correct?
1.Magnitude of ( overline{boldsymbol{F}} ) is ( (2+boldsymbol{s} boldsymbol{q} boldsymbol{r} boldsymbol{t} boldsymbol{2}) )
2.Magnitude of ( overline{boldsymbol{F}} ) is 2
3. ( bar{F} ) makes an angle of ( 45^{0} ) with the ( Z ) –
axis.
4. ( bar{F} ) makes an angle of ( 30^{0} ) with the ( Z )
axis.
Select the correct answer using the codes given below.
A . 1 and 3
B. 2 and 3
c. 1 and 4
D. 2 and 4
11
471 A ball is projected on smooth inclined
plane in direction perpendicular to line of greatest slope with velocity of ( 8 boldsymbol{m} / boldsymbol{s} )
t’s speed after ( left.1 s text { is (take } g=10 mathrm{m} / mathrm{s}^{2}right) )
( A cdot 10 mathrm{m} / mathrm{s} )
B. ( 15 mathrm{m} / mathrm{s} )
( c cdot 12 m / s )
( D cdot 16 mathrm{m} / mathrm{s} )
11
472 Find the time taken by the boat to reach
the opposite bank.
11
473 Vectors ( bar{A} ) and ( bar{B} ) are equal in
magnitude. The magnitude of ( bar{A}+bar{B} ) is larger than the magnitude of ( overline{boldsymbol{A}}-overline{boldsymbol{B}} ) by
a factor of ( n, ) then the angle between them is
A ( cdot 2 tan ^{-1}(1 / n) )
B. ( tan ^{-1}(1 / n) )
c. ( tan ^{-1}(1 / 2 n) )
D. ( 2 tan ^{-1}(1 / 2 n) )
11
474 In vertical circle, can the motion be uniform circular motion?
A. yes
B. no
c. sometimes
D. none of these
11
475 The captain of a plane wishes to proceed due west. The cruising speed of the plane is ( 245 m / s ) relative to the air.
A weather report indicates that a
( 38 m / s ) wind is blowing from the south to the north. In what direction, measured to due west, should the pilot
head the plane relative to the air? (in
degrees)
( A cdot 8 )
B. 9
( c .6 )
D. 5
11
476 Tlustration 5.44 A man wishes to cross a river in a boat. If
crosses the river in minimum time he takes 10 min with
drift of 120 m. If he crosses the river taking shortest route.
he takes 12.5 min. Find the velocity of the boat with respect
to water.
11
477 43. The velocity of point A on the rod is 2 ms(leftwards) at
the instant shown in Fig. 6.326. The velocity of the point
B on the rod at this instant is
60°
VA = 2 ms-‘
Fig. 6.326
2 mst
b. 1 ms-1
ms-1
d. 13 mst
2 ms
11
478 2. The resultant of A + B is à On reversing the vector B
the resultant becomes . What is the value of R + RŽ ?
(a) A2 + B2
(b) A2 – B2
(c) 2(A2 + B2)
(d) 2(A2 – B2)
11
479 A body of mass Mkg is on the top point of a smooth hemisphere of radius ( 5 mathrm{m} ). It is released to slide down the surface of
hemisphere it leaves the surface when its velocity is ( 5 m s^{-1} ) At this instant the
angle made by the radius vector of the body with the vertical is ( left(g=10 m s^{-2}right) )
A ( cdot cos ^{-1}left(frac{3}{4}right) )
B . ( 45^{circ} )
( c cdot 60 )
D. ( 90^{circ} )
11
480 13. A vector a is turned without a change in its length through
a small angle do. The value of|Aal and Aa are respectively
(a) 0, a de
(b) a do, o
(c) 0,0
(d) None of these
11
481 Find the unit vector in the direction of ( mathbf{3} hat{mathbf{i}}-mathbf{6} hat{mathbf{j}}+mathbf{2} widehat{mathbf{k}} ) 11
482 In uniform circular motion
A. both velocity and speed are constant
B. speed is constant but velocity changes
C. both speed and velocity change
D. velocity is constant but speed changes
11
483 A solid body rotates about a stationary axis according to the law
( varphi=a t-b t^{3}, ) where ( a=6.0 mathrm{rad} / mathrm{s} ) and
( boldsymbol{b}=mathbf{2} . mathbf{0} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}^{mathbf{3}} )
Find the mean values of the angular velocity and angular acceleration averaged over the time interval between
( t=0 ) and the complete stop. The sum of
their magnitudes is x. Find the value of
( mathbf{x} )
11
484 A body is projected horizontally from the top of a hill with a velocity of ( 9.8 m / s ) What time elapses before the vertical velocity is twice the horizontal velocity?
A . 0.5 sec
B. 1 sec
( c .2 s e c )
D. 1.5 sec
11
485 Rain is falling vertically. A man running on the the road keeps his umbrella
tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them
keep their umbrella vertical to avid the
vertical sun-rays. Explain.
11
486 A fielder on the ground throws a ball at an angle of ( 15^{circ} ) to the horizontal with
velocity ( V_{A} ) at the wicket to dismiss the
batsman. Had he thrown the ball at ( 45^{circ} )
with a speed ( V_{B} ) to hit the wicket, then ( frac{V_{B}}{V_{A}} ) is
( ^{A} cdot frac{1}{sqrt{3}} )
в. ( sqrt{2} )
c. ( sqrt{3} )
D. ( frac{1}{sqrt{2}} )
11
487 A projectile ofmass ( m ) is thrown with a
velocity v making an angle ( 60^{circ} ) with the horizontal, neglecting air resistance, the change in momentum from the departure A to its arrival at B, along the vertical directions:
( A cdot 2 m )
B. ( sqrt{3} mathrm{mv} )
( c .3 m v )
D. ( frac{m v}{sqrt{3}} )
11
488 A thin uniform bar of length L and mass ( 8 mathrm{m} ) lies on a smooth horizontal table.
Two point masses ( m ) and 2 m are moving in the same horizontal plane from opposite sides of the bar with
speeds ( 2 v ) and ( v ) respectively. The masses stick to the:
A ( cdot frac{6 v}{5 l} )
в. ( frac{3 v}{5 l} )
c. ( frac{6 v}{11 l} )
D. ( frac{6 v}{l} )
11
489 If the body is moving in a circle of
radius ( r ) with a constant speed ( V ), its angular velocity is
A ( cdot V^{2} / r )
в. ( V r )
c. ( V / r )
D. ( r / V )
11
490 The angular velocity of rotation of hour hand of a watch is how many times the angular velocity of Earth’s rotation
about its own axis?
A. Three
B. Four
c. Two
D. six
11
491 43. A car is moving in east direction. It takes a right turn an
moves along south direction without change in its spee
What is the direction of average acceleration of the car
a. North east
b. South east
c. North west
d. South west
11
11
492 3 m
3. Spotlight S rotates in a horizontal
plane with constant angular velocity of
0.1 rad s . The spot of light P moves
along the wall at a distance of 3 m. The
PO
velocity of the spot P when @ = 45°
spot P when 0 = 45 Fig. A.50
is ms?
(IIT JEE, 1987)
11
493 What will be the effect on the
centripetal acceleration, if both the
speed and the radius of the circular path of the body are doubled?
11
494 23. A particle has initial velocity 4i + 4 ms and an
acceleration -0.4i ms?, at what time will its speed be
5 ms?
a. 2.5
S b . 17.5 S c. S d. 8.5 s
11
495 25. Two particles are thrown horizontally in opposite
directions with velocities u and 2u from the top of a high
tower. The time after which their radius of curvature will
be mutually perpendicular is
a. 24 b. 2 c. –
1 u al u
12 g 2 g
11
496 The locus of a projectile relative to another projectile is a
A. straight line
B. circle
c. ellipse
D. parabola
11
497 The position of a particle is given by ( vec{r} ) ( =3 t hat{i}+2 t^{2} hat{j}+5 hat{k}, ) where ( t ) is in seconds and the coefficients have the proper
units for ( r ) to be in metres. The direction
of velocity of the particle at ( t=1 ) s is:
( A cdot 53^{circ} ) with ( x ) -axis
B. 37 ( ^{circ} ) with ( x ) -axis
c. ( 30^{circ} ) with ( y ) -axis
D. ( 60^{circ} ) with ( y ) -axis
11
498 A particle projected from the origin ( (x=y=0) ) moves in ( x y ) plane so that
its velocity is ( v=(2 hat{i}+4 x hat{j}) mathrm{m} / mathrm{s}, ) when it is at point ( (x, y) ) m. ( (hat{i} text { and } hat{j} ) are the unit vectors along ( x ) and ( y ) axis). What
is the value of ( y, ) when ( x=3 )
A . 15
B. 10
( c .9 )
D. 8
11
499 A projectile is fired with an initial speed
of ( 500 quad m s^{-1} ) horizontally from the top
of a cliff of height ( 19.6 mathrm{m} ). At what distance from the foot of the cliff does it
strike the ground?
11
500 A particle is projected from ground with some initial velocity making an angle
( 45^{circ} ) with the horizontal. It reaches at
height of ( 7.5 mathrm{m} ) above the ground while it travels a horizontal distance of ( 10 mathrm{cm} ) from the point of projection. The initia speed of the projection is
( A cdot 5 m / s )
B. ( 10 mathrm{m} / mathrm{s} )
( c cdot 20 m / s )
D. ( 40 mathrm{m} / mathrm{s} )
11
501 The velocity of the body at the end of 1 s from the start is:
A . 2N
в. ( frac{M+2 N}{4} )
c. ( 2(M+N) )
D. ( frac{2 M+N}{4} )
11
502 On rotating a wheel of radius ( 4 m, a )
force of ( 20 N ) is applied at an angle ( 30^{circ} ) to the radius, at a point of application. The resulting torque on the wheel is:
( mathbf{A} cdot 80 N-m )
B. ( 60 N-m )
c. ( 40 N-m )
D. ( 20 N-m )
11
503 A wheel starts from the rest and attains
an angular velocity of 20 radian/s after being uniformly accelerated for 10 s.The
total angle in radian through which it has turned in 10 second is
A ( .20 pi )
в. ( 40 pi )
( c .100 )
D. ( 100 pi )
11
504 istration 5.54 A person standing on a road has to hold
umbrella at 60° with the vertical to keep the rain away.
We throws the umbrella and starts running at 20 ms. He
find that rain drops are hitting his head vertically. Find the
speed of the rain drops with respect to (a) the road and
(b) the moving person.
1600
lvl = 0
Fig. 5.106
Fig. 5.107
11
505 Give an example of the motion of a body moving with a constant speed, but with a variable velocity. Draw a diagram to represent such a motion. 11
506 A rock is launched upward at 45°. A bee moves along the
trajectory of the rock at a constant speed equal to the initial
speed of the rock. What is the magnitude of acceleration
(in ms) of the bee at the top point of the trajectory? For
the rock, neglect the air resistance.
11
507 15. The direction of a projectile at a certain instant is inclined
at an angle a to the horizontal; after t second, it is inclined
at an angle B. Prove that the horizontal component of the
gt
velocity of the projectile is –
tan a – tan ß
11
508 When a body moves with a constant
speed along a circle:
A. no work is done on it
B. no acceleration is produced in the body
C. no force acts on the body
D. its velocity remains constant
11
509 Two forces each of ( 10 N ) act at an angle
( 60^{circ} ) with each other. The magnitude ( & ) direction of the resultant with respect
to one of the vectors is
11
510 A mass is performing vertical circular motion(see figure).lf The average velocity of theparticle is increased, then
at which point thestring will break:
( A cdot A )
B. B
( c cdot c )
D.
11
511 A body of mass ( 5 k g ) is acted upon by
two perpendicular force ( 8 N ) and ( 6 N ) find the magnitude and direction the
acceleration:
A ( cdot 3 m s^{-2}, theta=cos ^{-1}(0.8) ) from ( 8 N )
B . ( 2 m s^{-2}, theta=cos ^{-1}(0.6) ) from ( 6 N )
c. ( 3 m s^{-2}, theta=cos ^{-1}(0.9) ) from ( 6 N )
D. ( 5 m s^{-2}, theta=cos ^{-1}(0.81) ) from ( 8 N )
11
512 Illustration 5.52 A man moving with 5 ms observes rain
falling vertically at the rate of 10 ms. Find the speed and
direction of the rain with respect to ground.
11
513 There are three particles shown in the figure as I, II and III. The velocity and acceleration vectors associated with
the motion of three particles are shown. Which of the above could represent the
velocity and acceleration vectors for a projectile following a parabolic path?
I.
II.
III.
A. I only
B. II only
c. III only
D. I and II only
E. II and III only
11
514 A body is projected vertically upwards with a velocity of ( 19.6 ~ m / s . ) The total time for which the body will remain in
the air is (Take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} )
A . ( 4 s )
B. ( 6 s )
( mathrm{c} .9 mathrm{s} )
D. 12 s
11
515 A train of length 200 m travelling at 30 ( m s^{-1} ) overtakes another train of length
( 300 mathrm{m} ) travelling at ( 20 mathrm{ms}^{-1} ). The time
taken by the first train to pass the second is
A . 30 sec
B. 40 sec
c. ( 50 mathrm{sec} )
D. 60 sec
11
516 27. Obtain the total time taken to cross the river.
a. (3d/5)1/3
c. (60/5)12
b. (60/5)1/3
d. (2d/3)1/3
11
11
517 A person climbs up a stopped escalator
in ( 60 s . ) If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator?
A. ( 37 s )
в. 27 s
( c cdot 24 s )
D. ( 45 s )
11
518 A man can swim in still water with a
velocity 5 m/s. He wants to reach at
directly opposite point on the other bank of a river which is flowing at a rate of ( 4 m / s . ) River is 15 m wide and the man can run with twice the velocity
as compared with velocity of swimmer
with respect to river. If he swims
perpendicular to river flow and then run along the bank. Time, in seconds, taken by him to reach the opposite point is
A. 4.0
B. 4.2
( c .5 .4 )
D. 3.6
11
519 40. A ball thrown by one player reaches the other in 2 s. The
maximum height attained by the ball above the point of
projection will be about
a. 2.5 m b. 5 m c. 7.5 m d. 10 m
11
520 12. An object is projected from origin in x-y plane in which
velocity changes according to relation v=ai + bxſ. Path
of particle is
a. Hyperbolic b . Circular
c. Elliptical
d. Parabolic
le
200
11
521 Illustration 5.66 Find the time period of the meeting of
minute hand and second hand of a clock.
11
522 A stone is projected with a initial velocity at an angle to the horizontal. small piece separates from the stone
before the stone reaches its maximum
height. Then this piece will
A. fall to the ground vertically
B. fly side by side with the parent stone along parabolic path
c. fly horizontally initially and will trace a different parabolic path
D. lag behind the parent stone, increasing the distance from it.
11
523 4. Four bodies P, Q, R and Sare projected with equal velocities
having angles of projection 15°, 30°, 45° and 60° with the
horizontal respectively. The body having shortest range is
(a) P (b) e (c) R (d) s
11
524 A vector ( overline{boldsymbol{m}} ) of magnitude ( 2 sqrt{101} ) in the
direction of internal bisector of the
angle between the vector ( bar{b}=8 hat{i}-6 hat{j}- ) ( 6 hat{k} ) and ( bar{c}=4 hat{i}-3 hat{j}+4 hat{k} ) is
( A )
B . ( 16 hat{i}-12 hat{j}+2 hat{k} )
( frac{-16 hat{i}+12 hat{j}+2 hat{k}}{5} )
D . ( 16 hat{i}+12 hat{j}+2 hat{k} )
11
525 34. Projection angle with the horizontal is: 11
526 A particle of mass ( 1 mathrm{kg} ) has a velocity of
( 2 mathrm{m} / mathrm{s} . ) A constant force of ( 2 mathrm{N} ) acts on
the particle for 1 s in a direction perpendicular to its initial velocity. Find the velocity and displacement of the particle at the end of 1 s.
11
527 An object may have
This question has multiple correct options
A. Varying speed without having varying velocity
B. Varying velocity without having varying speed
C. Non zero acceleration without having varying velocity
D. Non zero acceleration without having varying speed
11
528 There are three forces acting on an object : 6 N to the left, 5 N to the right and ( 3 mathrm{N} ) to the left.What is the net force
acting on the object?
( A cdot 4 N )
B. 4 N left
c. 4 N right
D. 8 N left
E. None of above
11
529 Two particles having masses ( 1 k g ) and
7 kg respectively attract each other. Initially they are at rest and infinite separation.The velocity of approach of the particles are at a separation of ( 1 boldsymbol{m} ) is (G=universal gravitational constant)
( begin{array}{lll}text { A } cdot sqrt{2} G & text { m/s }end{array} )
B . ( 4 sqrt{G} ) m/s
c. ( sqrt{frac{G}{2} m / s} )
D. ( frac{G}{4} m / s )
11
530 65. The horiz
The horizontal range and maximum height attained by a
roiectile are R and H, respectively. If a constant horizontal
acceleration a = g/4 is imparted to the projectile due to
wind, then its horizontal range and maximum height will be
TH
a. (R+H),
b. R+- 1,2H
2
c. (R+ 2H), H
d. (R+ H), H
11
531 The objects pictured above are coins moving around on a record player. The coins are not sliding on the record player surface. Which coins is moving faster and how many times faster it is moving than the other one? The space between each vertical line along the horizontal arrow is one-
seventh the radius of the circular record
player surface.
A. 1-three times faster than slowest
B. 3-five-seventh’s faster than slowest
c. 3-five times faster than slowest
D. 1-five-seventh’s faster than slowest
E. 2 -three-seventh’s faster than slowest
11
532 A wall clock has a ( 5 mathrm{cm} ) long minute
hand. The average velocity of the tip of the hand reaching 06.00 hrs. to 18.30 hrs. is
A ( .2 .2 times 10^{-4} mathrm{cm} / mathrm{s} )
B. ( 1.2 times 10^{-4} mathrm{cm} / mathrm{s} )
C . ( 5.6 times 10^{-4} mathrm{cm} / mathrm{s} )
D. ( 3.2 times 10^{-4} mathrm{cm} / mathrm{s} )
11
533 A motor ship covers the distance of
( 300 k m ) between two localities on a river
in 10 hours downstream and in 12
hours upstream. Find the flow velocity of the river assuming that these velocities are constant.
A. ( 2.0 mathrm{km} / mathrm{h} )
B. 2.5 km/h
( c .3 mathrm{km} / mathrm{h} )
D. 3.5 km/h
11
534 8. A boat is moving with a velocity 3î +4j with respect to
ground. The water in the river is moving with a velocity
-3i – 4ſ with respect to ground. The relative velocity of
the boat with respect to water is
a. 8 ] b. 6i -87 c. 6i +8î d. 5/2
11
535 In the case of uniform circular motion, which one of the following physical quantities does not remain constant?
A . mass
B. speedd
c. linear momentum
D. kinetic energy
11
536 Fill in the blank.
When body is performing uniform circular motion, its ( _{-}-_{-}-_{-}- ) changes at every points.
11
537 Show that there are two values of time
for which a projectile is at the same height. Also show mathematically that the sum of these two times is equal to
the time of flight.
11
538 A train of length ( 100 m ) travelling at ( 20 m / s ) overtakes another of length
( 200 m ) travelling at ( 10 m / s . ) The time taken by the first train to pass the second train is
A . ( 30 s )
в. ( 50 s )
( c cdot 10 s )
D. ( 40 s )
11
539 If ( R ) is the maximum horizontal range of a particle, then the greatest height attained by it is:
A. ( R )
в. ( 2 R )
c. ( frac{R}{2} )
D. ( frac{R}{4} )
11
540 A wheel having a diameter of 3 m starts
from rest and accelerates uniformly to an angular velocity of 210 r.p.m.in 5 seconds. Angular acceleration of the wheel is
A ( cdot 4.4 pi frac{r a d}{s^{2}} )
В. ( _{3.3 pi} frac{r a d}{s^{2}} )
c. ( _{2.2 pi} frac{r a d}{s^{2}} )
D. ( _{1.1 pi} frac{r a d}{s^{2}} )
11
541 A body is projected up such that its
position vector with time as ( vec{r}= )
( left{3 t hat{i}+left(4 t-5 t^{2}right) hat{j}right} m . ) Here, tis in
seconds.
Find the time and ( x- ) coordinate of
particle when its ( y- ) coordinate is zero.
11
542 Two projectiles are thrown at angles ( Theta )
and ( left(90^{circ} Thetaright) ) with same speed. The ratio
of their horizontal ranges are
( A cdot 1: 1 )
B. ( 1: tan theta )
( c cdot tan theta: 1 )
( mathbf{D} cdot tan ^{2} Theta: 1 )
11
543 Which cannonball reaches a higher
elevation?
( A cdot A )
B. B
c. Both reaches same height
D. Cannot be judged
11
544 If ( S ) identical rain drops each falling with terminal velocity v combine to form a big drop during their fall the terminal velocity of big drop formed is :
( A )
B. ( frac{v}{8} )
( c cdot 4 v )
D. 2v
11
545 the car is moving towards east with a speed of ( 25 mathrm{km} / mathrm{h} ). To the driver of the
car, a bus appears to move towards north with a speed of ( 25 sqrt{3} k m / h . ) What
is the actual velocity of the bus?
A ( cdot 50 k m / h, 30^{circ} ) east of north
B. ( 50 k m / h, 30^{circ} ) north of east
( mathrm{c} cdot 25 k m / h, 30^{circ} ) east of north
D. ( 25 k m / h, 30^{circ} ) north of east
11
546 The diagram below shows four orange
spheres moving in circular paths at
constant speeds. The speeds are indicated by the red arrows.
The radius of the circular path for each
indicated by the green arrows. The mass of each sphere is labeled inside the
boundary of the sphere

How do the sphere rank, according to the magnitudes of their accelerations,
greatest first?
A ( cdot 4,3,1 ) and 2 tie
B. 3,1 and 4 tie, 2
( c .3,2 ) and 4 tie,
D. 1,2 and 3 tie,
E. 1,3,2,4

11
547 If two forces of equal magnitudes act simultaneously on a body in the east and the north directions then
A. The body will displace in the north direction
B. The body will displace in the east direction
c. The body will displace in the north-east direction
D. The body will remain at the rest
11
548 Illustration 3.11 A particle is moving with velocity
v = 100 m s. If one of the rectangular components of a
velocity is 50 ms. Find the other component of velocity and
its angle with the given component of velocity.
11
549 The position vector of a particle is ( r= ) ( (a cos omega t) hat{i}+(a sin omega t) hat{j} . ) The velocity
vector of the particle is
A. parallel to position vector
B. perpendicular to position vector
c. directed towards the origin
D. directed away from the origin
11
550 If a particle moves in a circle with
constant speed, its velocity :
A. remains constant
B. changes in magnitude
c. changes direction
D. changes both in magnitude and directions
11
551
Coro
One
Illustration 5.10 Two graphs of the same projectile motion in
the x- y-plane) projected from origin are shown in Fig. 5.10.
X-axis is along horizontal direction and Y-axis is vertically
upwards. Take g = 10 m s.
(²20)
(2,0)
-t(s)
(m)
(a)
(6)
11
552 What are the speeds of two objects if they move uniformly towards each other, they get ( 4 mathrm{m} ) closer in each second and if they move uniformly in the same direction with the original speeds they get ( 4 mathrm{m} ) closer in each ( 10 mathrm{sec} ? )
A. ( 2.8 mathrm{m} / mathrm{s} ) and ( 1.2 mathrm{m} / mathrm{s} )
B. 5.2 ( mathrm{m} / mathrm{s} ) and ( 4.6 mathrm{m} / mathrm{s} )
c. ( 3.2 mathrm{m} / mathrm{s} ) and ( 2.1 mathrm{m} / mathrm{s} )
D. 2.2 ( mathrm{m} / mathrm{s} ) and ( 1.8 mathrm{m} / mathrm{s} )
11
553 A car with a vertical windsheld moves in
a rain storm at a speed of ( 40 mathrm{km} / mathrm{hr} ) The rain drops fall vertically with constant speed of ( 20 m / s . ) The angle at
which rain drops strike the windsheild
is
A. ( tan ^{-1} frac{5}{9} )
в. ( tan ^{-1} frac{9}{5} )
c. ( quad ) tan ( ^{-1} frac{3}{2} )
D. ( tan ^{-1} frac{2}{3} )
11
554 It is possible to project a particle with a given speed in two possible ways so
that it has the same horizontal range ( boldsymbol{R} ) The product of the times taken by it in the two possible ways is
A ( cdot frac{R}{g} )
в. ( frac{2 R}{g} )
c. ( frac{3 R}{g} )
D. ( frac{4 R}{g} )
11
555 The velocity at the maximum height of projectile is half of its initial velocity projection. The angle of projection is
A . ( 30^{circ} )
B . ( 45^{circ} )
( c cdot 60^{circ} )
D. ( 76^{circ} )
11
556 2. The coordinates of a particle moving in a plane are give
by X(t) = a cos(pt) and y(t) = b sin(pt), where a, bls
and p are positive constants of appropriate dimension
Then
(IIT JEE, 1999
a. The path of the particle is an ellipse.
b. The velocity and acceleration of the particle are normal
to each other at t = Td2p.
c. The acceleration of the particle is always directed
towards a focus.
d. The distance travelled by the particle in time interval
t=0 to t = 7/2p is a.
11
557 W
5vou que veuww
38. A cyclist is riding with a speed of 27 kmh. As he
approaches a circular turn on the road of radius 80 m, he
applies brakes and reduces his speed at the constant rate
of 0.5 ms?. What is the magnitude and direction of the
net acceleration of the cyclist on the circular turn?
11
558 A bicycle travels ( 3.2 k m ) due east in ( 0.1 h )
the ( 3.2 k m ) at 15.0 degrees east of
north in ( 0.21 h ), and finally another
( 3.2 k m ) due east in ( 0.1 h ) to reach its
destination. The time lost in turning is negligible. What is the average velocity for the entire trip? (in ( mathrm{km} / mathrm{h}) )
A . 20
B . 21
c. 19
D. 30
11
559 A cyclist bends while taking turn to
A. Reduce friction
B. Generate required centripetal force
c. Reduce apparent weight
D. Reduce speed
11
560 30. As shown in Fig. 6.315, if acceleration of M with respect
to ground is 2 ms, then
sin 37° = 3/5
cos 37° = 4/5
a = 2 ms-2
M
37°N
Fig. 6.315
a. Acceleration of m with respect to M is 5 ms.
b. Acceleration of m with respect to ground is 5 ms2
c. Acceleration of m with respect M is 2 ms 2
d. Acceleration of m with respect to ground is 10 ms?.
11
561 In a Circus, a motor-cyclist having mass
of ( 50 k g ) moves in a spherical cage of
radius ( 3 m . ) Calculate the least velocity
with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point.
11
562 An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartment with velocity v. The middle part of the train passes past the same pole with a velocity of
A ( cdot frac{u+v}{2} )
в. ( frac{u^{2}+v^{2}}{2} )
c. ( sqrt{frac{u^{2}+v^{2}}{2}} )
D. ( sqrt{frac{u^{2}-v^{2}}{2}} )
11
563 A man wants to reach point B on the
opposite bank of river flowing at a speed as shown in figure. What
minimum speed relative to water
should the man have so that he can
reach point B?
11
564 A train ( S 1, ) moving with a uniform
velocity of ( 108 mathrm{km} / mathrm{h} ), approaches
another train ( S 2 ) standing on a platform. An observer 0 moves with a
uniform velocity of ( 36 mathrm{km} / mathrm{h} ) towards ( S 2 )
as shown in figure. Both the trains are
blowing whistles of same frequency 120
Hz. When 0 is 600 m away from ( S 2 ) and
distance between ( S 1 ) and ( S 2 ) is ( 800 m )
the number of beats heard by 0 is
(Speed of the sound ( = )
( 330 mathrm{m} / mathrm{s} )
11
565 A helicopter flies horizontally with
constant velocity in a direction ( boldsymbol{theta} ) east of
north between two points ( boldsymbol{A} ) and ( boldsymbol{B}, ) at distance d apart. Wind is blowing from south with constant speed u; the speed of helicopter relative to air is nu, where
( mathbf{n}>1 . ) Find the speed of the helicopter along AB. The helicopter returns from B
to A with same speed nu relative to air in same wind. Find the total time for the
journeys.
11
566 A player throws a ball which reaches the
other players in 4 sec.If the height of each player is ( 1.8 m . ) The maximum
height attained by the ball above the ground is ( -ldots-ldots )
A . 19.4
B. 20.4
c. 21.4
D. 22.4
11
567 9. A car is moving towards east with a speed of 25 kmh.
To the driver of the car, a bus appears to move towards
north with a speed of 2513 km h-. What is the actual
velocity of the bus?
a. 50 km h, 30º E of N
b. 50 km h, 30° N of E
c. 25 km h, 30° E of N
d. 25 km h, 30° N of E
11
568 A body of mass 5 kg is raised vertically to a height of ( 10 mathrm{m} ) by a force of ( 170 mathrm{N} ) the velocity of the body at this height will be
( mathbf{A} cdot 15 m / s )
в. ( 37 m / s )
c. ( 9.8 m / s )
D. ( 21.9 mathrm{m} / mathrm{s} )
11
569 A body of mass ( mathrm{m} ) is projected from
ground with speed ( u ) at an angle ( theta ) with
horizontal the power delivered by
gravity to it at half of maximum heigh from ground is
11
570 If the velocity of a particle is ( boldsymbol{v}=boldsymbol{A} boldsymbol{t}+ )
( B t^{2}, ) where ( A ) and ( B ) are constants, then
the distance travelled by it between 1 s
and ( 2 s ) is
A ( cdot frac{3}{2} A+4 B )
B. ( 3 A+7 B )
c. ( frac{3}{2} A+frac{7}{3} B )
D. ( frac{A}{2}+frac{B}{3} )
11
571 8. Two forces P and Q acting at a point are such that if P is
reversed, the direction of the resultant is turned through
90°. Prove that the magnitudes of the forces are equal.
11
572 U. TOM 010
21. Raindrops are hitting the back of a man walking at a
of 5 kmh. If he now starts running in the same direct
with a constant acceleration, the magnitude of the velo
of the rain with respect to him will
a. gradually increase
b. gradually decrease
c. first decrease then increase
d. first increase then decrease
11
573 In projectile motion, power of the gravitational force This question has multiple correct options
A. is constant throughout
B. is negative for first half, zero at topmost point and positive for rest half
c. varies linearly with time
D. is positive for complete path
11
574 3. A body is projected vertically up with a velocity v and
after some time it returns to the point from which it was
projected. The average velocity and average speed of the
body for the total time of flight are
(a) 7/2 and v/2
(b) O and v/2
(c) 0 and 0
(d) v/2 and 0
11
575 A ball is projected from the ground at an
angled of ( 45^{circ} ) with the horizontal surface. It reaches a maximum height of ( 120 mathrm{m} ) and returns to the ground.
Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of
( 30^{circ} ) with the horizontal surface. The
maximum height it reaches after the bounce, in metres, is
11
576 If a disc starting from rest acquires an
angular velocity of 240 revolution/ min in ( 10 s, ) then its angular acceleration
will be
A . 1.52 rads( ^{-1} )
B. 3.11 rads ( ^{-1} )
c. 2.51 rads ( ^{-1} )
D. 1.13 rads( ^{-1} )
11
577 A gramophone turntable rotating at an angular velocity of 3 rad( / )s stops after one revolution. Find the angular
retardation. (in ( left.r a d / s^{2}right) )
( mathbf{A} cdot 0.698 )
B. 0.125
c. 0.569
D. 0.716
11
578 Assertion
In case of uniform linear motion,
acceleration remains zero.
Reason Velocity remains constant in uniform
linear motion.
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
579 Matching con
iven and in list
10. In list I some straight line
corresponding signs of slopes
he straight lines graphs are given and in i
es and intercepts are given
ch the type of graphs of list I corresponding to sign
of slopes and intercepts in list
List I
(D)
T
(C)
4
List II
(i) Positive slopez
(iii) Positive intercept
(v) Zero intercept
(ii) Negative slope
(iv) Negative intercept
(vi) Zero slope
11
580 In uniform circular motion, the velocity vector and acceleration vector are:
A. perpendicular to each other
B. in the same direction
c. opposite in direction
D. not related to each other
11
581 19. During a projectile motion, if the maximum height equals
the horizontal range, then the angle of projection with the
horizontal is
a. tan-‘(1) b. tan-‘(2) c. tan-‘(3) d. tan-(4)
11
582 Three particles ( A, B ) and ( C ) are situated at the vertices of an equilateral triangle ABC of side d at time ( t=0 . ) Each of the
particles moves with constant speed v. A always has its velocity along ( mathrm{AB}, mathrm{B} ) along BC and ( C ) along CA. At what time will the particles meet each other?
A ( cdot frac{2 d}{3 v} )
в. ( frac{3 d}{2 v} )
c. ( frac{4 d}{3 v} )
D. ( frac{3 d}{4 v} )
11
583 The radius of the blade of fan is ( 0.3 mathrm{m} ). It
is making 1200 rev/min.The acceleration of a particle at the tip of the blade is:
A ( cdot 3733 m / s^{2} )
В. ( 2733 m / s^{2} )
c. ( 4733 m / s^{2} )
D. ( 5733 m / s^{2} )
11
584 A maglev train is gradually taking a ( 45^{circ} ) turn while moving with constant-speed
of ( pi m s^{-1} . ) For a special compartment
of train, turning process takes ( 220 m ) length on the track. Magnitude of centripetal acceleration of the train is:
A cdot Is constant and ( frac{pi}{88} m s^{-2} ) (approximately)
B. Is variable
c. zero, as speed is constant
D. Either (2) or (3)
11
585 A block of mass ( m=1 k g ) has speed
( v=4 m / s ) at ( theta=60^{circ} ) on a circular track
of radiu ( R=2 m ) as shown in figure.
Coefficient of kinetic friction between
the block and the track is ( mu_{k}=0.5 ) tangential acceleration of the block at this instant is approximately.
A ( .2 .1 m / s^{2} )
В ( cdot 5 m / s^{2} )
( mathrm{c} cdot 1.2 mathrm{m} / mathrm{s}^{2} )
D. ( 3 m / s^{2} )
11
586 Fig. 5.208
12. The vertical component
of the velocity of block at A is
a. 3 b. 2/8 c. 3/
d. 48
11
587 A particle is projected up an inclined plane of inclination ( beta ) at an elevation a
to the horizon. Show that
a. ( tan alpha+cot beta+2 tan beta, ) if the particle
strikes the plane at right angles
b. ( tan alpha=2 tan beta ) if the particle strikes
the plane horizontally.
11
588 A motorboat is racing towards the north at ( 25 k m h^{-1} ) and the water current in
that region is ( 10 mathrm{kmh}^{-1} ) in the direction
of ( 60^{circ} ) east of south. The resultant
velocity of the boat is:
( mathbf{A} cdot 11 mathrm{kmh}^{-1} )
B . 22 ( k m h^{-1} )
c. ( 33 mathrm{kmh}^{-1} )
D. ( 44 mathrm{kmh}^{-1} )
11
589 A man in a car at location ( Q ) on a
straight highway is moving with speed
( boldsymbol{v} . ) He decides to reach a point ( boldsymbol{P} ) in a
field at a distance ( boldsymbol{d} ) from highway
(point ( M) ) as shown in the figure. Speed
of the car in the field is half to that on
the highway. What should be the
distance ( R M, ) so that the time taken to
reach P is minimum?
A ( cdot frac{d}{sqrt{3}} )
B. ( d ) ( overline{2} )
c. ( frac{d}{sqrt{2}} )
D.
11
590 Assertion
In case of a projectile, the angle
between velocity and acceleration changes from point to point.
Reason
Because its horizontal component of
velocity remains constant, while vertical component of velocity changes from point to point due to gravitational acceleration.
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
c. Assertion is true, but the Reason is false
D. Assertion is false, but the Reason is true.
11
591 be
ical to keep
ms, and find
18. A man holds an umbrella at 30° with the vertical to
himself dry. He, then, runs at a speed of 10 ms, an
the rain drops to be hitting vertically. Study the follow
statements and find the correct options.
i. Velocity of rain w.r.t. Earth is 20 ms-
ii. Velocity of rain w.r.t. man is 10/3 ms!
iii. Velocity of rain w.r.t. Earth is 30 ms!
iv. Velocity of rain w.r.t. man is 10/2 ms-
a. Statements (i) and (ii) are correct.
b. Statements (i) and (iii) are correct.
c. Statements (iii) and (iv) are correct.
d. Statements (ii) and (iv) are correct.
D
.
11
592 The acceleration experienced by a moving boat after its engine is cut-off, of given by: ( a=-k v^{3} ) where ( k ) is a
constant. If ( v_{0} ) is the magnitude of
velocity at cut-off, then the magnitude
of the velocity at time ( t ) after the cut-off is :-
A ( cdot frac{v_{0}}{2 k t v_{0}^{2}} )
В. ( frac{v_{0}}{1+2 k t v_{0}^{2}} )
c. ( frac{v_{0}}{sqrt{1-2 k t v_{0}^{2}}} )
D. ( frac{v_{0}}{sqrt{1+2 k t v_{0}^{2}}} )
11
593 An object is moving in the ( x-y ) plane
with the position as a function of time ( operatorname{given} operatorname{by} vec{r}=x(t) hat{i}+y(t) hat{j} . ) Point ( O ) is at
( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0 .} ) The object definitely
moving towards 0 when
A ( cdot v_{x}>0, v_{y}>0 )
0
B ( cdot v_{x}<0, v_{y}<0 )
( mathbf{c} cdot x v_{x}+y v_{y}0 )
11
594 Consider the diagram of the trajectory
of a thrown tomato. At what point is the
potential energy greatest?
11
595 19. At the highest point of its trajectory
u² cos²0
√3u² cos² e
28
u² cos²0 a √3 u² cos²0
b. – 28
11
596 8. The horizontal distance between two bodies, when their
velocity are perpendicular to each other, is
a. I
m b . 0.5 m c. 2 m d. 4 m
11
597 Rain is falling vertically with a speed of ( 20 m / s . ) After sometime wind starts blowing with a speed of ( 12 m / s ) in east to west direction in which direction
should a boy waiting at a bus stop hold his umbrella.
11
598 8. A launch travels across a river from a point A to a point
B of the opposite bank along the line AB forming angle a
with the bank. The flag on the mast of the launch makes
an angle ß with its direction of motion. Determine the
speed of the launch w.r.t. the bank. The velocity of wind
is u perpendicular to the stream.
Δα
A
Fig. 5.188
11
599 14. The time taken by the block to move from A to C is
Ve b
at . 14v3
V8
11
600 If the frequency of the particle
performing circular motion increases from 60 rmp to 180 rpm is 20 seconds,
its angular acceleration is
A ( cdot 0.1 mathrm{rad} / mathrm{s}^{2} )
B. 3.142 ( r a d / s^{2} )
c. 0.6284 rad ( / s^{2} )
D. 0.3142 rad/s ( ^{2} )
11
601 A ball projected from the ground at a
certain angle has:
A. minimum velocity at the point of projection and maximum velocity at the maximum height
B. maximum velocity at the point of projection and minimum velocity at the maximum height
C. same velocity at any point in its path
D. zero velocity at the maximum height irrespective of the velocity of projection
11
602 Two vectors whose magnitudes are in ratio 1: 2 gives resultant of magnitude
30. If angle between these two vectors is
( 120^{circ}, ) then the magnitude of two vectors will be
A. ( 10 sqrt{3}, 20 sqrt{3} )
3
B . ( 5 sqrt{3}, 10 sqrt{3} )
D. ( 2 sqrt{3}, 4 sqrt{3} )
11
603 73. A body is moving in a circular path with a constant speed.
It has
a. A constant velocity
b. A constant acceleration
c. An acceleration of constant magnitude
d. An acceleration which varies with time in magnitude
A
1
1 with uniform
11
604 A stationary wheel starts rotating about its own axis with an angular acceleration of 5.5 rad ( / s^{2} . ) To acquire an angular velocity 420 revolutions per minute, the number of rotations made
by the wheel is:
A . 14
B . 21
( c cdot 28 )
D. 35
11
605 Identify the direction of the angular velocity vector for the second hand of a
clock going from 0 to 60 seconds?
A. Outward from the clock face
B. Inward toward the clock face
D. Downward
E. To the right
11
606 Illustration 5.75 Two particles A and B are moving as shown
in Fig. 5.158. At this moment of time, find the angular speed
of A relative to B.
11
607 A man in a minivan rounds a circular
turn at a constant speed.

Which of the following would cause the
minivan to experience less
acceleration?
A. Traveling faster
B. Traveling around a turn with a smaller circular radius
C. Traveling with more weight in the van
D. Traveling around a turn with a greater circular radius
E. Traveling the opposite direction around the same turn

11
608 The path followed by a projectile is called its:
A. trajectory
B. range
c. amplitude
D. none of these
11
609 A ball in thrown from a roof top at an
angle ( 45^{circ} ) above the horizontal. It hits
the ground a few second later. At what
point during its motion, does the ball have greatest acceleration?
11
610 Assertion
Linear momentum of a body changes even when it is moving uniformly in a
circle.
Reason
In uniform circular motion velocity
remains constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
611 A bus is moving with a speed of ( 10 mathrm{ms}^{-1} )
on a straight road. A scooterist wishes
to overtake the bus in 100 s. If the bus is
at a distance of ( 1 mathrm{km} ) from the scooterist, with what speed should the scooterist chase the bus?
A. ( 40 mathrm{ms}^{-1} )
B. 25 ( m s^{-1} )
( mathrm{c} cdot 10 mathrm{ms}^{-1} )
D. ( 20 mathrm{ms}^{-1} )
11
612 A body is moving along a straight line.
Its distance ( X_{t} ) from a point on its path
at a time ( t ) after passing that point is
given by ( X_{t}=8 t^{2}-3 t^{3}, ) where ( X_{t} ) is in
meter and ( t ) is in second. The correct
statement(s) is/are:
This question has multiple correct options
A. Average speed during the interval ( t=0 ) s to ( t=4 s ) is ( 20.21 mathrm{ms}^{-1} )
B. Average velocity during the interval ( t=0 ) s to ( t=4 s ) is
( -16 m s^{-1} )
C. The body starts from rest and at ( t=frac{16}{9} s ) it reverses its
direction of motion at ( x_{t}=8.43 mathrm{m} ) from the start
D. It has an acceleration of ( -56 mathrm{ms}^{-2} ) at ( t=4 mathrm{s} )
11
613 U TOM U
Us
10. Two forces 3 N and 2 N are at an angle o such that the
resultant is R. The first force is now increased to 6 N and
the resultant become 2R. The value of O is
(a) 30° (b) 60° (c) 90° (d) 120°
11
614 Which one of the following is most probably not a case of uniform circular
motion?
A. Motion of a racing car on a circular track
B. Motion of the moon around the earth
c. Motion of a toy train on a circular track
D. Motion of seconds hand on the circular dial of a watch
11
615 1. The shortest distance between the motorcyclist and the
car is
a. 10 m b. 20
m c . 30 m d. 40 m
11
616 Illustration 5.4 At what angle should a projectile be thrown
such that the horizontal range of the projectile will be equal
to half of its maximum value?
11
617 In uniform linear motion, the speed and
velocity are
A. Constant
B. Variable
c. zero
D. All
11
618 If it turns an angle of ( y ) rad in these ( 3 s )
then ( 2 y ) is equal to ( 250+x ). Find ( x )
11
619 If ( bar{a}=hat{i}-hat{j}+hat{k} ) and ( bar{b}=2 hat{i}-hat{j}+3 hat{k} )
then the unit vector along ( bar{a}+bar{b} ) is
A ( cdot frac{3 hat{i}+4 hat{k}}{5} )
B. ( frac{-3 hat{i}+4 hat{k}}{5} )
c. ( frac{-3 hat{i}-4 hat{k}}{5} )
D. none of these
11
620 The relation ( 3 t=sqrt{3 x}+6 ) describes
the displacement of a particle in one direction where ( x ) is in meters and ( t ) in
seconds. The displacement when velocity is zero is:
A ( .24 m )
B. ( 12 m )
( c .5 m )
D. zero
11
621 7. Two particles are projected from the same point with the
same speed at different angles e, & e, to the horizontal.
They have the same range. Their times of flight are t,& t2
respectively.
(a) 1 = tan²0, (b) 11 = 12
sin e, cos 2
t1 = tan ,
(d) 1 = tan? Q2
11
622 A stone tied to the end of a string ( 80 mathrm{cm} ) long is whirled in a horizontal circle
with a constant speed. If the stone makes 14 revolutions in 25 s, the magnitude of acceleration is :
A ( cdot 20 m s^{-2} )
В ( cdot 12 m / s^{2} )
c. ( 27.53 m s^{-2} )
( mathbf{D} cdot 8 m s^{-2} )
11
623 16. The vertical component of the velocity of projectile is
a. 3v sin o b. v sine c. vsin d v sin
12
3
11
624 If the magnitude of its angular speed at
( boldsymbol{t}=mathbf{3 . 0 s} ) is ( boldsymbol{x} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}, ) find ( boldsymbol{2} boldsymbol{x} )
11
625 Six particles situated at the corners of a regular hexagon of side ( a ) move at a
constant speed ( v ). Each particle maintains a direction towards the
particle at the next corner. Calculate the time the particles will take to meet each other.
A ( cdot frac{2 a}{3 v} )
в. ( frac{v}{a} )
c. ( frac{2 a}{v} )
D. ( frac{a}{3 v} )
11
626 A ship ( A ) is moving Westwards with a speed of ( 10 mathrm{km} h^{-1} ) and a ship ( mathrm{B} 100 mathrm{km} )
South of ( A ) is moving northwards with a speed of ( 10 mathrm{km} h^{-1} ). The time after
which the distance between them
becomes shortest is
( mathbf{A} cdot 0 h )
в. ( 5 h )
c. ( 5 sqrt{2} h )
D. ( 10 sqrt{2} h )
11
627 A body crosses the topmost point of a vertical circle with critical speed. What
will be its centripetal acceleration when the string is horizontal:
( mathbf{A} cdot g )
B. ( 2 g )
c. ( 3 g )
D. ( 6 g )
11
628 Is it possible to have an accelerated motion with a constant speed? Name such type of motion
A. Yes, Uniform Circular Motion
B. Yes, Non-Uniform Circular Motion
c. Yes, Uniform Linear Motion
D. No
11
629 When two bodies approach each other
with different uniform speeds, the distance between them decreases by
( 120 m ) per every 1 min. If they move in
the same direction, the distance between them increases by
( 90 m ) per every 1 min. The speeds of the
bodies are respectively.
A ( .2 m / s, 0.5 m / s )
B. ( 3 m / s, 2 m / s )
c. ( 1.75 m / s, 0.25 m / s )
D. ( 2.5 m / s, 0.5 m / s )
11
630 Two particles projected from the same point with same speed ( u ) at angles of
projection ( alpha ) and ( beta ) strike the horizontal
ground at the same point. If ( boldsymbol{h}_{1} ) and ( boldsymbol{h}_{mathbf{2}} ) are the maximum heights attained by
the projectile, ( boldsymbol{R} ) is the range for both ( boldsymbol{t}_{1} )
and ( t_{2} ) are their times of flights,
respectively, then This question has multiple correct options
( mathbf{A} cdot alpha+beta=frac{pi}{2} )
B . ( R=4 sqrt{h_{1} h_{2}} )
c. ( frac{t_{1}}{t_{2}}=tan alpha )
D ( cdot tan alpha=sqrt{frac{h_{1}}{h_{2}}} )
11
631 A ball is moving with speed ( 20 mathrm{m} / mathrm{s} ) collides with a smooth surface as
shown in figure. The magnitude of change in velocity of the ball will be
(Smooth horizontal surface)
( mathbf{A} cdot 10 sqrt{3} mathrm{m} / mathrm{s} )
B. ( 20 sqrt{3} mathrm{m} / mathrm{s} )
( c cdot frac{40}{sqrt{3}} m / s )
D. ( 40 mathrm{m} / mathrm{s} )
11
632 How does uniform circular motion differ
from uniform linear motion?
11
633 A particle is moving along a fixed
circular orbit with uniform speed. Then
the correct statement among the
following is:
A. Angular momentum of particle is constant only in magnitude but its direction changes from point to point
B. Angular momentum of particle is constant only in direction but its magnitude changes from point to point
C. Angular momentum of particle is constant both in magnitude and direction
D. Angular momentum of particle is not constant both in magnitude and direction
11
634 10
u. 20
S
shot is fired at an angle to the horizontal such that it
strikes the hill while moving horizontally. Find the initial
angle of projection 0.
370
Fig. 6.25
a. tan
=
b. tan e = 3
c. tan 0 = =
d. None of these
11
635 Which parameters shown below are common between uniform circular
motion and uniform linear motion
A. Velocity
B. Speedd
c. Displacement
D. Acceleration
11
636 Two masses are connected by a spring as shown in the figure. One of the
masses was given velocity ( v=2 k ) as
shown in figure where ( k ) is the spring
constant. Then maximum extension in
the spring will be? (initially spring is in natural length)
A . 2 m
в. ( m )
( mathrm{c} cdot sqrt{2 m k} )
D. ( sqrt{3 m k} )
11
637 Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity
( boldsymbol{v} ) and other with a uniform acceleration
( a . ) If ( alpha ) is the angle between the lines of
motion of two particles then the least value of relative velocity will be at time
given by
B. ( (v / a) cos alpha )
( mathbf{D} cdot(v / a) cot alpha )
11
638 8. A car moves on a circular road describing equal angles
about the centre in equal intervals of time. Which of the
following statements about the velocity of car are not
true?
a. Velocity is constant.
b. Magnitude of velocity is constant but the direction
changes.
c. Both magnitude and direction of velocity change.
d. Velocity is directed towards the center of circle.
11
639 Assertion
A particle has constant acceleration is
x-y plane. But neither of its acceleration
components ( left(a_{x} text { and } a_{y}right) ) is zero. Under
this condition particle can not have
parabolic path.
Reason
In projectile motion, horizontal component of acceleration is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
640 A man can row a boat with ( 4 k m / h ) in
still water. If he is crossing a river where the current is ( 2 k m / h . ) Width of river is 4 k ( m ). In what direction should he head
the boat if he wants to cross the river in
shortest time and what is this
minimum time?
A. Parallel to river current, 2 hrs
B. Perpendicular to river current, 2 hrs
C. Parallel to river current, 1 hrs
D. Perpendicular to river current, 1 hrs
11
641 On the application of a constant torque, a wheel is turned from rest through 400
radian in ( 10 s . ) Calculate its angular
acceleration. ( left(operatorname{in} r a d / s^{2}right) )
A . 8
B. 9
( c cdot 4 )
D.
11
642 **
*
*
*
1. Just as the student starts his free fall, he presses the button
of the stopwatch. When he reaches at the top of 100th floor,
he has observed the reading of stopwatch as 00:00:06:00
(hh: mm: ss: 100th part of the second). Find the value of
8. (Correct up to two decimal places)
a. 10.00 ms-2
b. 9.25 ms-2
c. 9.75 ms-2
d. 9.50 ms 2
11
643 16. If Tin the total time of flight, h is the maximum height
and R is the range for horizontal motion, the x and y co
ordinates of projectile motion and time t are related as
.. (-) -an)–)
6. -a-(1)-1) . =an(*)(* = 5)
11
644 Between ( t=10 ) s and ( t=20 s, ) the
merry-go-round.
A. rotates clockwise, at a constant rate
B. rotates clockwise, and slows down
C. rotates counterwise, at a constant rate
D. rotates counterclockwise, and slows, down
11
645 Two force ( 5 k g-w t . ) And ( 10 k g-w t ) are
acting with an inclination of ( 120^{circ} )
between them. Find the angle when the
resultant marks with ( 10 k g-w t )
11
646 A body tied to a string of length Lis
revolved in a vertical circle with
minimum velocity, when the body
reaches the upper most point the string breaks and the body moves under the
influence of the gravitational field of earth along a parabolic path.
The horizontal range ( A C ) of the body will be:
A ( . x=L )
В . ( x=2 L )
c. ( x=2 sqrt{2 L} )
D. ( x=sqrt{2 L} )
11
647 VI “PIO
I SUS.
24. Two particles start moving simultaneously with constant
velocities u, and uz as shown in Fig 5.194. First particle
starts from A along AO and second starts from O along
OM. Find the shortest distance between them during their
motion.
N
xo
Fig. 5.194
11
648 A particle is moving along a circular path of radius ( 5 m ) with a uniform
speed ( 5 m s^{-1} . ) What will be the average
acceleration when the particle completes half revolution?
A. Zero
B. ( 10 mathrm{ms}^{-2} )
( mathbf{c} cdot 10 pi mathrm{ms}^{-2} )
D. ( frac{10}{pi} m s^{-2} )
11
649 The equation of projectile is ( y=16 x- )
( frac{5 x^{2}}{4} ) Find the horizontal range.
( mathbf{A} cdot R=13.8 m )
В. ( R=8 m )
c. ( R=12.8 mathrm{m} )
D. ( R=9 m )
11
650 A train of ( 150 mathrm{m} ) length is going towards
north direction at a speed of ( 10 mathrm{ms}^{-1} . mathrm{A} )
parrot flies at a speed of ( 5 m s^{-1} ) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:
A . 12
B. 8 s
( c cdot 15 s )
D. 10 s
11
651 A wheel completes 2000 revolutions to cover the ( 9.5 mathrm{km} ) distance, then the diameter of the wheel is
A . ( 1.5 mathrm{m} )
B. ( 1.5 mathrm{cm} )
c. ( 7.5 mathrm{cm} )
D. 7.5 ( m )
11
652 The product of two vectors ( vec{A} ) and ( vec{B} ) may
be:
This question has multiple correct options
( mathbf{A} cdot geq A B )
в. ( leq A B )
c. ( <A B )
D. zero
11
653 The horizontal range of a projectile fired at an angle of ( 15^{circ} ) is ( 50 mathrm{m} ). If it is fired with the same speed at an angle of ( 45^{circ} ) its range will be:
A. ( 60 mathrm{m} )
B. 71
c. ( 100 mathrm{m} )
D. ( 141 mathrm{m} )
11
654 A blue car rounds a circular turn at a
constant speed of ( 30 m / s . ) A grey van rounds the same turn at a constant
speed of ( 15 m / s . ) How does the magnitude of the acceleration of the blue car compare to the magnitude of the acceleration of the grey van?
A. The accelerations of both vehicles are zero, since neither is changing speed
B. The magnitude of the blue car’s acceleration is twice the magnitude of the grey van’s acceleration
c. The magnitude of the blue car’s acceleration is four times the magnitude of the grey van’s acceleration
D. The magnitude of each car’s acceleration is the same, but is not zero
E. We do not have enough information to determine the relative magnitudes of acceleration for the cars in this questions
11
655 21. In going from one city to another, a car travels 75 km
north, 60 km north-west and 20 km east. The magni-
tude of displacement between the two cities is (take
1/2 = 0.7)
a. 170 km b. 137 km c. 119 km d. 140 km
11
656 A fighter plane flying horizontally at an altitude of ( 1.5 k m ) with speed ( 720 k m / h ) passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for
the shell with muzzle speed 600 ms( ^{-1} ) to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? Take ( g=10 m s^{-2} )
11
657 Two vectors ( X ) and ( Y ) are added together.
Which of the following statements
could be true?
I. The resultant magnitude is smaller
than X.
II. The resultant magnitude is larger
than ( Y )
III. The resultant direction is the same
as either ( X ) or ( Y )
A. I only
B. II only
C. I and III only
D. II and III only
E . ।, ॥।, and III
11
658 A centrifuge starts rotating from rest
and reaches a rotational speed of 8,000 radians/sec in 25 seconds. Calculate
the angular acceleration of the
centrifuge?
A. 160 radians ( / )sec( ^{2} )
B. 320radians/sec^
c. 640 radians / sec ( ^{2} )
D. 10,000 radians ( / )sec( ^{2} )
E .20,000 radians / sec ( ^{2} )
11
659 In uniform circular motion, direction of velocity goes on changing continuously, however the magnitude of velocity is constant.
A. True
B. False
11
660 8. In Fig. A.46, find the horizontal velocity
u (in ms-l) of a projectile so that it
hits the inclined plane perpendicularly.
Given H = 6.25 m.
30°
A
ialiniated from a static
11
661 5. The path of a projectile in the absence of air drag is shown
in the figure by dotted line. If the air resistance is not
ignored then which one of the path shown in the figure is
appropriate for the projectile
A
B
C
D
(a) B
(b) A
(c) D
(d) c
.
11
662 with a velocity of 5 ms. The
1. A river is flowing towards with a velocity 01
boat velocity is 10 ms. The boat crosses the river by
shortest path. Hence,
a. The direction of boat’s velocity is 30° west of
b. The direction of boat’s velocity is north-west.
c. Resultant velocity is 53 ms.
d. Resultant velocity of boat is 5/2 ms.
11
663 The position vector of a particle ( vec{R} ) as a function of time is given by:
( overrightarrow{boldsymbol{R}}=boldsymbol{4} sin (2 pi t) hat{hat{i}}+4 cos (2 pi t) hat{j} )
where ( R ) is in meters, ( t ) is in seconds
and ( hat{i} ) and ( hat{j} ) denote unit vectors along ( x ) and y- directions, respectively. Which one of the following statements is wrong for the motion of particle?
A. Path of the particle is a circle of radius ( 4 mathrm{m} )
B. Acceleration vector is along ( -vec{R} ).
C. Magnitude of acceleration vector is ( frac{v^{2}}{R} ), where ( v ) is th velocity of particle
D. Magnitude of the velocity of particle is ( 8 mathrm{m} / mathrm{s} )
11
664 Write down a unit vector in ( X Y ) – plane,
making an angle of ( 30^{circ} ) with the
positive direction of ( boldsymbol{x} ) – axis.
11
665 For a particle performing uniform circular motion, choose the incorrect
statement from the following.
A. Magnitude of particle velocity (speed) remains constant
B. Particle velocity remains directed perpendicular to radius vector
c. Direction of acceleration keeps changing as particle moves
D. Magnitude of acceleration does not remain constant
11
666 The maximum height attained by a projectile is found to be equal to 0.433 of horizontal range. The angle of projection of this projectile is
A ( .30^{circ} )
В ( cdot 45^{circ} )
( c cdot 60^{0} )
D. ( 75^{circ} )
11
667 A wheel is making revolutions about its axis with uniform angular acceleration.
Starting from rest, it reaches 100 rev/sec in 4 seconds.Find the angular
acceleration. Find the angle rotated during these four seconds.
11
668 15. Twelve persons are initially at 12 corners of a regular
polygon of 12 sides of side a. Each person now moves
with a uniform speed v in such a manner that 1 is always
directed towards 2, 2 towards 3, 3 towards 4, and so on.
The time after which they meet is
a.
La

b.
b.
– 2a
2a
c. v(2+√3)
d. v(2-√3)
11
669 A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ( omega . ) Show that a small bead on the wire loop remains at its lower most point for ( omega leq sqrt{g / R} ). What
is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ( omega= )
( sqrt{2 g / R} ? ) Neglect friction.
11
670 If a particle is kept at rest at origin,
another particle starts from (5,0) with a velocity of ( -4 hat{i}+3 hat{j} ). Find their
closest distance of approach.
( A .3 m )
в. ( 4 m )
( c .5 m )
D. ( 2 m )
11
671 A police jeep is chasing with velocity of ( 45 k m / h ) a thief in another jeep moving with velocity ( 153 k m / h . ) Police fires a
bullet with muzzle velocity of ( 180 m / s ) The velocity it will strike the car of the
thief is?
A. ( 150 mathrm{m} / mathrm{s} )
в. ( 27 mathrm{m} / mathrm{s} )
c. ( 450 m / s )
D. ( 250 mathrm{m} / mathrm{s} )
11
672 59. A particle is moving in the x-y plane. At certain instant
of time, the components of its velocity and acceleration
are as follows: v; = 3 ms-, v = 4 ms’, az = 2 ms and
a, = 1 ms. The rate of change of speed at this moment is
a. V10 ms 2
b. 4 ms-2
c. 15 ms-2
d. 2 ms-2
11
673 ct is projected with a velocity of 20 m/s making an
OI 45° with horizontal. The equation for the trajectory
is h = Ax – Bx2 where his height, x is horizonta
A and B are constants. The ratio A:B is (g = 10 ms)
(a) 1:5
(b) 5:1
(c) 1:40
(d) 40:1
onge R for
11
674 Two runners start simultaneously from
the same point on a circular ( 200 m )
track in the same direction. Their
speeds are ( 6.2 m s^{-1} ) and ( 5.5 m s^{-1} . ) How
far from the starting point the faster and the slower runner would be side by
side again?
A. ( 150 mathrm{m} ) away from the starting point
B. ( 170 m ) away from the starting point
c. ( 120 m ) away from the starting point
D. none
11
675 A solid body starts rotating about a stationary axis with an angular acceleration ( boldsymbol{alpha}=left(mathbf{2 . 0} times mathbf{1 0}^{-mathbf{2}}right) boldsymbol{t} boldsymbol{r a d} / boldsymbol{s}^{2} )
where ( t ) is in seconds. How soon(in
seconds) after the beginning of rotation will the total acceleration vector of an
arbitrary point of the body form an angle
( boldsymbol{theta}=mathbf{6 0}^{circ} ) with its velocity vector?
11
676 A body ties to a string of length ( boldsymbol{L} ) is
revolved in a vertical circle with
minimum velocity, when the body
reaches the upper most point the string
breaks and the body moves under the influence of the gravitational field of
earth along a parabolic path. The
horizontal range ( A C ) of the body will be:
A ( . x=L )
B. ( x=2 L )
C ( . x=2 sqrt{2 L} )
( mathbf{D} cdot x=sqrt{2 L} )
11
677 The figure represents a displacement
time graph of a body moving in a
straight line. The instantaneous velocity
of the body at ( 3 s ) is :
A ( cdot 4 m s^{-1} )
B. ( 3 m s^{-1} )
( c )
D. ( 1 mathrm{ms}^{-1} )
11
678 The formula ( v=R omega ) relating linear and
angular velocity is true, only if
A. The velocities are instantaneous velocities
B. The velocities are average velocities
c. The velocities are initial velocities and the particle is moving with constant acceleration
D. The velocities are initial velocities and the particle is moving with constant retardation
11
679 The force on a particle of mass 10 g is ( (10 hat{i}+5 hat{j}) N . ) if it starts from rest, what would be its position at time ( t=5 s ? )
A . ( 12500 hat{i}+6250 hat{j} mathrm{m} )
B. 6250hat ( +12500 hat{j} mathrm{m} )
c. ( 12500 hat{i}+12500 hat{j} mathrm{m} )
D. 6250hat + 6250hat m
11
680 When a force ( F_{1} ) acts on a particle,
frequency ( 6 mathrm{Hz} ) and when a force ( F_{2} ) acts frequency is 8 Hz. What is the frequency when both the force act simultaneously in same direction?
A . 12 нᅩ
в. 25нд
с. 10 н
D. ( 5 mathrm{Hz} )
11
681 Driver of a train travelling at ( 115 k m / h ) sees on a same track, ( 100 m ) infront of him, a slow train travelling in the same direction at ( 25 k m / h ). The least
retardation that must be appiled to faster train to avoid a collision is
A. ( 3.125 mathrm{m} / mathrm{s}^{2} )
в. ( 3.5 m / s^{2} )
( mathbf{c} cdot 2.75 m / s^{2} )
D. ( 3.0 m / s^{2} )
11
682 A projectile at any instant during its
flight has velocity ( 5 ~ m / s ) at ( 30^{circ} ) above
the horizontal. How long after this
instant, will it be moving at right angle to the given direction?
11
683 A train of length ( 100 m ) is moving in a
hilly region. At what speed must it approach a tunnel of length ( 80 m ) so that
a person at rest with respect to the tunnel will see that the entire train is in
the tunnel at one time?
A. ( 1.25 c )
B. ( 0.8 c )
c. ( 0.64 c )
D. ( 0.6 c )
E ( .0 .36 c )
11
684 You spin a globe at 2.5 rads/sec and
then give it a push to speed it up to 3 rads/ sec. If it takes 0.2 secs to change the speed of the globe, what is the
angular acceleration in ( r a d / s e c^{2} ? )
A . 2.5
B. 3
( c cdot 5 )
D. 10
11
685 5un. 15
10 10 )
34. A particle is projected up an inclined plane of inclination
B at an elevation a to the horizon. Show that
a. tan a=cot B+ 2 tan B, if the particle strikes the plane
at right angles
b. tana = 2 tan B, if the particle strikes the plane
horizontally
25
T
L
1:
lined to the horizon
11
686 A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an
acceleration of ( 1 mathrm{ms}^{-2} ) and the
projection velocity in the vertical direction is ( 9 cdot 8 m s^{-2} . ) How far behind
the boy will the ball fall on the car?
11
687 (I JUL, 1J)
2. Four persons K, L, M, N are initially at the four corners of
a square of side d. Each person now moves with a uniform
speed v in such a way that K always moves directly
towards L, L directly towards M, M directly towards N,
and N directly towards K. The four persons will meet at
a time
(IIT JEE, 1984)
11
688 The projection of the vector ( A=hat{i}-2 hat{j}+ ) ( hat{k} ) on the vector ( mathrm{B}=4 hat{i}-4 hat{j}+7 hat{k} ) is:
A . ( 19 / 9 )
в. 38/9
( c cdot 8 / 9 )
( D cdot 4 / 9 )
11
689 A train of length ( 50 m ) is moving with a
constant speed of ( 10 m / s . ) Calculate the
time taken by the train to cross an electric pole and a bridge of length
( mathbf{2 5 0 m} )
11
690 The maximum and the minimum
magnitude of the resultant two vectors
are 17 and 7 units respectively. Then the magnitude of the resultant vector when they act perpendicular to each other is:
A . 14
B. 16
c. 18
D. 13
11
691 1. If a particle moves from point P (2,3,5) to point Q (3,4,5).
Its displacement vector be
(a) i + i +10k
(b) î + i +5k
(c) i
tŷ preg (d) zi +47 + 6k
11
692 unc magnitude oi A.
13. Three vectors as shown in Fig. 3.71 have magnitudes
lal = 3,1b1 = 4, and lcl=10.
Ty
1.90
30°
21,30
Fig. 3.71
a. Find the x and y components of these vectors.
b. Find the numbers p and q such that c = pā+qb.
11
693 An aeroplane flying horizontally with speed ( 90 mathrm{km} / mathrm{hr} ) releases a bomb at a
height of ( 78.4 mathrm{m} ) from the ground, when will the bomb strike the ground?
A. 8 sec
B. 6 sec
c. 4 sec
D. 10 sec
11
694 A particle is projected from ground with velocity ( 40 sqrt{2} m / s a t 45^{circ} . ) Find the displacement of the particle after 2 s.
( left(g=10 m / s^{2}right) )
11
695 Is the claim of Mr.Kirkpatrick right?
A . yes
B. No
c. cannot say
D. may be correct or may be not
11
696 11. Two forces of magnitudes P and Q are inclined at an angle
(O). The magnitude of their resultant is 3Q. When the
inclination is changed to (180° – 0), the magnitude of the
resultant force becomes Q. Find the ratio of the forces.
11
697 average velocity, 11
698 What is the equation of parabolic trajectory of a projectile? ( (boldsymbol{theta}= ) angle between the projectile motion and the horizontal)
A ( cdot y=x^{2} tan theta-frac{g x}{2 u^{2} cos ^{2} theta} )
B. ( y=x tan theta-frac{g x^{2}}{2 u^{2} cos ^{2} theta} )
c. ( y=x tan theta-frac{g x^{2}}{u^{2} cos 2 theta} )
D. ( y=x tan theta-frac{g x^{2}}{u^{2} sin ^{2} theta} )
11
699 Is the acceleration of a particle in uniform circular motion constant or
variable?
A. Variable
B. Constant
c. Sometimes constant
D. Always constant
11
700 single Correct Answer Type The path of a projectile is given by the
equation ( y=a x-b x^{2}, ) where ( a ) and ( b )
are constants and ( x ) and ( y ) are
respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively:
A ( cdot frac{2 a^{2}}{b}, tan ^{-1}(a) )
B. ( frac{b^{2}}{2 a}, tan ^{-1}(b) )
c. ( frac{a^{2}}{b}, tan ^{-1}(2 b) )
D ( cdot frac{a^{2}}{4 b}, tan ^{-1}(a) )
11
701 There are two force vectors, one of ( 5 N )
and other of ( 12 N . ) At what angle should
the two vectors be added to get the
resultant vector of ( 17 N, 7 N, ) and ( 13 N )
respectively?
11
702 Three forces of magnitudes 30,60 and
( P ) Newton acting at a point are in
equilibrium. If the angle between the
first two is ( 60^{circ} ), the value of ( P ) is:
A ( cdot 25 sqrt{2} )
в. ( 30 sqrt{3} )
c. ( 30 sqrt{6} )
D. ( 30 sqrt{7} )
11
703 A unit vector in the direction of vector ( overrightarrow{P Q}, ) where ( P ) and ( Q ) are the points
(1,2,3) and (4,5,6) respectively is
A ( cdot frac{1}{sqrt{3}} hat{i}+frac{1}{sqrt{3}} hat{j}+frac{1}{sqrt{3}} bar{k} )
B. ( frac{1}{sqrt{3}} hat{i}+frac{1}{sqrt{3}} hat{j}-frac{1}{sqrt{3}} hat{k} )
c. ( 2 hat{i}-hat{j}+bar{k} )
D. None
11
704 Two vectors ( A ) and ( B ) have equal
magnitudes. If magnitude of ( A+B ) is equal to ( n ) times the magnitude of ( A-B )
then the angle between ( A ) and ( B ) is
A ( cdot cos ^{-1}left(frac{n-1}{n+1}right) )
B. ( cos ^{-1}left(frac{n^{2}-1}{n^{2}+1}right) )
c. ( sin ^{-1}left(frac{n-1}{n+1}right) )
D. ( sin ^{-1}left(frac{n^{2}-1}{n^{2}+1}right) )
11
705 21. A ball is projected from ground with speed u, at an angle
above horizontal. Let v be its speed at any moment t and
s be the total distance covered by it till this moment, the
correct graph(s) is/are
a. 1
b.
11
706 When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36
rotations. The number of rotations it will
make further before coming to rest is Assuming angular retardation to be
uniform
A . 10
B . 20
( c .18 )
D. 12
11
707 The instantaneous velocity of a body can be measured :-
A. Graphically
B. By speedometer
c. Both of above
D. vectorially
11
708 On a foggy day, two drivers spot in front of each other when 80 metre apart. They
were traveling at ( 70 mathrm{kmph} ) and ( 60 mathrm{kmph} ) Both apply brakes simultaneously which retard the cars at the rate
( 5left[boldsymbol{m} / boldsymbol{s}^{2}right] ) Which of the following statements is correct?
A. The collision will be averted
B. The collision will take place
c. They will across each other
D. They will just collide
11
709 Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the
particle at the next corner. If the time taken by the particles to meet each other is ( frac{n a}{v} . ) Then ( n ) is given by
11
710 Find the radius and energy of a ( H e^{+} ) ion
in the state ( n=4 )
11
711 Find how the total acceleration ( omega ) of the
balloon depends on the height of ascent.
A. ( omega=2 a v_{0} )
B. ( omega=-2 a v_{0} )
c. ( omega=a v_{0} )
D. ( omega=-a v_{0} )
11
712 What is the angle between ( vec{P} ) and the resultant of ( (vec{P}+vec{Q}) ) and ( (vec{P}-vec{Q}) ? )
A. zero
в. ( tan ^{-1} frac{P}{Q} )
c. ( tan ^{-1} frac{Q}{P} )
D. ( tan ^{-1}left(frac{P-Q}{P+Q}right) )
11
713 A rope is wound around a hollow
cylinder of mass ( 3 k g ) and radius ( 40 c m ) What is the angular acceleration of the cylinder if the rope is pulled with a force
of ( 30 N ? )
( mathbf{A} cdot 5 m / s^{2} )
B . ( 25 mathrm{m} / mathrm{s}^{2} )
c. ( 0.25 mathrm{rad} / mathrm{s}^{2} )
( mathbf{D} cdot 25 mathrm{rad} / mathrm{s}^{2} )
11
714 What is centripetal acceleration? Drive an impression for centripetal acceleration. 11
715 A body of mass ( m ) is projected with
initial speed ( u ) at an angle ( theta ) with the
horizontal. The change in momentum of body after time ( t ) is
A ( . m u sin theta )
B . ( 2 m u sin theta )
( mathrm{c} cdot m g t )
D. zero
11
716 Which one of the following diagrams best represents the path followed by a projectile that has been launched horizontally from a countertop?
( A )
в.
( c )
D.
11
717 The motion of a bus going around a traffic roundabout is curvilinear
motion. True or false
A. True
B. False
11
718 A particle moves in a circle describing equal angle in equal times, its velocity vector
A. remains constant
B. changes in magnitude
c. change in direction
D. changes in magnitude and direction
11
719 A boy of height ( 1.5 mathrm{m}, ) making move on a skateboard due east with velocity ( 4 mathrm{m} ) s
( -1, ) throws a coin vertically up with a
velocity of ( 3 mathrm{m} mathrm{s}^{-1} ) relative to himself.
a. Find the total displacement of the coin relative to ground till it comes to the hand of the boy.
b. What is the maximum height attained by the coin w.r.t to ground?
11
720 Select incorrect statement
A ( cdot ) for any two vectors ( |vec{A} cdot vec{B}| leq A B )
B. for any two vectors ( |vec{A} times vec{B}| leq A B ).
C. a vector is not changed if it is slid parallel to itself.
D. a vector is necessarily changed if it is rotated through an angle
11
721 74. A particle is moving along a circular path with uniform
speed. Through what angle does its angular velocity
change when it completes half of the circular path?
a. 0° b. 45º c. 180° d. 360°
75 Anarticle is moving along a cirenlar nath The anana
11
722 20. Time of flight of the particle
a. 8
b. 6 s c. 4s
d. 2 s
11
723 A ball of mass ( m ) is projected from the
ground with an initial velocity ( u ) making
an angle of ( theta ) with the horizontal. What
is the change in velocity between the point of projection and the highest point?
A . ( u sin theta )
B . ( u^{2} cos theta )
c. ( u cos theta )
D. ( u^{2} sin theta )
11
724 The path of a projectile is a parabola
A. True
B. False
11
725 Find how the tangential acceleration ( omega_{tau} )
of the balloon depends on the height of
ascent.
A ( cdot_{omega_{tau}}=frac{2 a^{2} y}{sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} )
B. ( _{omega_{tau}}=frac{a^{2} y}{sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} )
( ^{mathbf{c}} cdot_{omega_{tau}}=frac{a^{2} y}{sqrt{1+left(frac{2 a y}{v_{0}}right)^{2}}} )
D. ( omega_{tau}=frac{a^{2} y}{2 sqrt{1+left(frac{a y}{v_{0}}right)^{2}}} )
11
726 In one second, a particle goes from
point ( A ) to point ( B ) moving in a semicircle. Find the magnitude of the
average velocity.
( A cdot 1 mathrm{m} / mathrm{s} )
B. 2 m/s
c. ( 0.5 mathrm{m} / mathrm{s} )
D. None of the above
11
727 A particle is projected from horizontal
making an angle ( 60^{circ} ) with initial
velocity ( 40 m s^{-1} . ) Find the time taken by
the particle to make angle ( 45^{circ} ) from
horizontal.
A . ( 1.5 s )
в. 2.5 ( s )
( c .3 .5 s )
D. 4.5
11
728 Find a unit vector in the direction of the
vector ( overrightarrow{boldsymbol{a}}=hat{boldsymbol{i}}+mathbf{2} hat{boldsymbol{j}}+mathbf{3} hat{boldsymbol{k}} )
11
729 Assertion : When a particle moves in a
circle with a uniform speed, its velocity and acceleration both changes.

Reason : The centripetal acceleration in circular motion is dependent on angular velocity of the body.
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 the Reason i not the correct explanation of the Assertion
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements

11
730 The coordinates of a moving particle at time ( t ) are given by ( x=c t^{2} ) and ( y=b t^{2} )
The speed of the particle is given by
A ( cdot 2 t(c+b) )
B . ( 2 t sqrt{left(c^{2}-b^{2}right)} )
c. ( t sqrt{left(c^{2}+b^{2}right)} )
D. ( 2 t sqrt{left(c^{2}+b^{2}right)} )
11
731 Particle A and B moving in co-planar circular paths centered at O.They are
rotating in the same sense.Time periods of rotation of ( A ) and ( B ) around 0
( operatorname{are} boldsymbol{T}_{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{T}_{B}, ) respectively, with ( boldsymbol{T}_{B}> )
( T_{A} . ) Time required for ( B ) to make one
rotation around 0 relative to a is :
A ( cdot T_{B}-T_{A} )
в. ( T_{B}+T_{A} )
c. ( frac{T_{A} T_{B}}{T_{A}-T_{B}} )
D. ( frac{T_{B} T_{A}}{T_{B}-T_{A}} )
11
732 U. TOJ MIS
0. A bird is flying towards north with a velocity 40 km
and a train is moving with velocity 40 km h towards
east. What is the velocity of the bird noted by a man in
the train?
a. 40/2 km h-‘N-E b. 40/2 km h-S-E
c. 40/2 km h-N-W d. 40/2 km h-‘S-W
11
733 d. 2 cm along negative x-axis
10. What is the angle between two vector forces of equal
magnitude such that their resultant is one-third of either
of the original forces?
a. cos
b. cos’ (-3)
d. 120°
c. 45°
11
734 The velocity vector of a particle moving in the xy plane is given by ( vec{v}=t hat{i}+x hat{j} ). If
initially, the particle was at origin then
the equation of trajectory of the projectile is?
11
735 An aeroplane is moving in a circular path with a speed ( 250 mathrm{km} / mathrm{hr} ) in a horizontal plane. The change in magnitude of velocity in half the revolution is:
A. ( 500 mathrm{km} / mathrm{hr} )
B. ( 250 mathrm{km} / mathrm{hr} )
c. ( 125 mathrm{km} / mathrm{hr} )
D.
11
736 A system is shown in the figure. Block ( boldsymbol{A} )
moves with velocity ( 10 m / s . ) The speed
of the mass ( B ) will be: ( left(sin 15^{circ}=right. )
( left.frac{sqrt{3}-1}{2 sqrt{2}}right) )
A. ( 10 sqrt{2} mathrm{m} / mathrm{s} )
в. ( 5 sqrt{3} ) m/
c. ( frac{20}{sqrt{3}} m / s )
D. ( 10 mathrm{m} / mathrm{s} )
11
737 The force ( F ) which is applied to ( 1 k g )
block initially at rest varies linearly with
time as shown in the figure. Find velocity of the block at ( t=4 s )
A ( .100 mathrm{m} / mathrm{s} )
B. ( 200 mathrm{m} / mathrm{s} )
( c cdot 20 m / s )
D. ( 4 m / s )
11
738 The magnitude of vector product of two vectors ( overline{mathbf{P}} times overline{mathbf{Q}} ) may be:
A. equal to PQ
B. less than PQ
c. equal to zero
D. all the above
11
739 Illustration 4.8 A particle moves along the curve
=1,
with constant speed v. Express its velocity vectorially as a
function of (x, y).
11
740 The path of projectile is represented by y = Px – Ox’.
Column I
Column II
L. Range a . PIQ
ü. Maximum height b. P
Time of flight c . P2140
Tangent of angle of d.
projection is
Vog
11
741 The position of an object moving along ( x ) -axis is given by ( x=a+b t^{2}, ) where ( a= )
( 8.5 mathrm{m} ) and ( mathrm{b}=2.5 mathrm{m} mathrm{s}^{-2} ) and ( mathrm{t} ) is
measured in seconds. The
instantaneous velocity of the object at ( t )
( =2 operatorname{sis} )
A ( cdot 5 mathrm{m} s^{-1} )
B. ( 10 mathrm{m} s^{-1} )
c. ( 15 mathrm{m} mathrm{s}^{-1} )
D. 20 ( mathrm{m} mathrm{s}^{-1} )
11
742 The position vector of a particle is ( vec{r}= ) ( boldsymbol{a}[cos omega boldsymbol{t} hat{boldsymbol{i}}+sin omega boldsymbol{t} hat{j}] . ) The velocity of the
particle is
A. parallel to position vector
B. directed towards origin
c. directed away from origin
D. perpendicular to position vector
11
743 A steamer is going downstream
overcome a raft point ( A .2 h r ) later it
turned back and after some time
passed the raft at a distance ( 4 mathrm{km} ) from point ( A . ) The speed of the river is
A. ( 1 mathrm{km} / mathrm{h} )
B. ( 2 mathrm{km} / mathrm{h} )
( mathrm{c} .3 mathrm{km} / mathrm{h} )
D. ( 4 mathrm{km} / mathrm{h} )
11
744 A particle starts from the origin at ( t=0 ) with an initial velocity of ( 3.0 hat{i} m / s ) and
moves in the ( x-y ) plane with a constant acceleration ( (mathbf{6 . 0} hat{mathbf{i}}+ ) ( 4.0 hat{j}) m / s^{2} . ) The ( x- ) coordinates of the
particle at the instant when its ( y- )
coordinates is ( 32 m ) is ( D ) meters. The
value of ( D ) is:
( mathbf{A} .50 )
B. 60
c. 40
D. 32
11
745 For the same two projectiles, after ( 3 s ) from the initial launch, what will be the
difference between the two projectiles
speeds? The previous problem’s text:
A projectile is fired 30.0 degrees above
the horizontal with speed ( left|boldsymbol{v}_{1}right|=mathbf{4 0 m} / boldsymbol{s} )
and a second one 60.0 degrees above
the horizontal with speed ( left|boldsymbol{v}_{2}right|=mathbf{3 0 m} / boldsymbol{S} )
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air
resistance and that they are fired from the same spot, and that each moves independent of the outer projectile. Take ( boldsymbol{g}=mathbf{9 . 8 1 m} / boldsymbol{s}^{2} )
A. ( 10 mathrm{m} / mathrm{s} )
B. ( 15.4 m / s )
c. ( 20.5 m / s )
D. ( 30.0 mathrm{m} / mathrm{s} )
E . ( 35.9 mathrm{m} / mathrm{s} )
11
746 If ( overrightarrow{boldsymbol{A}}=mathbf{3} hat{boldsymbol{i}}-mathbf{2} hat{boldsymbol{j}}+hat{boldsymbol{k}}, overrightarrow{boldsymbol{B}}=hat{boldsymbol{i}}-boldsymbol{3} hat{boldsymbol{j}}+ )
5 ( hat{k} a n d vec{C}=2 hat{i}+hat{j}-4 hat{k} ) form a right
angled triangle then out of the following which one is satisfied?
A ( cdot vec{A}=vec{B}+vec{C} )and ( A^{2}=B^{2}+C^{2} )
B . ( vec{A}=vec{B}+vec{C} )and( B^{2}=A^{2}+C^{2} )
c. ( vec{B}=vec{A}+vec{C} a n d B^{2}=A^{2}+C^{2} )
D. ( vec{B}=vec{A}+vec{C} a n d A^{2}=B^{2}+C^{2} )
11
747 1. In a square cut, the speed of the cricket ball changes from
30 m sto 40 ms during the time of its contact At=0.01
s with the bat. If the ball is deflected by the bat through
an angle of 0 = 90°, find the magnitude of the average
acceleration (in x 102ms 2) of the ball during the square
cut.
11 maad
11
748 A body moves ( 6 mathrm{m} ) north. ( 8 mathrm{m} ) east and 10m vertically upwards, what is its resultant displacement from initial position (only magnitude)
A ( cdot 10 sqrt{2} m )
the
в. ( 10 m )
c. ( frac{10}{sqrt{2}} m )
D. ( 10 times 2 m )
11
749 6. A boy standing on a long railroad car throws a ball straight
upwards. The car is moving on the horizontal road with
an acceleration of 1 ms and the projection velocity in
the vertical direction is 9.8 ms. How far behind the boy
will the ball fall on the car? (in meters)
11
750 Illustration 4.1 A particle moves in the x-y plane according
to the scheme x = -8 sin it and y = -2 cos 27t, where t is
time. Find the equation of the path of the particle. Show the
path on a graph.
11
751 1. Rain is falling vertically downwards with a speed of
4 kmh. A girl moves on a straight road with a velocity
of 3 kmh. The apparent velocity of rain with respect to
the girl is
a. 3 km h-‘ b. 4 kmh. c. 5 kmh’ d. 7 km h-
11
752 Find a vector of magnitude 4 units which is parallel to the vector ( sqrt{mathbf{3}} hat{mathbf{i}} ) 11
753 The given diagram shows a hill with four labelled positions ( mathrm{W}, mathrm{X}, mathrm{Y} ) and ( mathrm{Z} ) When a ball is rolled down the hill, then
from which position will it finish rolling
with the greatest speed?
A. Position ( mathrm{w} )
B. Position ( x )
c. Position Y
D. Position z
11
754 d. 1
D. 3h
C. (515N U. ”
36. A juggler keeps on moving four balls in air t
eeps on moving four balls in air throwing the
balls after regular intervals. When one ball leaves his hand
(speed = 20 ms-1), the position of other balls (height in
meter) will be (take g = 10 ms)
a. 10, 20, 10
. b. 15, 20, 15
c. 5, 15, 20
d. 5, 10, 20
11
755 12. At the highest point of the path of a projectile, its
(a) speed is zero
(b) speed is minimum
(C) Kinetic energy is minimum
(d) Potential energy is maximum
11
756 A car travelling at ( 60 k m / h ) overtakes another car travelling at ( 42 k m / h ) Assuming each car to be ( 5.0 m ) long, the time taken for the over taking is
( mathbf{A} cdot 6 s )
B . ( 4 s )
c. ( 3 s )
D. ( 2 s )
11
757 A particle rotates along a circle of radius ( R=sqrt{2} mathrm{m} ) with an angular acceleration ( boldsymbol{alpha}=frac{boldsymbol{pi}}{boldsymbol{4}} boldsymbol{r} boldsymbol{a} boldsymbol{d} / boldsymbol{s}^{2} ) starting
from rest. Calculate the magnitude of average velocity of the particle over the time it rotates a quarter circle.
11
758 A particle starts from the origin of coordinates at time ( t=0 ) and moves in
the ( x y ) plane with a constant
acceleration ( alpha ) in the ( y ) -direction. Its
equation of motion is ( y=beta x^{2} ). Its
velocity component in the x-direction is
A. variable
B. ( sqrt{frac{2 alpha}{beta}} )
c. ( frac{alpha}{beta} )
D. ( sqrt{frac{alpha}{2 beta}} )
11
759 When the earth completes one revolution around the sun, the
displacement of the earth is zero. True
or false.
A. True
B. False
11
760 A body is projected at ( t=0 ) with a
velocity ( 10 m s^{1} ) at an angle of 60 with
the horizontal.The radius of curvature of
its trajectory at ( t=1 s ) is ( R . ) Neglecting
air resistance and taking acceleration due to gravity ( g=10 ) ms2, the value of
( boldsymbol{R} ) is :
A ( .2 .4 m )
B. ( 10.3 m )
( c .2 .8 m )
D. ( 5.1 mathrm{m} )
11
761 Find the magnitude of the angular
acceleration of the cone
A ( .3 .3 mathrm{rad} / mathrm{s}^{2} )
B . ( 2.6 mathrm{rad} / mathrm{s}^{2} )
c. 2.3 rad / ( s^{2} )
D. ( 3.6 mathrm{rad} / mathrm{s}^{2} )
11
762 A projectile is fired 30.0 degrees above the horizontal with speed ( left|boldsymbol{v}_{1}right|=mathbf{4 0 m} / boldsymbol{s} )
and a second one 60.0 degrees above
the horizontal with speed ( left|boldsymbol{v}_{2}right|=mathbf{3 0 m} / boldsymbol{S} )
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air resistance and that they are fired from
the same spot, and that each moves independent of the outer projectile. Take ( boldsymbol{g}=mathbf{9 . 8 1 m} / boldsymbol{s}^{2} )
A . ( 11.96 m )
в. ( 28.11 m )
( mathrm{c} .39 .28 mathrm{m} )
D. 41.06 m
E . ( 41.99 mathrm{m} )
11
763 40. The horizontal distance of the ball from the foot of the
building where the ball strikes the horizontal ground will
be
a. V2R
b. (1 + V2)R
c. 2(1+12)
d. 12R
11
764 U
TU – 1
8. For a given velocity, a projectile has
en velocity, a projectile has the same range R for
two angles of projection if t, and t, are the
of projection if t, and t, are the times of flight
in the two cases then
(a) tt, « R2
(b) 112 «R
(C) 4t2«
(d) 1126
11
765 A body of mass m moving at a constant velocity v hits another body of the same mass moving with a velocity v/2 but in the opposite direction and sticks to it. The common velocity after collision is
( A )
B. v/
c. ( 2 v )
D. v/2
11
766 (2) Explaıri clearly, wırn ex ( mathbf{S}, ) Ine
distinction between:
(a) magnitude of displacement over an interval of time and the total length of
path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average
speed over the same interval.
Show in both (a) and (b) that the second
quantity is either greater than or equal
to the first. When is the equality sign
true?
(ii) A man walks on a straight road
from his home to a market ( 2.5 k m ) away
with a speed of ( 5 k m h^{-1} ). Finding the
market closed, he instantly turns and walks back home with a speed of
( 7.5 k m h^{-1} . ) What is the:
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to
( mathbf{5 0 m i n},(text { iii) } 0 text { to } 40 m i n ? )
11
767 A particle is revolving in a circle of radius ( r . ) Its displacement after
completing half the revolution will be
( mathbf{A} cdot pi r )
B . ( 2 r )
c. ( 2 pi r )
D. ( frac{r}{2} )
11
768 Find the time dependence of the velocity
( overrightarrow{boldsymbol{v}} ) vector.
A ( . vec{v}=2 a vec{i}-b t vec{j} )
B . ( vec{v}=-2 a vec{i}-2 b t vec{j} )
C ( . vec{v}=-2 a vec{i}-b t vec{j} )
D. ( vec{v}=a vec{i}-2 b t vec{j} )
11
769 A body is projected with velocity ( 24 m s^{-1} ) making an angle ( 30^{circ} ) with the horizontal. The vertical component of its
velocity after ( 2 s ) is ( left(g=10 m s^{-2}right) )
A. ( 8 m s^{-1} ) upward
B. ( -8 m s^{-1} ) downward
c. ( 32 m s^{-1} ) upward
D. ( 32 m s^{-1} ) downward
11
770 Two stones ( A ) and ( B ) are projected simultaneously from the top of a ( 100- )
( m ) high tower. Stone B is projected
horizontally with speed ( 10 m s^{-1} ). and stone ( A ) is dropped from the tower. Find out the following:
(a) Time of flight of the two stone
(b) Distance between two stones after 3
( mathbf{S} )
(c) Angle of strike with ground
11
771 A particle is projected horizontally with a speed u from the top of a plane inclined at an angle ( theta ) with the horizontal. How far from the point of projection will the particle strike the
plane?
( ^{mathrm{A}} cdot frac{2 u^{2}}{g} tan theta sec theta )
B. ( frac{2 u}{8} tan ^{2} theta sec theta )
c. ( frac{2 u^{2}}{g} tan theta cos theta )
D. ( frac{2 u}{g} tan theta cos ^{2} theta )
11
772 Motion of wheel of a bicycle is (projectile, circular)
motion.
11
773 Illustration 5.41 A political party has to start its procession
in an area where wind is blowing at a speed of 30v2 kmh
and party flags on the cars are fluttering along north-east
direction. If the procession starts with a speed of 40 km h-
towards north, find the direction of flags on the cars .
11
774 Is it possible to have an accelerated motion with a constant speed? Explain 11
775 8. A body is projected up with a speed ‘u’ and the time taken
by it is T to reach the maximum height H. Pick out the
correct statement
(a) It reaches H/2 in T/2 sec
(b) It acquires velocity ul2 in T/2 sec
(c) Its velocity is u/2 at H/2
(d) Same velocity at 2T
11
776 Which of the following remains constant in uniform circular motion:
Speed or Velocity or both?
11
777 Fig. 3.73
21. A particle of m = 5 kg is momentarily at rest at
1=0. It is acted upon by two forces F and F. F IO
• The direction and magnitude of F, are unknown. The
particle experiences a constant acceleration, a , in the
direction as shown in Fig. 3.74. Neglect gravity.
ут
t = 70 ÎN
a = 10 m/s2
53°
Fig. 3.74
a. Find the missing force F.
b. What is the velocity vector of the particle at
t = 10 s?
c. What third force, F3, is required to make the
acceleration of the particle zero? Either give magnitude
and direction of F, or its components.
11
778 900
29. A projectile is fired with a velocity v at right
angle to the slope inclined at an angle with
the horizontal. The range of the projectile
along the inclined plane is
2v2 tane
v² seco
A
Fig. A.13
a.
2v2 tan 0 sec o
Eco

d.
v² sino
s
20
A 111
11
1
11
11
779 A truck starts from rest and accelerates
uniformly at ( 2.0 m s^{-2} . ) At ( t=10 s, ) a
stone is dropped by a person standing on the top of the truck (6 ( m ) high from the ground). What are the
(a) velocity, and (b) acceleration of the stone at ( t= )
11 ( s ) ? (Neglect air resistance.)
11
780 An elevator is going up vertically with a
constant acceleration of ( 2 mathrm{m} / mathrm{s}^{2} ). at the
instant when its velocity is ( 4 mathrm{m} / mathrm{s} ) a ball is projected from the floor of the elevator with a speed of ( 4 mathrm{m} / mathrm{s} ) relative to the floor with an angular elevation of
( 30^{circ} . ) the time taken by te ball to return
to the floor is : (take ( g=10 m / s^{2} ) )
A ( cdot frac{1}{3} mathrm{sec} )
B. ( frac{1}{sqrt{3}} sec )
c. ( frac{2}{sqrt{3}} sec )
D. ( sqrt{3} mathrm{sec} )
11
781 The velocity vector of a particle moving in the xy plane is given by ( v=t i+x j ). If initially, the particle was at origin then the equation of trajectory of the projectile is:
A ( cdot 4 x^{2}-9 y=0 )
B. ( 9 x^{2}-2 y^{3}=0 )
c. ( 16 x^{3}-9 y^{2}=0 )
D. ( 9 x^{3}-2 y^{2}=0 )
11
782 A particle stars from rest covers a distance of x with constant acceleration
then move with constant velocity and
cover distance ( 2 x ) then after come to
rest will constant retardation with cover
distance of ( 3 x, ) then ratio of ( V_{max } / V_{text {avg }} )
will be
( A cdot 3: 5 )
B. 5: 3
c. 7:
D. 5:
11
783 When particles moves in a circle at a constant speed then the motion is said
to be
A. Uniform motion
B. Non uniform motion
c. Projectile motion
D. All
11
784 5. A ball is projected from the Fig. A.44
origin. The r- and y-coordinates
of its displacement are given by x = 3t and y = 41 – 51.
Find the velocity of projection (in ms).
maximum distances while
Al
11
785 A body moving along a circular path may have
A. A constant speed
B. A constant velocity
c. No tangential velocity
D. No radial acceleration
11
786 U. Slalomuus (1) un
ain appears
19. Rain appears to fall vertically to a man walking at 3 km
but when he changes his speed to double, the rain app
to fall at 45° with vertical. Study the following stater
and find which of them are correct.
i. Velocity of rain is 213 km –
. The angle of fall of rain (with vertical) i
O= tan –
iii. The angle of fall of rain (with vertical) je
8 = sin
iv. Velocity of rain is 312 kmh !
a. Statements (i) and (ii) are correct.
b. Statements (i) and (iii) are correct.
c. Statements (iii) and (iv) are correct.
d. Statements (ii) and (iv) are correct.
:
200
11
787 Let ( vec{F} ) be the force acting on a particle having position vector ( vec{r} ) and ( vec{tau} ) be the torque of this force about the origin then:
( mathbf{A} cdot vec{r} cdot vec{Gamma}=0 ) and ( vec{F} cdot vec{Gamma} neq 0 )
B . ( vec{r} . vec{Gamma} neq 0 ) and ( vec{F} . vec{Gamma}=0 )
c. ( vec{r} . vec{Gamma} neq 0 ) and ( vec{F} cdot vec{Gamma} neq 0 )
D. ( vec{r} . vec{Gamma}=0 ) and ( vec{F} cdot vec{Gamma}=0 )
11
788 ( (overline{mathbf{A}}+overline{mathbf{B}}) times(overline{mathbf{A}}-overline{mathbf{B}}) ) is:
A ( cdotleft(bar{A}^{2}-bar{B}^{2}right) )
в. ( 2 overline{mathrm{AB}} )
c. ( 2(overline{mathrm{A}} times overline{mathrm{B}}) )
D. ( 2(overline{mathrm{B}} times overline{mathrm{A}}) )
11
789 Two balls are projected making an angle of 30 and 45 respectively with the horizontal. If both have the same
velocity at the highest points of their paths, then the ratio of their velocities of projection is
A. ( sqrt{3}: sqrt{2} )
B. ( sqrt{2}: 1 )
c. ( sqrt{2}: sqrt{3} )
D. ( sqrt{3}: 2 )
11
790 Show that ( mathbf{a} .(mathbf{b} times mathbf{c}) ) is equal in
magnitude to the volume of the
parallelopiped formed on the three
vectors, a, b and c.
11
791 I nree points are located at the vertıces
of an equilateral triangle having each
side as ( alpha . ) All the points move
simultaneously with speed ( u ) such that
first point continually heads for second,
the second for the third and the third for
the first. Time taken by the points to
meet at the centre is
A ( cdot frac{alpha}{3 u} )
B. ( frac{2 alpha}{3 u} )
c. ( frac{alpha^{2}}{u^{3}} )
( D cdot 3 alpha )
( 2 u )
11
792 100 m
100 m
16. Three boys are running on a
equitriangular track with the same
speed 5 ms. At start, they were at
the three corners with velocity along
indicated directions. The velocity of BAO
100 m
approach of any one of them towards
Fig. A.9
another at t = 10 s equals
a. 7.5 ms-1 b. 10 ms-c. 5 ms-1 d. Oms-1
60°C
11
793 What is the centripetal acceleration of the ball if its mass is doubled?
( A cdot a / 4 )
B. a/2
( c )
D. 2a
E. ( 4 a )
11
794 If the magnitude of sum of two vectors
is equal to the magnitude of difference of the two vectors, the angle between
these vectors is:
( mathbf{A} cdot 0^{circ} )
B. ( 90^{circ} )
( c cdot 45^{circ} )
D. ( 180^{circ} )
11
795 Fig. A.31
14. The distance of the point from point
lands is
a. 80 m b. 100 m c. 200 m
where the package
d. 160 m
11
796 It takes you 9.5 minutes to walk with an average velocity of ( 1.2 m / s ) to the north
from the bus stop to museum entrance. What is your displacement? (in m)
A. 684
в. 540
c. 525
D. 565
11
797 A ball is thrown horizontally from a point ( 100 mathrm{m} ) above the ground with a speed of ( 200 mathrm{m} / mathrm{s} ). Find (a) the time it takes to reach the ground,
(b) the horizontal distance it travels before
reaching the ground,
(c) the velocity (direction and magnitude) with which it strikes the ground.
11
798 30. A grasshopper can jump a maximum distance 1.6 m. It
spends negligible time on the ground. How far can it go
in 10 s?
a. 52 m
b. 102 m
c. 2012 m
d. 40 V2 m
11
799 Illustration 3.9 A force of 15 N acts on a box as shown in
Fig. 3.25. What are the horizontal component and vertical
components of the force?
15 N
Vertical
component
60°
Horizontal
component
Fig. 3.25
11
800 Find the unit vector in the direction of
sum of the vectors (1,1,1),(2,-1,-1) and ( (mathbf{0}, mathbf{2}, mathbf{6}) )
11
801 simultaneously from point A. P moves
along a smooth horizontal wire ( A B . Q )
moves along a curved smooth track. ( Q )
has sufficient velocity at ( A ) to reach ( B ) always remaining in contact with the curved track. At A, the horizontal
component of velocity of ( Q ) is same as
the velocity of ( mathrm{P} ) along the wire. The
plane of motion is vertical. If ( t_{1}, t_{2}, ) are
times taken by ( P & Q ) respectively to
reach B then (Assume velocity of P is
constant)
( mathbf{A} cdot t_{1}=t_{2} )
( mathbf{B} cdot t_{1}>t_{2} )
( mathbf{c} cdot t_{1}<t_{2} )
D. none of these
11
802 A river flows ( 3 mathrm{km} / mathrm{h} ) and a man is capable of swimming at the rate of
( 2 k m / h . ) He wishes to cross it such that the displacement parallel to river is minimum. In which direction should he
swim?
( ^{A} cdot sin ^{-1}left(frac{2}{3}right) )
B. ( cos ^{-1}left(frac{2}{3}right) )
( ^{mathbf{c}} cdot tan ^{-1}left(frac{2}{3}right) )
D. ( cot ^{-1}left(frac{2}{3}right) )
11
803 6. A stone projected with a velocity u at an angle with
the horizontal reaches maximum height H. When it is
projected with velocity u at an angle(
-e with the
horizontal, it reaches maximum height H,. The relation
between the horizontal range R of the projectile H, and
H is
(a) R=4/H,H, (b) R = 4(H, -H)
H2
(c) R = 4(H, +H)
(d) R=HT
11
804 (1):In uniform circular motion,
tangential acceleration is zero.
(2) : In uniform circular motion, velocity is constant.
A. Both 1 and 2 are true and 2 is correct explanation of
B. Both 1 and 2 are true and 2 is not correct explanation of 1
c. 1 is true and 2 is false
D. 1 is false and 2 is true
11
805 A vehicle starts from rest and moves at
uniform acceleration such that its
velocity increases by ( 3 m s^{-1} ) per every second. If diameter of wheel of that vehicle is ( 60 mathrm{cm}, ) the angular acceleration of wheel is:
A .5 rads( ^{-2} )
B. 10 rads( ^{-2} )
C .15 rads( ^{-2} )
D. 20 rads ( ^{-2} )
11
806 A particle moves in the ( x ) -y plane with the velocity ( overrightarrow{boldsymbol{v}}=boldsymbol{a} hat{boldsymbol{i}}+boldsymbol{b} boldsymbol{t} hat{j} . ) AT the instant
( mathrm{t}=a sqrt{3} / b ) the magnitude of tangential normal and total acceleration are
11
807 An aeroplane pilot wishes to fly due
west. A wind of ( 100 mathrm{km} h^{-1} ) is blowing
towards south.
a. If the speed of the plane (its speed in
still air) is ( 300 mathrm{km} h^{-1}, ) in which
direction should the pilot head?
What is the speed of the plane with respect to ground? IIlustrate with a vector diagram.
11
808 A pendulum bob of mass ( m=80 m g )
carrying a charge of ( boldsymbol{q}=boldsymbol{2} times mathbf{1 0}^{-8} boldsymbol{C} ), is
at rest a horizontal uniform electric
field of ( boldsymbol{E}=mathbf{2 0}, mathbf{0 0 0} boldsymbol{V} / boldsymbol{m} . ) The tension ( boldsymbol{T} )
in the thread of the pendulum and the angle ( alpha ) it makes with vertical is (take
( boldsymbol{g}=mathbf{9} . boldsymbol{8} boldsymbol{m} / boldsymbol{s}^{2} boldsymbol{)} )
This question has multiple correct options
A ( cdot alpha approx 27^{circ} )
в. ( T approx 880 mu N )
c. ( T=8.8 mu N )
D. ( alpha approx 356 o )
11
809 10. A body is projected with velocity u at an angle of
projection with the horizontal. The direction of velocity
of the body makes angle 30° with the horizontal at t=2s
and then after 1 s it reaches the maximum height. Then
a. u= 20/3 ms, b. 0 = 60°
c.
= 30°
d. u=1073 ms-
11
810 8. A police jeep is chasing a culprit going on a motorbike
The motorbike crosses a turning at a speed of 72 kmh!
The jeep follows it at a speed of 90 kmh-, crossing the
turning 10 s later than the bike.
Assuming that they travel at constant speeds, how far from
the turning will the jeep catch up with the bike? (In km)
11
811 A man crosses a ( 320 mathrm{m} ) wide river
perpendicular to the current in 4 min. If in still water he can swim with a speed
( 5 / 3 ) times that of the current, then the
speed of the current, in ( m ) min( ^{-1} ) is?
A . 30
B . 40
c. 50
D. 60
11
812 A particle is projected horizontally from
the top of a tower with a velocity ( v_{0} . ) If ( v )
be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to
( mathbf{A} cdot v^{3} )
B ( cdot v^{2} )
c.
D. ( frac{1}{v} )
11
813 Distinguish clearly between distance and displacement of a projectile. 11
814 If we hang a body of mass ( m ) with the
cord, the tension can be given as:
11
815 9. Consider a disc rotating in the horizontal plane with a
constant angular speed o about its center 0. The disc
has a shaded region on one side of the diameter and an
unshaded region on the other side as shown in Fig. A.54.
When the disc is in the orientation as shown, two pebbles
Pand Q are simultaneously projected at an angle towards
R. The velocity of projection in the y-z plane and is same
for both pebbles with respect to the disc. Assume that (1)
they land back on the disc before the disc has completed
1/8 rotation, (ii) their range is less than half the disc radius,
and (iii) o remains constant throughout. Then
Fig. A.54
(IIT JEE, 2012)
a. P lands in the shaded region and Q in the unshaded
region.
b. P lands in the unshaded region and Q in the shaded
region.
c. Both P and land in the unshaded region.
d. Both P and Q land in the shaded region.
11
816 c. a = d2
61. If block A is moving horizontally with velocity
find the velocity of block B at the instant as
Fig. 6.341.
locity then
as shown
Fig. 6.341
HVA
XVA
2√x² +h²
UVA
hva
24x²+h²
x² +h²
11
817 A particle is moving around a circular path with uniform angular speed ( ( omega ) ).
The radius of the circular path is ( (r) ) The acceleration of the particle is
A. ( frac{omega^{2}}{r} )
в. ( frac{omega}{r} )
( c . v_{w} )
D. ( v r )
11
818 Prove that the distance s metres, which
a body falling from rest covers in time
seconds is 4.9 times the square of the time t.
11
819 A body falling freely from rest covers ( frac{7}{16} ) of the total height in the last second of its fall. What is the height from which it falls?
( mathbf{A} cdot 24.2 m )
в. ( 40 m )
c. ( 80 m )
D. ( 46.8 m )
11
820 A particle moves on the curve ( y=frac{x^{4}}{4} )
where ( boldsymbol{x}=boldsymbol{t} / 2, mathbf{x} ) and ( mathbf{y} ) are measured in
metre and ( t ) in second. At ( t=4 s, ) find
the velocity of particle.
11
821 A boy is running along the circumference of a stadium with
constant speed. Which of the following is changing in this case?
A. Centripetal force acting on the boy
B. Distance covered per unit time
c. Direction in which the boy is running
D. Magnitude of acceleration
11
822 Figure ( (3-E 6) ) shows ( x-t ) graph of a
particle. Find the time ( t ) such that the average velocity of the particle during the period 0 to ( t ) is zero
11
823 53. A body is projected up along a
smooth inclined plane with velocity
u from the point A as shown in Fig.
5.199. The angle of inclination is 45°Ã
40 m
and the top is connected to a well of
diameter 40 m. If the body just
Fig. 5.199
manages to cross the well, what is the value of u? The
length of inclined plane is 2012 m.
a. 40 ms -1
b. 40/2 ms -1
c. 20 ms-1
d. 20/2 ms -1
11
824 The rate of change of displacement with time is
A. Speedd
B. Acceleration
c. Retardation
D. Velocity
11
825 23. A ship A streams due north at 16 kmh- and a ship B due
west at 12 kmh . At a certain instant B is 10 km north
east of A. Find the
a. magnitude of velocity of A relative to B.
b. nearest distance of approach of ships.
11
826 A man is going in a topless car with a velocity of ( 10.8 k m / h . ) It is raining vertically downwards. He has to hold the
umbrella at an angle of ( 53^{circ} ) to the vertical to protect himself from rain. The
actual speed of the rain is ( left(cos 53^{circ}=right. ) ( left.frac{3}{5}right) )
A ( .2 .25 mathrm{ms}^{-1} )
B. ( 3.75 mathrm{ms}^{-1} )
c. ( 0.75 mathrm{ms}^{-1} )
D. ( 2.75 mathrm{ms}^{-1} )
11
827 u. Nesuitaill verOCITY UI Dual Is JV
2. A stationary person observes that rain is falling
down at 30 kmh . A cyclist is moving up on an mo
plane making an angle 30° with horizontal at 10 kmh .
In which direction should the cyclist hold his umorena
prevent himself from the rain?
3)
a. At an angle tan
with inclined plane
b. At an angle tan
with horizontal
c. At an angle tam ” ( 19 ) with inclined plane
C. At an angle tan
with inclined plane
d. At an angle tan
with vertical
11
828 A object starts from rest at ( t=0 ) and
accelerates at a rate given by ( a=6 t )
What is its velocity?
A ( .6 t )
B. ( 3 t^{2} )
( c cdot 6 t^{2} )
D. 0
11
829 1. A body of mass m is thrown upwards at an angle with
the horizontal with velocity v. While rising up the velocity
of the mass after 1 seconds will be
(a) V(v cos 0)2 + (v sin o)?
(b) Viv cos 0 – v sin 0)2 – gt
(e) Vo?+ g?-(2v sin O) g
(d) Vu2+g2 – (2v cos 6) gt
11
830 When particle revolves with uniform speed on a circular path
A. no force acts on it
B. no acceleration acts on it it
c. no work is done by it
D. its velocity is constant
11
831 9. If the resultant of n forces of different magnitudes acting
at a point is zero, then the minimum value of n is
(a) 1 (6) 2 (c) 3 (d) 4
11
832 -U13
U12 U15
C2015
.
09. The height y and the distance x along the horizontal
plane of a projectile on a certain planet (with no
surrounding atmosphere) are given by y=(8t – 50) m and
x = 6t m, where t is in seconds. The velocity with which
the projectile
11
833 30. A ball rolls off the top of a stairway with a horizontal
velocity of magnitude 1.8 ms. The steps are 0.20 m
high and 0.20 m wide. Which step will the ball hit first
(8 = 10 ms?)
30
11
834 The free end of a thread wound on a
bobbin is passed round a nail ( boldsymbol{A} )
hammered into the wall. The thread is
pulled at a constant velocity. Assuming
pure rolling of bobbin, find the velocity
( v_{0} ) of a center of theybobbin at heh
center at he instant when the thread
forms an angle ( alpha ) with the vertical.
A ( cdot frac{v R}{R sin alpha-r} )
в. ( frac{v R}{text { R } sin alpha+r} )
c. ( frac{2 v R}{text { Rsind }+r} )
D. ( frac{v}{text { Rsin } alpha+r} )
11
835 8. The displacement of ball w.r.t. ground during its flight
is
a. 32.64 m b. 2 m c. 52 m d. 30.64 m
11
836 The velocity ( v ) of waves produced in
water depends on their wavelength ( lambda )
the density of water ( rho, ) and acceleration
due gravity ( g ). The square of velocity is
proportional to:
( mathbf{A} cdot K sqrt{(g lambda)} )
B . ( lambda^{-1} g^{-1} rho^{-1} )
c. ( lambda rho g )
D. ( lambda^{2} g^{-2} rho^{-1} )
11
837 Illustration 5.61 Two particles A and B are moving with
constant velocities v, and v2. At t = 0, v, makes an angle e,
with the line joining A and B and v, makes an angle e, with
the line joining A and B. Find their velocity of approach.
VI
02
Fig. 5.126
11
838 In a Rutherford scattering experiment
when a projectile of charge ( Z_{1} ) and
mass ( M_{1} ) approaches a target nucleus
of charge ( Z_{2} ) and mass ( M_{2} ) the distance
to closest approached is ( r_{0} . ) The energy
of the projectile is
A . directly proportional to ( M_{1} times M_{2} )
B. directly proportional to ( Z_{1} Z_{2} )
C. directly proportional to to ( Z_{1} )
D. directly proportional to mass ( M_{1} )
11
839 Which of the following is the unit vector perpendicular to ( vec{A} ) and ( vec{B} ) ?
( A cdot frac{widehat{A} times widehat{B}}{A B sin theta} )
B. ( frac{widehat{A} times widehat{B}}{A B cos theta} )
c. ( frac{vec{A} times vec{B}}{A B sin theta} )
D. ( frac{vec{A} times vec{B}}{A B cos theta} )
11
840 34. Which of the following pairs of forces cannot be added to
give a resultant force of 4 N?
a. 2 N and 8N
b. 2 N and 2 N
c. 2 N and 6N
d. 2 N and 4 N
11
841 Uniform circular motion is called
continuously accelerated motion mainly because its :
A. direction of motion changes
B. speed remains the same
c. velocity remains the same
D. direction of motion does not change
11
842 The shortest possible time required by
the boat to cross the river will be:-
A. 125 sec
B. 250 sec
C . 500 sec
D. ( frac{250}{sqrt{3}} ) sec
11
843 If air resistance is not considered in
projectiles, the horizontal motion takes place with :
A. Constant velocity
B. Constant acceleration
c. constant retardation
D. Variable velocity
11
844 6. The resultant of two vectors A and B is perpendicular to the
vector A and its magnitude is equal to half the magnitude
of vector B. The angle between A and B is
(a) 120°
(b) 150°
(c) 135°
(d) None of these
11
845 On a linear escalator running between
two points ( A ) and ( B, ) a boy takes time ( t_{1} )
to move from ( A ) to ( B ), if the boy runs with a constant speed on the escalator.
If the boy runs from ( B ) to ( A ), he takes
time ( t_{2} ) to reach ( B ) from ( A ). The time
taken by the boy to move from ( boldsymbol{A} ) to ( boldsymbol{B} ) if he stands still on the escalator will be
(The escalator moves from ( boldsymbol{A} ) to ( boldsymbol{B} ) )
A ( cdot frac{t_{1} t_{2}}{t_{2}-t_{1}} )
В. ( frac{2 t_{1} t_{2}}{t_{2}-t_{1}} )
c. ( frac{t_{1}^{2}+t_{2}^{2}}{t_{1} t_{2}} )
D. ( frac{t_{1}^{2}-t_{2}^{2}}{t_{1} t_{2}} )
11
846 For two particular vectors ( vec{A} ) and ( vec{B} ) it is known that ( overrightarrow{boldsymbol{A}} times overrightarrow{boldsymbol{B}}=overrightarrow{boldsymbol{B}} times overrightarrow{boldsymbol{A}} . ) What
must be true about the two vectors?
A. At least one of the two vectors must be the zero vector
в. ( vec{A} times vec{B}=vec{B} times vec{A} ) is true for any two vectors
c. one of the two vectors is a scalar multiple of the other vector.
D. The two vectors must be perpendicular to each other
11
847 If ( A B C D ) is a parallelogram, ( A B= ) ( mathbf{2} hat{mathbf{i}}+mathbf{4} hat{mathbf{j}}-mathbf{5} hat{boldsymbol{k}} ) and ( boldsymbol{A} boldsymbol{D}=hat{boldsymbol{i}}+mathbf{2} hat{boldsymbol{j}}+mathbf{3} hat{boldsymbol{k}} )
then the unit vectors in the direction of
( B D ) is
A ( cdot frac{1}{sqrt{69}}(hat{i}+2 hat{j}-8 hat{k}) )
B ( cdot frac{1}{69}(hat{i}+2 hat{j}-8 hat{k}) )
c. ( frac{1}{sqrt{69}}(-hat{i}-2 hat{j}+8 hat{k}) )
D ( cdot frac{1}{69}(-hat{i}-2 hat{j}+8 hat{k}) )
11
848 Position vector that defines position of
vector in three dimensions having
formula of
A ( cdot sqrt{left(a^{2}+b^{2}+c^{2}right)} )
B. ( sqrt{(a+b+c)} )
C ( cdot sqrt{left(a^{2}-b^{2}+c^{2}right)} )
D. ( left(a^{2}+b^{2}+c^{2}right) )
11
849 A person observes that rain strikes him
normally when he is moving with 2 kmph. When he reverses his direction and moves with the same speed, the
rain will strike him at an angle ( 45^{circ} ) with the vertical. Determine the true velocity of rainfall is?
A ( cdot 2 sqrt{5} ) kmph
B. ( sqrt{2} ) kmph
c. ( 5 sqrt{2} ) kmph
D. ( sqrt{5} ) kmph
11
850 29. A stone is projected from the point on the ground in sa
a direction so as to hit a bird on the top of a telegraph po
of height h and then attain the maximum height 3h/2 above
the ground. If at the instant of projection the bird were to
fly away horizontally with uniform speed, find the ratio
between horizontal velocities of the bird and stone if the
stone still hits the bird while descending.
11
851 A rotating wheel has a speed of 1200 rpm and the it is made to slow down at
a constant rate at 2 rad( / s^{2} ). The number of revolution it makes before coming to rest will be:
11
852 A golfer swings a golf club so that the end of the club is moving ( 30 mathrm{m} / mathrm{s} ) when it strikes the ball. The radius of the
circular path for the end of the club (which includes the club and the
golfer’s arms ) is ( 1.8 mathrm{m} )
What is the centripetal acceleration of
the end of the club as it strikes the
ball?
( mathbf{A} cdot 500 m / s^{2} )
B. ( 1.7 mathrm{m} / mathrm{s}^{2} )
( mathbf{c} cdot 0.06 m / s^{2} )
D. ( 54 mathrm{m} / mathrm{s}^{2} )
E . ( 0 mathrm{m} / mathrm{s}^{2} )
11
853 . 21
a. 1 1
10. An object is moving in the x-y plane with the position as
a function of time given by i = x(t)i + y(t)j. Point O is
at x = 0, y = 0. The object is definitely moving towards O
when
a. V > 0,, > 0 b. Vx < 0,vy < 0
c. xvx + yv, 0
11
854 =
16. The relative velocity of B as seen from A in
a. -8√2 + 6/2 b. 4√2 + 3/3)
c. 3/5i + 2√3 d. 3/27 +4√37
e
11
855 When a body moves along a circular path,its direction of speed
A. remains constant
B. keep changing continuosly
c. may change sometime
D. cant be predicted
11
856 The rear wheels of a car are turning at an angular speed of 60 rad/s. The brakes are applied for 5 s, causing a uniform angular retardation of
( 8 r a d / s^{-2} . ) The number of revolutions turned by the rear wheels during the braking period is about:
A . 48
B. 96
( c .32 )
D. 12
11
857 The distance PQ is?
( mathbf{A} cdot 20 mathrm{m} )
( mathbf{B} cdot 10 sqrt{3} mathrm{m} )
( c cdot 10 m )
D. 5 m
11
858 In uniform circular motion, the factor
that remains constant is :
A. acceleration
B. momentum
c. kinetic energy
D. linear velocity
11
859 ( |overline{mathbf{a}} cdot overline{mathbf{b}}|^{2}-|overline{mathbf{a}} times overline{mathbf{b}}|^{2}= )
( mathbf{A} cdot a b cos theta )
B ( cdot a^{2} b^{2} cos theta )
C ( cdot a^{2} b^{2} cos 2 theta )
( mathbf{D} cdot a b cos 2 theta )
11
860 The position of a particle moving in the ( X ) -Y plane from origin at any time ( t )
is given by ( boldsymbol{x}=left(mathbf{3} boldsymbol{t}^{2}-mathbf{6} boldsymbol{t}right) mathbf{m} ; boldsymbol{y}=left(boldsymbol{t}^{2}-right. )
( 2 t) mathrm{m}, ) where ( t ) is in seconds. Select the
correct statement(s) about the moving particle from the following.
A. The acceleration of the particle is zero at ( t=0 ) second
B. The velocity of the particle is zero at ( t=0 ) second
c. The velocity of the particle is zero at ( t=1 ) second
D. The velocity and acceleration of the particle are never zero
11
861 33. The projection speed is :
a. 137 ms
c. 114 ms -1
b. 141 ms-1
d. 140 ms-1
11
862 3. The range R of projectile is same when its maximum
heights are h, and hy. What is the relation between R, hj,
and h?
a. R=sh
b. R= √2hh
c. R=2 sm
d. R=4 /hh
11
863 21. The vertical height h of P from 0,
a. 10
m b . 5 m c. 15 m
d. 20 m
um boicotettoia
L..
.1.
C.
11
864 DULU. MULTI
26. Find the magnitude of the unknown forces 11
all forces is zero Fig. 3.75.
15
539
90°
10
Fig. 3.75
11
865 turp
lali
A boy on a train of height h, projects a coin to his friend
of height h, standing on the same train, with a velocity v
relative to the train, at an angle with horizontal. If the
train moves with a constant velocity V’ in the direction of
x-motion of the coin, find the (a) distance between the boys
so that the second boy can catch the coin, (b) maximum
height attained by the coin, and (c) speed with which the
second boy catches the coin relative to himself (train) and
ground
11
866 A bead of mass ( m ) slides on a
hemispherical surface with a velocity ( boldsymbol{v} )
at an angular position ( theta ). If the coefficient of friction between the bead
and hemispherical surface is ( mu, ) Find
the magnitude of Angular momentum of the bead about ( O ) in the position
shown.
11
867 A trian of length ( 200 m ), travelling at ( 30 m s^{-1} ) overtakes another train of
length ( 300 m ) travelling at ( 20 m s^{-1} . ) The time taken by the first train to pass the second train is
A .30 sec
B. 50 sec
c. 10 sec
D. 40 sec
11
868 L. 48WS
5. The correct velocity-time graph for the rocketeer would
be
a. VA
b. 1
d. vf
11
869 A small object of mass ( m, ) on the end of
a light cord, is held horizontally at a distance ( r ) from a fixed support as
shown. The object is then released. What is the tension in the cord when the
object is at the lowest point of its
swing?
A. ( m g / 2 )
в. ( m g )
( mathbf{c} cdot 2 m g )
D. ( 3 m g )
11
870 At the height ( 80 m, ) an aeroplane is moving with ( 150 m / s . ) A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? ( (text { Given } g= )
( left.10 m / s^{2}right) )
A. ( 605.3 mathrm{m} )
B. ( 600 m )
( c .80 m )
D. 230 ( m )
11
871 A projectile is given an initial velocity of ( hat{mathbf{i}}+2 hat{j} . ) The cartesian equation of its
path is ( left(boldsymbol{g}=mathbf{1 0} boldsymbol{m} boldsymbol{s}^{-2}right) )
A ( cdot y=2 x-5 x^{2} )
В . ( y=x-5 x^{2} )
C ( .4 y=2 x-5 x^{2} )
D. ( y=2 x-25 x^{2} )
11
872 Find the moments of time when the
particle is at the distance ( 10.0 mathrm{cm} ) from the origin.
A. ( 1.1,9, ) and ( 11 s )
B. ( 1,10, ) and ( 11 s )
c. ( 1.1,10, ) and ( 11 s )
D. ( 1.1,9, ) and ( 13 s )
11
873 What is banking of roads? Why banking is necessary for a curved road? 11
874 7. A scooter going due east at 10 ms-1 turns right through an
angle of 90°. If the speed of the scooter remains unchanged
in taking turn, the change is the velocity of the scooter is
(a) 20.0 ms-1 south eastern direction
(b) Zero
(c) 10.0 ms- in southern direction
(d) 14.14 ms-l in south-west direction
11
875 A stone is moved in a horizontal circle of
radius ( 4 mathrm{m} ) by means of a string at a height of ( 20 mathrm{m} ) above the ground. The string breaks and the particle’ flies off horizontally, striking the ground 10m away. The centripetal acceleration during circular motion is
A ( cdot 6.25 m s^{-2} )
B. ( 12.5 m s^{-2} )
c. ( 18.75 mathrm{ms}^{-2} )
D. ( 25 m s^{-2} )
11
876 The distances covered by a particle thrown in a vertical plane, in horizontal and vertical directions at any instant of
time ‘t’ are ( x=3 t ) and ( y=4 t-5 t^{2} )
.The acceleration due to gravity is
A ( .8 m / s^{2} )
B . ( 9 m / s^{2} )
( mathrm{c} cdot 10 mathrm{m} / mathrm{s}^{2} )
D. ( 16 m / s^{2} )
11
877 The velocity and acceleration vectors of a particle undergoing circular motion ( operatorname{are} overrightarrow{boldsymbol{v}}=2 hat{boldsymbol{i}} boldsymbol{m} / boldsymbol{s} ) and ( overrightarrow{boldsymbol{a}}=boldsymbol{2} hat{boldsymbol{i}}+ )
( 4 hat{j} m / s^{2} ) respectively at an instant of
time. The radius of the circle is
A . ( 1 m )
B. ( 2 m )
( c .3 m )
D. ( 4 m )
11
878 22. The maximum height attained by the particle (from the
line O)
a. 20.5 m b. 5 m c. 16.25 m d. 11.25 m
11
879 Why is the motion of a body moving with a constant speed around a circular path said to be accelerated? 11
880 A particle moves according to the equation ( t=sqrt{x}+3 . ) When the particle
comes to rest for the first time?
A . ( 3 s )
в. 2.5 ( s )
( mathrm{c} .3 .5 mathrm{s} )
D. None of these
11
881 A ball thrown with a velocity of ( 49 m s^{-1} ) got the maximum range recorded in the atmosphere as ( 225 m ). The decrease in
range due to the atmosphere is
A. ( 0 m )
B. ( 245 m )
( mathbf{c} .225 m )
D. 20m
11
882 1. Tivo particles were projected one by one with the same
initial velocity from the same point on level ground. They
follow the same parabolic trajectory and are found to be
in the same horizontal level, separated by a distance of
1 m. 2 s after the second particle was projected. Assume
that the horizontal component of their velocities is
0.5 ms! Find
a. the horizontal range of the parabolic path.
b. the maximum height for the parabolic path.
11
883 An object moving with a speed of 6.25 ( mathrm{m} / mathrm{s}, ) is decelerated at a rate given by ( frac{d v}{d t}=-2.5 sqrt{v} ) where ( v ) is the instantaneous speed. The time taken by the object, to come to rest, would be then
( mathbf{A} cdot 2 s )
B . ( 4 s )
c. ( 8 s )
D. ( 1 s )
11
884 26. A ball thrown by one player reaches the other in 2 s. The
maximum height attained by the ball above the point of
projection will be about
a. 2.5 m b. 5
m c . 7.5 m d. 10 m
1.
T
If the ti
11
885 37. The equation of motion of a projectile is y=1
The horizontal component of velocity is 3 ms. What is
the range of the projectile?
a. 18
m b . 16 m c. 12
m d . 21.6 m
ubon its maximum
.
.1
.
11
886 Two trains are each 50 m long moving
parallel towards each other at speeds ( 10 m / s ) and ( 15 m / s ) respectively, at what time will they pass each other?
11
887 The components of a vector along the ( x ) and ( y ) -directions are ( (n+1) ) and 1
respectively. If the coordinate system is
rotated by an angle ( theta=60^{circ} ), then the
components change to ( n ) and ( 3 . ) The
value of ( n ) is
A .2
B. ( 1+sqrt{3} )
( c cdot 1-sqrt{3} )
D. ( 1 pm sqrt{3} )
11
888 A train at rest has a length of ( 100 mathrm{m} . ) At what speed must it approach a tunnel of length ( 80 mathrm{m} ) so that an observer at rest with respect to the tunnel will see
that the entire train is in the tunnel at
one time?
A . 1.25c
B. 0.8ç
c. ( 0.64 c )
D. 0.6c
E . ( 0.36 c )
11
889 A curved road of ( 50 m ) in radius is
banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should
be changed to
A. 200 ( mathrm{m} )
B. 100 ( m )
( c cdot 50 m )
D. None of the above
11
890 The horizontal ranges described by two
projectiles, projected at angles ( left(45^{circ}-right. )
( theta ) ) and ( left(45^{circ}+thetaright) ) from the same point
and same velocity are in the ratio.
A . 2: 1
B. 1: 1
( c cdot 2: 3 )
D. 1: 2
11
891 The resultant of two forces ( P ) and ( Q ) is ( R )
If ( Q ) is doubled and when ( Q ) is reversed ( R ) is again doubled. Show that ( P: Q: )
( boldsymbol{R}=sqrt{mathbf{2}}: sqrt{mathbf{3}}: sqrt{mathbf{2}} )
11
892 The sum and difference of two
perpendicular vectors of equal length
are
A. Perpendicular to each other and of equal length
B. Perpendicular to each other and of different lengths
c. of equal length and have an obtuse angle between them
D. of equal length and have an acute angle between them
11
893 Six persons are situated at the corners
of a hexagon of side ( l ). They move at a
constant speed ( v . ) Each person
maintains a direction towards the
person at the next corner. When will the
persons meet?
A.
в. ( frac{2 l}{3 v} )
c. ( frac{3 l}{2 v} )
D. ( frac{2 l}{v} )
11
894 d. 25 b. 3.
c. ls d . 2. 5
38. Two balls are projected from points A and B BRO
in vertical plane as shown in Fig. A.17. AB is
a straight vertical line. The balls can collide
in mid air if vi/v2 is equal to
sine,
sin 02
b. –
sine,
Fig. A.17
cos,
coso
cos O2
cos
portiole in throunot met with
Aloi
a.
sin 02
11
895 5
nakes an angle
20. At the point where the particle’s velocity makes an
0/2 with the horizontal
e
u² cos²0 sec
u² cos² O sec ² 0

a.
b.
2u? cos? O sec
C.
u? cos? A sec30
138
11
896 A moves with constant velocity u along
then ( x ) -axis. ( B ) always has velocity
towards A. After how much time will B
meet ( A ) if ( B ) moves with constant speed
V? What distance will be travelled by A
and B?
11
897 Illustration 5.21 A boy of height 1.5 m, making move
a skateboard due east with velocity 4 m s’, throws a com
vertically up with a velocity of 3 ms relative to himself
a. Find the total displacement of the coin relative to grown
till it comes to the hand of the boy.
b. What is the maximum height attained by the coin wrt
ground?
CUL
m
an from hav Aletenih
11
898 A car A moves with velocity ( 15 m s^{-1} ) and B with velocity ( 20 m s^{-1} ) are moving in opposite directions as shown in the figure. Find the relative velocity of B
w.r.t. ( A ) and ( A ) w.r.t. ( B ).
11
899 A small body is thrown at an angle to
the horizontal with the initial velocity ( vec{v}_{0} ) Neglecting the air drag, find the mean
velocity vector ( langlevec{v}rangle ) averaged over the
first ( t ) sec and over the total time of
motion.
A ( cdot(vec{v})_{t}=vec{v}_{0}-frac{g t}{2},langlevec{v}rangle=vec{v}_{0}-g frac{left(vec{v}_{0} gright)}{g^{2}} )
B ( cdot(vec{v})_{t}=vec{v}_{0}-frac{g t}{2},langlevec{v}rangle=vec{v}_{0}+g frac{left(vec{v}_{0} gright)}{g^{2}} )
c. ( (vec{v})_{t}=vec{v}_{0},langlevec{v}rangle=vec{v}_{0}-g frac{left(vec{v}_{0} gright)}{g^{2}} )
D. None of these
11
900 001
ov2
39. A particle is thrown at time t = 0 with a 10
velocity of 10 ms at an angle 60° with the 13
horizontal from a point on an inclined plane, a
making an angle of 30° with the horizontal. Fig. A.18
The time when the velocity of the projectile becomes
parallel to the incline is
2
a. FSb. Tas
C. 13 s
d.
Tas
11
901 Name a physical quantity that remains constant in a uniform circular motion.
A. Velocity
B. Acceleration
c. Momentum
D. Angular speed
11
902 13. Two equal forces (P each) act at a point inclined to each
other at an angle of 120°. The magnitude of their resultant
is
(a) P/2 (b) P/4 (c) P (d) 2P
11
903 A glass wind screen whose inclination with the vertical can be changed is
mounted on a car. The car moves
horizontally with a speed of ( 2 m / s . A t )
what angle ( alpha ) with the vertical should
the wind screen be placed so that the rain drops falling vertically downwards
with velocity ( 6 m / s ) strike the wind
screen perpendicularly?
( mathbf{A} cdot tan ^{-1}(3) )
B ( cdot tan ^{-1}(4) )
c. ( tan ^{-1}left(frac{1}{3}right) )
D. ( tan ^{-1}left(frac{1}{4}right) )
11
904 In the cube of side ‘ ( a^{prime} ) shown in the
figure, the vector from the central point
of the face ( A B O D ) to the central point
of the face ( B E F O ) will be
A ( cdot frac{1}{2} a(hat{i}-hat{k}) )
B ( cdot frac{1}{2} a(hat{j}-hat{i}) )
c. ( frac{1}{2} a(hat{k}-hat{i}) )
D. ( frac{1}{2} a(hat{j}-hat{k}) )
11
905 A car is moving in a circular track of radius ( 10 mathrm{m} ) with a constant speed of 10 ( mathrm{m} / mathrm{s} . mathrm{A} ) plumb bob is suspended from the roof of the car by a light weight rigid rod of ( 1 mathrm{m} ) long.The angle made by the rod with track is:
A. 0
B. 30
( c cdot 45 )
D. 60
11
906 A projectile fired from the top of a ( 40 m ) high cliff with an initial speed of ( 50 m / s ) at an unknown angle. Find its speed when it hits the ground. ( (g= ) ( left.10 m / s^{2}right) ) 11
907 If a ball is thrown vertically upwards with speed ( u, ) the distance covered during the last ( t ) seconds of its ascent is
( mathbf{A} cdot u )
в. ( frac{1}{2} g t^{2} )
c. ( u t-frac{1}{2} g t^{2} )
D. ( (u+g t) t )
11
908 If particle takes ( t ) seconds less and acquires a velocity of ( mathrm{v} mathrm{m} / mathrm{s} ) more in falling through the same distance on to planets where the acceleration due to gravity are ( 2 g ) and ( 8 g ) respectively, then
A. ( v=4 g t )
B. ( v=5 g t )
c. ( v=2 g t )
D. ( v=16 g t )
11
909 A man can swim in still water with a
velocity ( 5 mathrm{m} / mathrm{s} ). He wants to reach at
directly opposite point on the other bank
of a river which is flowing at a rate of ( 4 m / s . ) River is ( 15 m ) wide and the man can
run with twice the velocity as compared
with velocity of swimming. If he swims perpendicular to river flow and then run
along the bank, then time taken by him to reach the opposite point is:
A. 3 sec
B. less than 3 sec
c. 5 sec
D. 4.2 sec
11
910 A stone is thrown vertically upward with
an initial velocity ( V_{0} . ) The distance
traveled in time ( 4 v_{0} / 3 g ) is
( ^{A} cdot frac{2 v_{0}^{2}}{g} )
в. ( frac{v_{0}^{2}}{2 g g g} )
( ^{mathrm{c}} cdot frac{4 v_{0}^{2}}{9 g} )
D. ( frac{5 v_{0}^{2}}{9 g} )
11
911 3. The time taken to cross the river is
a. h
b. En
czten d. none
11
912 Why is the work done on an object
moving with uniform circular motion
zero?
11
913 A triangular plate of uniform thickness and density is made to rotate about an
axis perpendicular to the plane of the
paper and
(a) passing through ( boldsymbol{A} ) passing through ( B, ) by the
application of some force ( boldsymbol{F} ) at ( boldsymbol{C}(operatorname{mid}- )
point of ( A B) ) as shown in fig. In which
case is angular acceleration more
A ( . ) in case ( (a) )
B. in case (b)
c. both ( (a) ) and ( (b) )
D. none of these
11
914 A stationary man observes that the rain
strikes him at an angle of ( 60^{circ} ) to the horizontal. When he begins to move with
the velocity of ( 25 m / s ) then the drops
appear to strike him at an angle ( 30^{circ} )
from horizontal. The velocity of the rain drops is :
( mathbf{A} cdot 25 m / s )
B. ( 50 mathrm{m} / mathrm{s} )
c. ( 12.5 m / s )
D. ( 25 sqrt{2} )
11
915 Locating position vector of a point object 11
916 k
a
28. Two particles A and B are placed A-
as shown in Fig. A.12. The particle
VB
A, on the top of tower, is projected
horizontally with a velocity u and
particle B is projected along the surface
Fig. A.12
towards the tower, simultaneously. If both particles meet
each other, then the speed of projection of particle B is
[ignore any friction]
a.
d) 8
b.
d.
V2H
c. de
tu
d. u
11
917 If a body is projected horizontally from the top of the tower then acceleretions
of the body along the vertical direction of path is
A. Decreases
B. Increases
c. Remains same
D. zero
11
918 25. The front wind screen of a car is inclined at an angle 60°
with the vertical. Hailstones fall vertically downwards
with a speed of 513 ms. Find the speed of the car so
that hailstones are bounced back by the screen in vertically
upward direction with respect to car. Assume elastic
collision of hailstones with wind screen.
11
919 Illustration 5.67 A particle moves in a circle of radius 2 cm
at a speed given by v = 4t, where v is in cms and t is in
seconds.
a. Find the tangential acceleration at t = 1s.
b. Find total acceleration at t = 1s.
Sol
11
920 COMPONCINO
A stone is projected from level ground with speed u
an angle with horizontal. Somehow the acceleration
gravity (8) becomes double (that is 2g) immediately art
stone reaches the maximum height and remains same thereafter.
Assume direction of acceleration due to gravity always vertically
downwards.
14. The total time of flight of particle is:
3 usine
(b) u sin 0(1+1)
gl72)
2u sin e
2
g
11
921 Two projectiles ( A ) and ( B ) thrown with
same speed but angles are ( 40^{circ} ) and ( 50^{circ} ) with the horizontal.Then
A . A will fall earlier
B. B will fall earlier
c. both will fall at the same time
D. None of these
11
922 Assertion
Projectile motion is called a two dimensional motion, although it takes
place in space.
Reason
In space it takes place in a plane.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion is incorrect but Reason is correct.
11
923 A ball is projected from the ground with a speed of ( 20 m / s ) at an angle of 45 with
horizontal. There is a wall of ( 25 m ) height
at a distance of ( 10 m ) from the
projection point. The ball will hit the wal at a height of
( A cdot 5 m )
в. ( 7.5 m )
c. ( 10 m )
D. ( 12.5 m )
11
924 се со цього часу
15. Two horizontal forces of magnitudes 10 N and PN act on
a particle. The force of magnitude 10 N acts due west and
the force of magnitude PN acts on a bearing of 30° east of
north as shown in figure. The resultant of these two force
acts due north. Find the magnitude of this resultant.
PN
309
10 N
Fig. 3.72
11
925 If ( overrightarrow{boldsymbol{u}}=overrightarrow{boldsymbol{a}}-overrightarrow{boldsymbol{b}} ; overrightarrow{boldsymbol{v}}=overrightarrow{boldsymbol{a}}+overrightarrow{boldsymbol{b}} ) and ( |overrightarrow{boldsymbol{a}}|=|overrightarrow{boldsymbol{b}}|= )
2 then ( |vec{u} times vec{v}| ) is equal to
( sqrt[A cdot]{2left(16-(vec{a} cdot vec{b})^{2}right)} )
в. ( 2 sqrt{left(16-(vec{a} . vec{b})^{2}right)} )
( ^{mathrm{c}} sqrt[2]{left(4-(vec{a} cdot vec{b})^{2}right)} )
D . ( left[4-(vec{a} . vec{b})^{2}right] )
11
926 Illustration 5.51 Rain is falling vertically and a man
moving with velocity 6 ms. Find the angle at which the man
should hold his umbrella to avoid getting wet.
11
927 A particle is revolving in a circle, clockwise in the plane of the circle. The angular acceleration in directed
A. Towards the center in the plane of the paper.
B. Radially outwards in the plane of the paper
c. Perpendicular to the plane of the paper.
D. Veertically in the plane of the paper.
11
928 A steamer crosses a river having a width of ( 240 m ) which is flowing with a
speed of ( 8 m / s . ) In order to cross the
river along the shortest path, find the time of crossing the river. [velocity of steamer in still water is ( 10 mathrm{ms}^{-1} ) ].
11
929 27. A ball is projected for maximum range with speed
20 ms. A boy is located at a distance 25 m from poin
of throwing start run to catch the ball at the time when
the ball was projected. Find the speed of the boy so that
he can catch the ball (Take g = 10 ms)
11
930 A ball is projected from the ground at angle ( theta ) with the horizontal. After ( 1 s, ) it
is moving at angle ( 45^{circ} ) with the horizontal and after ( 2 s ) it is moving
horizontally. What is the velocity of projection of the ball?
A ( cdot 10 sqrt{3} m s^{-1} )
B ( cdot 20 sqrt{3} m s^{-1} )
D. ( 20 sqrt{2} mathrm{ms}^{-1} )
11
931 toppr
Q Type your question
( r, ) as seen in the picture.
If each of the diagrams among the
possible answers shows flies with the same acceleration as the one pictured
directly below, which fly has a speed that is twice the speed of the fly pictured directly below?
( A )
B.
( c )
radius ( =r / 2 )
D.
radius ( =r / 4 )
E. None of the objects in this question are accelerating
since thev al speed
11
932 Juur av uy munt un ground!
4. A platform is moving upwards with a constant acceleration
of 2 ms. At time t = 0, a boy standing on the platform
throws a ball upwards with a relative speed of 8 ms.At
this instant, platform was at the height of 4 m from the
ground and was moving with a speed of 2 ms.
Take g = 10 ms. Find
a. when and where the ball strikes the platform.
b. the maximum height attained by the ball from the
ground.
c. the maximum distance of the ball from the platform.
11
933 A particle is moving in a circular path of radius r. Its displacement after moving through half the circle would be:
A. zero
B.
( c cdot 2 r )
D. ( frac{2}{r} )
11
934 The angle between velocity and acceleration of a particle describing uniform circular motion is
( mathbf{A} cdot 180^{circ} )
B . ( 45^{circ} )
( mathrm{c} cdot 90^{circ} )
D. ( 60^{circ} )
11
935 Man A is sitting in a car moving with a speed of ( 54 mathrm{km} / mathrm{hr} ) observes a man ( mathrm{B} ) in
front of the car crossing perpendicularly a road of width ( 15 mathrm{m} ) in three seconds. Then the velocity of man
( mathrm{B}(text { in } mathrm{m} / mathrm{s}) ) will be
A ( .5 sqrt{10} ) towards the car at some angle
B. ( 5 sqrt{10} ) away from the car at some angle
c. 5 perpendicular to the road
D. 15 along the road
11
936 Three forces ( vec{P}, vec{Q} ) and ( vec{R} ) acting along ( I A )
IB and IC, where I is the incentre of a
( Delta mathrm{ABC}, ) are in equilibrium. Then ( overrightarrow{mathbf{P}}: overrightarrow{mathbf{Q}}: )
( overrightarrow{mathbf{R}} ) is:
( ^{A} cdot cos frac{A}{2}: cos frac{B}{2}: cos frac{C}{2} )
B ( cdot sin frac{mathrm{A}}{2}: sin frac{mathrm{B}}{2}: sin frac{mathrm{C}}{2} )
c. ( sec frac{mathrm{A}}{2}: sec frac{mathrm{B}}{2}: sec frac{mathrm{C}}{2} )
D ( operatorname{cosec} frac{mathrm{A}}{2}: operatorname{cosec} frac{mathrm{B}}{2}: operatorname{cosec} frac{mathrm{C}}{2} )
11
937 3. A boat which has a speed of 5 kmh in still water crosses
a river of width 1 km along the shortest possible path in
15 min. The velocity of the river water in kmh is
b. 3
c. 4
d. 141 (IIT JEE, 1988)
10.
c
11
938 35. Shots are fired simultaneously from the
top and bottom of a vertical cliff with the
elevation a = 30°, B = 60°, respectively
(Fig. A.15). The shots strike an object AB
simultaneously at the same point. If a = a = 30 3 m
30 V3 m is the horizontal distance of the Fig. A.15
object from the cliff, then the height h of
the cliff is
a. 30 m b. 45 m c. 60 m d. 90 m
11
939 The component of a vector r along x-axis
will have maximum value if:
( A cdot r ) is along positive ( y ) -axis
B. r is along positive x-axis
C . r makes an angle of ( 45^{circ} ) with the x-axis
D. r is along negative y-axis
11
940 A particle moves according to the
equation ( boldsymbol{x}=mathbf{2} boldsymbol{t}^{2}-mathbf{5} boldsymbol{t}+boldsymbol{6} . ) The average
velocity in the first ( 3 s ) and velocity at
( t=3 s ) are repectively
A ( cdot 1 m s^{-1}, 7 m s^{-1} )
B. ( 4 m s^{-1}, 3 m s^{-1} )
( mathrm{c} cdot 2 m s^{-1}, 5 m s^{-1} )
D. ( 3 m s^{-1}, 7 m s^{-1} )
11
941 A particle located at ( x=0 ) at time ( t=0 )
starts moving along the positive ( x ) direction with a velocity ‘v’ that varies as ( boldsymbol{v}=boldsymbol{alpha} sqrt{boldsymbol{x}} . ) The displacement of the
particle varies with time as?
11
942 Two trains, each ( 50 m ) long, are travelling in opposite directions with velocity ( 10 m / s ) and ( 15 m / s . ) The time of crossing is-
( mathbf{A} cdot 2 s )
B . ( 4 s )
c. ( 2 sqrt{3} s )
D. ( 4 sqrt{3} s )
11
943 Find out the angular acceleration of a washing machine, starting from rest, accelerates within ( 3.14 s ) to a point
where it is revolving at a frequency of
( mathbf{2 . 0 0 H z} )
A. ( 0.100 r a d / s^{2} )
B. ( 0.637 r a d / s^{2} )
c. 2.00 rad ( / s^{2} )
D. 4.00 rad ( / s^{2} )
E ( .6 .28 mathrm{rad} / mathrm{s}^{2} )
11
944 Figure shows the trajectory of a projections fired at an angle ( theta ) with the horizontal. The elevation angle of the
highest point as seen from the point of
launching is ( varphi . ) The relation between ( varphi )
( operatorname{ans} theta ) is
A ( cdot tan phi=frac{1}{2} tan theta )
B. ( tan ^{2} phi=frac{1}{2} tan ^{2} )
( mathbf{c} cdot sin phi=frac{1}{2} sin theta )
D. ( cos ^{2} phi=frac{1}{2} cos ^{2} theta )
11
945 toppr
Q Type your question
objects moving at constant speed in circular paths are shown. The objects speeds, circular path radii, and masses
are given in each diagram.
In which situation does the pictured object have the greatest amount of acceleration due to its circular motion?
( A )
B.
( c )
( D )
E. None of the object in this question is accelerating, since they all are moving at a constant speed
11
946 A particle ( P ) is fixed at certain point in
horizontal plane and another particle ( Q )
is moving around ( mathrm{P} ) in circular path (with centre 0 ) of radius ‘r’ with
constant speed ‘u’.’ ‘P’ observes the
motion of ‘Q’. Pick out correct statement
A. Velocity of approach between ( mathrm{P} ) and ( mathrm{Q} ) will be variable.
B. Velocity of approach between ( P ) and ( Q ) will be always negative.
C. Velocity of approach between ( mathrm{P} ) and ( mathrm{Q} ) will be always constant.
D. None of these
11
947 Define centripetal acceleration. Derive an expression for the centripetal
acceleration of a particle moving with
uniform speed ‘v’ along a circular path
of radius ‘r’. Give the direction of this
acceleration.
11
948 ards north at an angle of 45° to the
n travels distance of 4 km towards north at an
to the east. How far is the point from the
What angle does the straight line joining
12. A car travels 6 km towards north at an
east and then travels distance of 4 km
angle of 135º to the east. How far is
starting point? What angle does the
its initial and final position makes with the e
(a) 50 km and tan-? (5)
(b) 10 km and tan-? (15)
(c) 52 km and tan-? (5)
(d) 52 km and tan-‘(15)
11
949 ( m ) 11
950 A man on a moving cart, facing the direction of motion throws a ball
straight up with respect to himself. Which of the following statements is(are) correct?
This question has multiple correct options
A. The ball will always return to him
B. The ball will never return to him.
c. The ball will return to him if the cart moves with a constant velocity
D. The ball will fall behind him if the cart moves with some acceleration
11
951 Calculate the angle between two vectors 2F and ( sqrt{2} mathrm{F} ) so that the resultant force is ( mathrm{F} sqrt{10} )
A. 120 degrees
B. 90 degrees
c. 60 degrees
D. 45 degrees
11
952 The resultant of ( vec{P} ) and ( vec{Q} ) is ( vec{R} ). If ( vec{Q} ) isdoubled, ( vec{R} ) is doubled; when ( vec{Q} ) is reversed, ( overrightarrow{boldsymbol{R}} ) is again doubled. Find ( boldsymbol{P} ) :
( boldsymbol{Q}: boldsymbol{R} )
11
953 The resultant of two vectors ( vec{P} ) and ( vec{Q} ) is
( vec{R} ). If the magnitude of ( vec{Q} ) is doubled, the new resultant vector becomes
perpendicular to ( vec{P} ). Then, the magnitude of ( overrightarrow{boldsymbol{R}} ) is equal to
( A cdot P+Q )
в. ( P )
c. ( P-Q )
D. ( Q )
11
954 The centripetal acceleration of a particle varies inversely with the square of the radius ( r ) of the circular path. The
KE of this particle varies directly as:
( A )
B ( cdot r^{2} )
c. ( r^{-} 2 )
D. ( r^{-1} )
11
955 A particle is acted upon by a force of
constant magnitude which is always perpendicular to the velocity of the
particle The motion of he particle takes place in a plane It follows that
A. Its velocity is constant
B. Its acceleration is constant
C. Its kinetic energy is conserved
D. None of these
11
956 A body has an initial velocity of ( 3 m / s )
and has an acceleration of ( 1 mathrm{ms}^{-2} )
normal to the direction of the initial
velocity. Then its velocity ( 4 s ) after the
start is
A ( cdot 7 m s^{-1} ) along the direction of initial velocity
B. ( 7 m s^{-1} ) along the normal to the direction of the initial velocity
c. ( 7 m s^{-1} ) mid-way between the two directions
D ( cdot 5 m s^{-1} ) at an angle of ( tan ^{-1} frac{4}{3} ) with the direction of the initial velocity
11
957 A particle is projected at an angle ( theta )
from ground with speed ( uleft(g=10 m / s^{2}right) )
then which of the following is true? This question has multiple correct options
A ( cdot ) If ( u=10 m / s ) and ( theta=30^{circ}, ) then time of flight will be 1
( sec )
B . If ( u=10 sqrt{3} m / s ) and ( theta=60^{circ} ), then time of flight will be ( 3 sec )
C . If ( u=10 sqrt{3} m / s ) and ( theta=60^{circ} ), then after 2 sec velocity
becomes perpendicular to initial velocity
D. If ( u=10 m / s ) and ( theta=30^{circ} ), then velocity never becomes
perpendicular to intial velocity during its flight
11
958 A stone is thrown from a bridge at an
angle of ( 30^{circ} ) down with the horizontal
with a velocity of ( 25 m / s ). If the stone
strikes the water after 2.5 seconds, then calculate the height of the bridge from
the water surface.
11
959 A point ( P ) moves in counter-clockwise
direction on a circular path as shown in
the figure. The movement of ( boldsymbol{P} ) is such
that it sweeps out a length ( s=t^{2}+5 )
where ( s ) is in metres and ( t ) is in seconds.
The radius of the path is ( 20 m ). The
acceleration of ( boldsymbol{P} ) when ( boldsymbol{t}=boldsymbol{2} boldsymbol{s} ) is
approximately :
A ( cdot 13 m / s^{2} )
В. ( 2.15 m / s^{2} )
( c cdot 7 cdot 2 m / s^{2} )
11
960 When a particle moves along a straight
path, then the particle has
A. tangential acceleration only
B. centripetal acceleration only
c. both tangential and centripetal acceleration
D. none of the mentioned
11
961 A red cart starts from rest at the top of a
ramp and coasts down the ramp with a constant acceleration. A blue motor car
starts at the top of the same ramp
directly beside the red cart. The blue motor car moves down the ramp with a
constant speed.
When the red cart catches up to the blue car, how does the speed of the red cart compare with the speed of the blue
car?
A. The red cart is moving at the same speed as the blue car
B. The red cart is moving slightly faster than the blue car
c. The red cart is moving more slowly than the blue car
D. The red cart is moving twice as fast as the blue car
11
962 If a body is projected with a velocity of
( 9.8 m / s ) making an angle of ( 45^{circ} ) with the horizontal, then the range of the
projectile is (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s}^{2} ) )
( mathbf{A} cdot 39.2 m )
в. ( 9.8 m )
( mathrm{c} .4 .9 mathrm{m} )
D. ( 19.6 m )
11
963 If the vectors ( vec{A}=2 hat{i}+4 hat{j} ) and ( vec{B}= ) ( mathbf{5} hat{mathbf{i}}-boldsymbol{p} hat{boldsymbol{j}} ) parallel to each other, the
magnitude of ( bar{B} ) is:
A ( 5 sqrt{5} )
5
B. 10
c. 15
D. ( 2 sqrt{5} )
11
964 A body is first displaced by ( 5 mathrm{m} ) and then by ( 12 mathrm{m} ) in different directions. The minimum displacement it can have is
( mathrm{m} )
( A cdot 7 )
B. 13
( c .0 )
D. 17
11
965 Consider two children riding on the merry-go-round Child 1 sits near the edge, child 2 sits closer to the centre.
Let ( v_{1} ) and ( v_{2} ) denote the linear speed of
child 1 and child ( 2, ) respectively. Which of the following is true?
( A cdot v_{1}>v_{2} )
В . ( v_{1}=v_{2} )
( mathrm{c} cdot v_{1}<v_{2} )
D. (4) we cannot determine which is true, without mo nformatio
11
966 41. Figure A.20 shows the velocity and acceleration
point line body at the initial moment of its motion
acceleration vector of the body remains constant. T
minimum radius of curvature of trajectory of the body i
Vo = 8 ms-1
a = 2 m 526 = 150°
Fig. A.20
a. 2 m b. 3 m c. 8 m d. 16 m
11
967 Find a unit vector in direction of ( overrightarrow{boldsymbol{A}}= ) ( mathbf{5} hat{mathbf{i}}+hat{boldsymbol{j}}-mathbf{2} boldsymbol{k} ) 11
968 A particle is moving along a circle with uniform speed. The physical quantity which is constant both in magnitude and direction, is
A. velocity
B. centripetal acceleration
c. centripetal force
D. angular velocity
11
969 1. A particle is projected from the horizontal x-z plane, in
vertical x-y plane where x-axis is horizontal and positive
y-axis vertically upwards. The graph of ‘y’ coordinate of
the particle v/s time is as shown. The range of the particle
is 3. Then the speed of the projected particle is:
403
(a) 13 m/
s
lid
(b)
3 m/s
(c) 275 m/s
(d)
28 m/s
)
11
970 onu
UBIC
CODY Tum
18. A ship is sailing due north at a speed of 1.25 ms. The
current is taking it towards east at the rate of 2 ms’ and
a sailor is climbing a vertical pole in the ship at the rate
of 0.25 ms. Find the magnitude of the velocity of the
sailor with respect to ground.
10
1
11
971 A smooth ball ‘A’ moving with velocity ‘V’ collides with another smooth initial ball
at rest. After collision both the balls
move the same speed with angle
between their velocities ( 60^{0} . ) No external
force acts on the systems of balls.
Choose the correct option(s).
A ( cdot ) The speed of each ball after the collision is ( frac{V}{sqrt{3}} )
B. The speed of each ball after the collision is ( frac{2 V}{sqrt{3}} )
C. The magnitude of change in momentum of ball B is ( left(frac{m V}{sqrt{3}}right) )
D. The magnitude of change in momentum of ball B is ( left(frac{2 m V}{sqrt{3}}right) )
11
972 the
Illustration 5.26 Two inclined planes OA and OB having in
clination (with horizontal) 30° and 60°, respectively, intersect
each other at O as shown in Fig. 5.44. A particle is projected
from point P with velocity u=103 ms’ along a direction
perpendicular to plane OA. If the particle strikes plane OB
perpendicularly at Q, calculate the
3060°
Fig. 5.44
a. velocity with which particle strikes the plane OB.
b. time of flight.
c. vertical height h of P from O.
d. maximum height from 0, attained by the particle.
e. distance PQ.
11
973 Which cannonball travels farther?
( A cdot A )
B. B
C. Both reaches same height
D. cannot be judged
11
974 33. A ball is thrown with a velocity whose horizontal
component is 12 ms from a point 15 m above the ground
and 6 m away from a vertical wall 18.75 m high in such a
way so as just to clear the wall. At what time will it reach
the ground? (g = 10 ms)
11
975 The equations of motion of a projectile
are given by ( boldsymbol{x}=mathbf{3 6} boldsymbol{t m} ) and ( mathbf{2} boldsymbol{y}=mathbf{9 6} boldsymbol{t}- )
( 9.8 t^{2} mathrm{m} . ) The angle of projection is
( A cdot sin ^{-1}(4 / 5) )
B. ( sin ^{-1}(3 / 5) )
( c cdot sin ^{-1}(4 / 3) )
( D cdot sin ^{-1}(3 / 4) )
11
976 A metal piece of mass ( 160 g ) lies in equilibrium inside a glass of water. The pieces touch the glass at small number of point. If the density of the metal is ( 8000 mathrm{kg} / mathrm{m}^{3} ) then the normal force exerted by the bottom of the glass on the metal piece is
( A cdot 2 N )
В. 8 N
c. ( 0.16 N )
D. 1.4
11
977 A point moves on the ( x-y ) plane
according to the law ( x=a sin omega t ) and
( boldsymbol{y}=boldsymbol{a}(mathbf{1}-cos boldsymbol{omega} boldsymbol{t}) ) where ( boldsymbol{a} ) and ( boldsymbol{omega} ) are
positive constants and ( t ) is in seconds.
Find the distance covered in time ( t_{0} )
A ( . a omega t_{0} )
B. ( sqrt{2 a^{2}+2 a^{2} cos omega t_{0}} )
( ^{mathrm{C}} 2 a sin frac{omega t_{0}}{2} )
D. ( 2 a cos frac{omega t_{0}}{2} )
11
978 The displacement of a particle moving
along ( boldsymbol{x} ) axis is given by ( boldsymbol{X}=left(mathbf{4} boldsymbol{t}^{2}+right. )
( 3 t+7) mu . ) Calculate instantaneous
velocity and instantaneous acceleration at ( t=2 S )
11
979 For a particle in circular motion the centripetal acceleration should be
A. Equal to tangential acceleration
B. More than to is tangential acceleration
c. Less than to its tangential acceleration
D. May be more or less than its tangential acceleration
11
980 a. 125
. 05
L. 13
2. A man can swim in still water with a speed of 2 ms. If
he wants to cross a river of water current speed ✓
along the shortest possible path, then in which direction
should he swim?
a. At an angle 120° to the water current
b. At an angle 150° to the water current
c. At an angle 90° to the water current
d. None of these
mit of 54 mb-1
11
981 Q Type your question-
car has a constant speed corresponding
to a normal acceleration of ( 8 m / s^{2} ) The
tracks abcde and ( 2 C 3 ) are semicircular
track while tracks ( 1-2 ) and ( 3-4 ) are
straight track Point ( a ) and point 1 are
the starting point of race and point 4 and point e are finishing point of race
and point 4 and point ( e ) are finishing
point of the race Choose the correct
statements
A ( cdot ) Car A wins the race with time difference ( frac{14+3}{3} s )
B. car A wins the race with time difference ( frac{14-3}{3} )
C car B wins the race with time difference ( frac{14+3}{3} s )
D. car B wins with the race with time difference ( frac{14-3}{3} s )
11
982 A boy can throw a stone up to maximum
height of 10cm. The maximum
horizontal distance that the boy can
throw the same stone up to will be?
11
983 A projectile is fired with a velocity at
right angle ( theta ) to the slope which is
inclined at an angle ( theta ) with the horizontal. The expression for the range ( boldsymbol{R} ) along the incline is:
( ^{mathbf{A}} cdot frac{2 v^{2}}{g} sec theta )
B ( cdot frac{2 v^{2}}{g} tan theta )
( ^{mathrm{c}} cdot frac{2 v^{2}}{g} sec theta tan theta )
D ( cdot frac{2 v^{2}}{g} tan ^{2} theta )
11
984 Find the horizontal velocity of the
particle when it reach the point ( Q ) Assume the block to the frictionless.
take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} )
A ( cdot v=3.13 frac{m}{s} )
B. ( 5 mathrm{m} / mathrm{s} )
c. ( sqrt{g} mathrm{m} / mathrm{s} )
D. ( 3.6 mathrm{m} / mathrm{s} )
11
985 и
мышvмvv v
v vvрисеппопол Спо опи.
6. Find the vector sum of N coplanar forces, each of
magnitude F, when each force makes an angle of 21t/N
with that preceding it.
11
986 murun me SUMI U. UVIUM
d with the same speed but making
46. Two stones are projected with the same speed but
erent angles with the horizontal. Their ranges are equal.
If the angle of projection of one is t3 and its maximum
height is h, then the maximum height of the other
be
a. 37
b. 2h
c. 1,12
d. h,13
11
987 2. A particle is projected from a point (0, 1) on Y-axis (assume
+ Y direction vertically upwards) aiming towards a point
(4,9). It fell on ground along x axis in 1 sec.
Taking g = 10 m/s2 and all coordinate in metres. Find the
X-coordinate where it fell.
(a) (3,0)
(b) (4,0)
(c) (2,0)
(d) (273,0)
11
988 A particle is going with constant speed
along a uniform helical and spiral path
separately as shown in figure then

Essume that the vertical acceleration
of the particle is negligible in case (a)]
A. The velocity of the particle is constant in both cases
B. The magnitude of acceleration of the particle is constant in both cases
C. The magnitude of acceleration is constant in (a) and decreasing in (b)
D. The magnitude of acceleration is decreasing continuously in both the cases

11
989 For three non-zero vectors ( vec{a}, vec{b}, vec{c} ) the elation ( |(vec{a} times vec{b}) cdot vec{c}|=|vec{a}||vec{b}||vec{c}| ) will hold
true if and only if:
( mathbf{A} cdot vec{a} cdot vec{b}=0, vec{b} cdot vec{c}=0 )
В . ( vec{c} . vec{a}=0, vec{a} . vec{b}=0 )
C ( . vec{a} . vec{c}=0, vec{b} . vec{c}=0 )
D. ( vec{a} . vec{b}=vec{b} . vec{c}=vec{c} . vec{a}=0 )
11
990 21. At the point where the particle is at a height half of
maximum height H attained by it
2u? (1+cos e)/2 u? (1 + cos? 0)3/2
82√2 coso
82/2 cos
?(1-sin’0)3/2
u? (1-tane)3/2
8272 cos
8 V2 cos e
11
991 The time after which bolt hit the floor of
the elevator
11
992 Assertion
In projectile motion at any two positions ( frac{overrightarrow{boldsymbol{v}}_{2}-overrightarrow{boldsymbol{v}}_{1}}{boldsymbol{t}_{2}-boldsymbol{t}_{1}} ) always remains constant.
Reason
The given quantity is average
acceleration, which should remain
constant as acceleration is constant
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion is incorrect but Reason is correct
11
993 Rain appears to fall vertically to a man
walking at ( 3 k m h^{-1}, ) but when he changes his speed to double, the rain
appears to fall at ( 45^{circ} ) with vertical

Study the following statements and find which of them are correct.
i. Velocity of rain is ( 2 sqrt{3} k m h^{-1} )
ii. The angle of fall of rain (with vertical) is ( boldsymbol{theta}=tan ^{-1}left(frac{mathbf{1}}{sqrt{mathbf{2}}}right) )
iii. The angle of fall of rain (with vertical) is ( boldsymbol{theta}=sin ^{-1}left(frac{mathbf{1}}{sqrt{mathbf{2}}}right) )
iv. Velocity of rain is ( 3 sqrt{2} k m h^{-1} )
A. Statement (i) and (ii) are correct
B. Statement (i) and (iii) are correct
c. statement
(iii) and (iv) are correct
D. statement (ii) and (iv) are correct

11
994 Which of the sport is most affected by variation of ‘g’?
A. swimming
B. jump
c. horse riding
D. shooting
E. all are equally affected
11
995 Two cars 1 and 2 move with velocities ( v_{1} )
and ( v_{2} ) respectively, on a straight road in same direction. When the cars are
separated by a distance d, the driver of car 1 applies brakes and the car moves
with uniform retardation ( a_{1} )
Simultaneously, car 2 starts
accelerating with ( a_{2} ). If ( v_{1}>v_{2} ). Find the minimum initial separation between the cars to avoid collision between
them.
11
996 A ( 100 m ) long train at ( 15 m / s ) overtakes a man running on the platform in the same direction in ( 10 s . ) How long the
train will take top cross the man if he
was running in the opposite direaction?
A . ( 7 s )
B. 5 s
( c .3 s )
D. ( 1 s )
11
997 A particle moves uniformly in a circle of radius ( 25 mathrm{cm} ) at two revolution per
second. Find the acceleration of the
particle in ( boldsymbol{m} / boldsymbol{s}^{2} )
11
998 When a man moves down the inclined
plane with a constant speed ( 5 m s^{-1} )
which makes an angle of ( 37^{circ} ) with the horizontal, he finds that the rain is
falling vertically downward. When he moves up the same inclined plane with
the same speed, he finds that the rain makes an angle ( theta=tan ^{-1}left(frac{7}{8}right) ) with the horizontal. The speed of the rain is
A ( cdot sqrt{116} mathrm{ms}^{-1} )
B. ( sqrt{32} mathrm{ms}^{-1} )
c. ( 5 m s^{-1} )
D. ( sqrt{73} mathrm{ms}^{-1} )
11
999 An athlete completes one round of a circular track of diameter ( 200 mathrm{m} ) in 40
s. What will be the distance covered and
also the displacement at the end of 2 ( min 20 s ? )
11
1000 muzzle speed UI UNTUT IT
32. Figure 5.196 shows an elevator cabin, which is movin
downwards with constant acceleration a. A particle
projected from corner A, directly towards diagonally
opposite corner C. Then prove that
Fig. 5.196
a. Particle will hit C only when a = 8.
b. Particle will hit the wall CD if a g.
11
1001 9. Ship A is located 4 km north and 3 km east of ship B.
Ship A has a velocity of 20 kmh-‘ towards the south and
ship B is moving at 40 km h-‘ in a direction 37° north of
east. Take x- and y-axes along east and north directions,
respectively.
a. Velocity of A relative to B is -32i – 44j.
b. Position of A relative to B as a function of time is given
by
FAB = (3 – 32t)î + (4 – 44t)ſ
where t = 0 when the ships are in position described
above.
c. Velocity of B relative to A is -32 – 44ſ.
d. At some moment A will be west of B.
11
1002 The length of a seconds hand in a watch
is ( 1 mathrm{cm} . ) The change in its velocity in 15 s is
A. ( 0 mathrm{cm} / mathrm{s} )
B. ( frac{pi}{30 sqrt{2}} mathrm{cm} / mathrm{s} )
c. ( frac{pi}{30} mathrm{cm} / mathrm{s} )
D. ( frac{pi}{30} sqrt{2} mathrm{cm} / mathrm{s} )
11
1003 A carrom board (4ft ( times 4 ) ft square) has the queen at the centre. The queen, hit by the stricker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen from the centre to the hole. 11
1004 A particle moves along the side ( A B, B C )
CD of a square of side 25 m with a
velocity of 15 m/s. Its average velocity
is
A ( .15 mathrm{m} / mathrm{s} )
в. ( 10 mathrm{m} / mathrm{s} )
( mathrm{c} .7 .5 mathrm{m} / mathrm{s} )
D. ( 5 mathrm{m} / mathrm{s} )
11
1005 The tip of seconds’ hand of a watch
exhibits uniform circular motion on the
circular dial of the watch
State whether given statement is True/False?
A. True
B. False
11
1006 Pictured above are four disks rotating
counter-clockwise (as viewed from
above) at a constant speed. Which disk
is experiencing greatest acceleration?
A. green
B. red
c. blue
D. yellow
E. All disks are experiencing the same acceleration
11
1007 5. The speed of rain with respect to the stationary man is
a. 0.5
b. 1.0 ms
c. 0.5 v3 ms-1
d. 0.43 ms-1
11
1008 A force ( F=5 t ) is applied on a block of
mass ( 10 mathrm{kg} ) kept on rough horizontal surface ( (mu=0.5), ) in rest what is speed of the block at ( t=20 ) s?
( A cdot 15 mathrm{m} / mathrm{s} )
B. ( 18 mathrm{m} / mathrm{s} )
( c cdot 2.5 mathrm{m} / mathrm{s} )
D. cannot be calculated
11
1009 A boat travels from south bank to north
bank of a with a maximum speed of 8
km/h. To arrive at a opposite to the point of start, the boat should start angle :
( mathbf{A} cdot tan ^{-1}(1 / 2) W ) of ( mathrm{N} )
B. ( tan ^{-1}(1 / 2) N ) of ( w )
c. ( 30^{circ} mathrm{WofN} )
D. ( 30^{circ} ) Nof ( W )
11
1010 Motion of satellite around the earth is
A. retarded
B. accelerated
c. diverted
D. None
11
1011 Two trains ( A ) and ( B ) of length ( 400 m )
each are moving on two parallel tracks with a uniform speed of ( 72 mathrm{km} / mathrm{h} ) in the same direction, with ( A ) ahead of ( B )
decides to overtake ( A ) and accelerates
by ( 1 m / s^{2} . ) If after ( 50 s ) the guard of ( B )
just brushes past the driver of ( A ), what
was the original distance between the
guard of ( boldsymbol{B} & ) driver of ( boldsymbol{A} ) ?
11
1012 the net displacement and distance
travelled by the bolt, with respect to earth. (Take ( left.g=9.8 m / s^{2}right) )
11
1013 1. A particle is projected from the ground at an angle 30
with the horizontal with an initial speed 20 ms. After
how much time will the velocity vector of projectile de
perpendicular to the initial velocity? [in second]
flicht 80 m to stones are
11
1014 Illustration 5.34 Two roads intersect at right angle; one goes
along the x-axis, another along the y-axis. At any instant, two
cars A and B moving along y and x directions, respectively,
meet at intersection. Draw the direction of the motion of car
A as seen from car B.
Car A
Car A
7
VB
Car B
Fig. 5.65
11
1015 Two vectors, each of magnitude ( A ) have
a resultant of same magnitude ( A ). The angle between the two vectors is
( A cdot 30 )
B. ( 60^{circ} )
( c cdot 120^{circ} )
D. 150
11
1016 A person is sitting on a moving train and is facing the engine. He tosses up a coin which falls behind him. The train is
moving:
This question has multiple correct options
A. forward and gaining speed.
B. forward and losing speedd
c. backward and losing speed
D. backward and gaining speed.
11
1017 10. The maximum separation between the floor of elevat
and the ball during its flight would be
a. 30 m b. 15 m c. 7.5 m d. 9.5 m
11
1018 Find the magnitude of the angular
acceleration at the moment ( t=10.0 s )
A. ( 1.3 mathrm{rad} / mathrm{s} )
B. 3 rad / ( s )
c. 1 rad ( / s )
D. ( 0.3 mathrm{rad} / mathrm{s} )
11
1019 Two particles start moving from the same position on a circle of radius 20 ( mathrm{cm} ) with speed ( 40 pi mathrm{m} / mathrm{s} ) and ( 36 pi mathrm{m} / mathrm{s} )
respectively in the same direction. Find
the time after which the particles will meet again.
11
1020 Two roads intersect at right angle; one
goes along the ( x ) -axis, another along the
y-axis. At any. two cars ( A ) and ( B ) moving
along ( boldsymbol{y} ) and ( boldsymbol{x} ) directions; respectively, meet at intersection. Draw the direction
of the motion of car ( A ) as seen from car
( boldsymbol{B} )
11
1021 Find the distance scovered by the
particle during the first 4.0 and ( 8.0 s )
A. ( 3 c m )
B. ( 5 mathrm{cm} )
( mathrm{c} cdot 10 mathrm{cm} )
D. ( 15 mathrm{cm} )
11
1022 The displacement ( x ) of a particle varies
with time ( t ) as ( x=a e^{-alpha t}+b e^{beta t}, ) where
( a, b, alpha ) and ( beta ) are positive constants. The velocity of the particle will
A. be independent of ( alpha ) and ( beta )
B. drop to zero when ( alpha=beta )
c. go on decreasing with time
D. go on increasing with time
11
1023 15. Three forces P, Q and R are acting on a particle in the plane,
the angle between P and Q & Q and R are 150° and 120°
respectively. Then for equilibrium, forces P, Q and R are
in the ratio
(a) 1:2:3
(b) 1:2: 13
(c) 3:2:1
(d) 13:2:1
11
1024 Je and position
udents have
anot be true
12. Figure A.21 shows path followed by a particle and po
of a particle at any instant. Four different students
represented the velocity vectors and acceleration vect
at the given instant. Which vector diagram cannot be
in any situation? (In each figure velocity is tangential
the trajectory).
Trajectory of
PL particle L.90
60 > 90° /04
I
Particle at a
0>99
Sita
given instant
A Ram
Fig. A.21
a. Sita b. Gita c. Ram d. Shyam
Shyan
11
1025 The angular displacement of an object
having uniform circular motion is ( frac{pi}{4} ) rad in every 3 s.Find the frequency of revolution.
11
1026 51. There are two values of time for which a projectile is al
the same height. The sum of these two times is equal to
(T = time of flight of the projectile)
a. 3 T/2 b. 4 T/3 c. 3 T/4 d. T
11
1027 The displacement ( x ) of a particle at time t is given by ( boldsymbol{x}=boldsymbol{A} boldsymbol{t}^{2}+boldsymbol{B} boldsymbol{t}+boldsymbol{C} ) where ( boldsymbol{A} )
B, ( C ) are constants and ( v ) is velocity of a particle, then the value of ( 4 A x-v^{2} ) is:
( mathbf{A} cdot 4 A C+B^{2} )
В. ( 4 A C-B^{2} )
c. ( 2 A C-B^{2} )
D. ( 2 A C+B^{2} )
11
1028 24. A cubical box dimension L = 5/4 m starts moving with an
acceleration a=0.5 ms from the state of rest. At the
same time, a stone is thrown from the origin with velocity
v =v, i + v, -yk with respect to earth. Acceleration
due to gravity g = 10 ms (-)). The stone just touches
the roof of box and finally falls at the diagonally opposite
point. then:
b. v, = 5
|
C
Vi=
d. 13
11
1029 1. A radius vector of point A relative to the origin varies with
time t as ř = at i-bt’ſ where a and b are constants. Find
the equation of point’s trajectory.
mi-
11
1030 A machine gun is mounted on the top of
a tower 100 m high. At what angle
should the gun be inclined to cover a maximum range of firing on the ground below? The muzzle speed of bullet is ( 150 m s^{-1} . ) Take ( g=10 m s^{-2} )
11
1031 toppr
Q Type your question
aimed towards ( Q ) and velocity ( vec{u} ) of ( Q ) is
perpendicular to ( vec{v} ). The two projectiles
meet at time ( boldsymbol{T}= )
( A )
B.
[
frac{(v+u) d}{v^{2}}
]
( c )
[
frac{v(v-u)}{d}
]
D.
[
frac{v d}{left(v^{2}-u^{2}right)}
]
11
1032 A particle of mass ( mathrm{m} ) is moving in a
circular path of constant radius r such that centripetal acceleration is varying
with time ( t ) as ( k^{2} r t^{2}, ) where ( k ) is a
constant. The power delivered to the
particle by the force acting on it is
A ( cdot m^{2} k^{2} r^{2} t^{2} )
B. ( m k^{2} r^{2} t )
( mathbf{c} cdot m k^{2} r t^{2} )
( mathbf{D} cdot m k r^{2} t )
11
1033 A mass is attached to the end of a
string of which is tied to a fixed point 0 The mass is released from the initial
horizontal position of the string. Below the point 0 at what minimum distance a peg ( P ) be should fixed so that the mass
tums about ( P ) and can describe a
complete circle in the vertical plane?
A ( cdotleft(frac{3}{5}right) l )
B・(frac{2 } { 5 } )
( c )
( D cdot frac{2}{3} )
11
1034 Write vector relation between angular velocity ( (vec{omega}), ) tangential velocity ( (vec{V}) ) and position vector ( (vec{r}) ) 11
1035 A boat is moving with a velocity ( vec{v}= ) ( mathbf{3} hat{mathbf{i}}+mathbf{4} hat{mathbf{j}} ) with respect to ground. The
water in the river is moving with a velocity ( vec{u}=-3 hat{i}-4 hat{j} ) with respect to
ground. The relative velocity of boat with
respect to water is :
A ( .6 hat{i}+8 hat{j} )
B.
c. ( 6 hat{i}-8 hat{j} )
D. ( -6 hat{i}+8 hat{j} )
11
1036 State whether the given statement is
True or False :
A uniform linear motion is
unaccelerated, while a uniform circular
motion is an accelerated motion
A. True
B. False
11
1037 20. A particle is projected from ground at some angle with
the horizontal. Let P be the point at maximum height
At what height above the point P should the particle he
aimed to have range equal to maximum height?
a. H b. 2H c. H/2 d. 3H
11
1038 Obtain the relation between the
magnitude of linear acceleration and angular acceleration in circular motion.
11
1039 Define uniform circular motion. 11
1040 A point moves along a circle having a radius ( 20 c m ) with a constant tangential
acceleration ( 5 mathrm{cm} s^{-2} . ) How much time
is needed after motion begins for the normal acceleration of the point to be
equal to tangential acceleration?
A . ( 1 mathrm{s} )
B. 2
( c cdot 3 s )
D. 4 s
11
1041 A body is projected with velocity
( 24 m s^{-1} ) making an angle ( 30^{circ} ) with the horizontal. The angle made by the direction of the projectile with the horizontal at ( 2 s ) from start is:
A ( cdot tan ^{-1} frac{2}{3 sqrt{3}} )
B. ( tan ^{-1} frac{1}{3 sqrt{3}} )
c. ( tan ^{-1} frac{2}{3} )
D. ( tan ^{-1} frac{1}{3} )
11
1042 Three point masses ( m_{1}, m_{2} ) and ( m_{3} ) are
located at the vertices of an equilateral
triangle of length ( a ). Determine the
moment of inertia of the system anout
an axis along the altitude of the triangle
passing through ( boldsymbol{m}_{1} )
11
1043 In Uniform circular motion direction of
velocity is along the drawn
to the position of particle on the circumference of the circle.
A. normal
B. tangent
c. can be both
D. none of these
11
1044 A projectile shot at an angle of ( 45^{circ} ) above the horizontal strikes the wall of a
building ( 30 m ) away at a point ( 15 m )
above the point of projection. Initial velocity of the projectile is
( left(operatorname{take} g=9.8 m / s^{2}right) )
( mathbf{A} cdot 14 m / s )
B. ( 14 sqrt{2} mathrm{m} / mathrm{s} )
c. ( 14 sqrt{3} mathrm{m} / mathrm{s} )
D. ( 14 sqrt{5} mathrm{m} / mathrm{s} )
11
1045 11. A particle moves in a circle of radius 20 cm. Its linear
speed is given by v = 2t where t is in seconds and v in
ms. Then
a. The radial acceleration at t = 2 s is 80 ms.
b. Tangential acceleration at t = 2 s is 2 ms.
c. Net acceleration at t = 2 s is greater than 80 ms
d. Tangential acceleration remains constant in
magnitude.
11
1046 5. A projectile A is projected from ground. An observer B
running on ground with uniform velocity of magnitude ‘v’
observes A to move along a straight line. The time of flight
of A as measured by B is T. Then the range R of projectile
on ground is
(a) R=VT
(b) RvT
(d) information insufficient to draw inference
11
1047 A ball thrown by your friend towards you, undergoes:
A. curvilinear motion
B. linear motion
c. rotational motion
D. projectile motion
11
1048 3. Forces F, and F2 act on a point mass in two mutually
perpendicular directions. The resultant force on the point
mass will be
(a) Fi + F2
(b) F,-F2
(c) VF+ F2 (d) F? + F2
11
1049 In a uniform circular motion
(horizontal) of a ball tied with a string,
velocity at any time is at an angle, ( boldsymbol{theta} )
with acceleration. Then ( boldsymbol{theta} ) is:
A ( cdot 60^{circ} )
B. ( 30^{circ} )
( c .90^{circ} )
D. none of the above
11
1050 Given that ( vec{P}+vec{Q}=vec{P}-vec{Q} ). This can
be true when :-
A ( cdot vec{P}=vec{Q} )
B . ( vec{Q} ) is a null vector
C. Niether ( vec{P} ) and ( vec{Q} ) is a null vector
D. ( vec{P} ) is perpendicular to ( vec{Q} )
11
1051 u. OSOITIE INIMICITIA WII UE WESL OID.
10. An object moves with constant acceleration ā. Which of
the following expressions is/are also constant?

dt
dt
dullil
ed(v²)
dt
dt
11
1052 Resolve a weight of ( 10 N ) in two
directions which are parallel and
perpendicular to a slope inclined at ( 30^{circ} )
to the horizontal.
11
1053 To a man walking at the rate of ( 3 k m / h ) the rain appears to fall vertically. When he increases his speed to ( 6 k m / h ) it
appears to meet him at an angle of ( 45^{circ} )
with vertical. The speed of rain is
( mathbf{A} cdot 2 sqrt{2} k m / h )
B. ( 3 sqrt{2} mathrm{km} / mathrm{h} )
( mathrm{c} cdot 2 sqrt{3} mathrm{km} / mathrm{h} )
D. ( 3 sqrt{3} mathrm{km} / mathrm{h} )
11
1054 Two ships ( A ) and ( B ) are ( 10 k m ) apart on a line running south to north. Ship ( boldsymbol{A} ) farther north is streaming west at ( 20 k m / h r ) and ship ( B ) is streaming north at ( 20 k m / h r . ) What is their
distance of closest approach and how long do they take to reach it?
A. ( 4 sqrt{2} mathrm{km}, 15 mathrm{min} )
В. ( 5 sqrt{5} ) km, 15 min
c. ( 5 sqrt{2} mathrm{km}, 20 mathrm{min} )
D. ( 2 sqrt{2} mathrm{km}, 15 mathrm{min} )
11
1055 A car runs at constant speed on a circular track of radius ( 100 mathrm{m} ) taking
( 62.8 mathrm{s} ) on each lap. What is the average speed and average velocity on each complete lap? ( (boldsymbol{pi}=mathbf{3 . 1 4}) )
A. Velocity 10 ( mathrm{m} / mathrm{s} ), speed ( 10 mathrm{m} / mathrm{s} )
B. Velocity zero, speed 10 m/s
c. Velocity zero, speed zero
D. Velocity 10 ( mathrm{m} / mathrm{s} ), speed zero
11
1056 A particle is travelling along a straight line ( O X . ) The distance ( x ) (in metre) of
the particle from ( boldsymbol{O} ) at a time ( ^{prime} boldsymbol{t}^{prime} ) is given
by ( boldsymbol{x}=mathbf{3 7}+mathbf{2 7 t}-boldsymbol{t}^{3}, ) where ‘t’ is time in
second. The distance of the particle
from ( O ),when it comes to rest is:
A. ( 81 m )
в. ( 91 m )
c. ( 101 m )
D. ( 111 m )
11
1057 Assertion
In the motion of projectile the horizontal component of velocity remains constant
Reason
The force on the projectile is gravitational force which acts only in vertically downward 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. Assertion is incorrect but Reason is correct
11
1058 The motion of the arm of a fast bowler
while bowling is an example of nonuniform circular motion.

State whether given statement is True/False?
A. True
B. False

11
1059 Find the ( x ) coordinate of the particle at
the moment of time ( t=6 s )
( mathbf{A} cdot x=0.4 m )
B. ( x=0.24 m )
c. ( x=0.42 mathrm{m} )
D. ( x=0.44 mathrm{m} )
11
1060 7. A river is flowing from west to east at a speed of 5 m min.
A man on the south bank of the river, capable of swimming
at 10 m minin still water, wants to swim across the river
in the shortest time. Finally, he will move in a direction
a. tan-(2) E of N b. tan- (2) N of E
c. 30° E of N
d. 60° E of N
11
1061 If the range of a gun which fires a shell with muzzle speed ( v ), is ( R ), then the angle of elevation of the gun is
( ^{mathbf{A}} cdot cos ^{-1} frac{v^{2}}{R g} )
B. ( cos ^{-1} frac{R g}{v^{2}} )
c. ( frac{1}{2} sin ^{-1} frac{v^{2}}{R g} )
D. ( frac{1}{2} sin ^{-1} frac{R g}{v^{2}} )
11
1062 Two boys are standing at the ends ( A ) and B of a ground, where ( A B=a ). The boy at ( B ) starts running in a direction perpendicular to AB with velocity ( v_{1} ). The boy at A starts running simultaneously with velocity ( v ) and catches the other boy in a time ( t, ) where ( t ) is
A. ( frac{a}{sqrt{v^{2}+v_{1}^{2}}} )
в. ( sqrt{frac{a^{2}}{v^{2}-v_{1}^{2}}} )
c. ( frac{a}{left(v-v_{1}right)} )
D. ( frac{a}{left(v+v_{1}right)} )
11
1063 A student is standing at a distance of
( mathbf{5 0} ) meters behind a bus. As soon as the
bus starts with an acceleration of
( 1 m s^{-2}, ) the student starts running towards the bus with a uniform velocity
( u ). Assuming the motion to be along straight road the minimum value of ( u )
so that the student is able to catch the
bus is:
A ( .5 mathrm{ms}^{-1} )
B. ( 8 m s^{-1} )
( mathrm{c} cdot 10 mathrm{ms}^{-1} )
D. ( 12 mathrm{ms}^{-1} )
11
1064 4. In Q. 1, what would be the approximate retardation to be
given by jet pack along for safe landing?
a. 58 ms
b. 2g ms
c. 4g ms-2
d. Cannot be determined
11
1065 Q Type your question
speed ( v ) in such a way that ( K ) always
moves directly towards ( L, L ) directly
moves towards ( M, M ) directly towards
( N ) and ( N ) directly towards ( K . ) The four
persons will meet at time ( t= )
( ^{A} cdot underline{4 d} )
( v )
в. ( frac{3 d}{v} )
c. ( frac{2 d}{v} )
( D cdot d )
11
1066 2. A=2ỉ +ì, B = 3j – k and © = 6ỉ – 2k .
Value of A-2B+ 3C would be
(a) 20î +59 + 4Â (b) 20î – 5 – 4Â
(c) 4 +59 + 20 (d) si + 4 + 10k
11
1067 toppr
Q Type your question.
as shown. At the same instant, a man ( P ) throws a ball vertically upwards with
initial velocity ‘ ( u^{prime} ). Ball touches (coming
to rest) the base of the plane at point ( B )
of plane’s journey when it is vertically
above the mans. ‘ ( s^{prime} ) is the distance of
point ( B ) from point ( A ). Just after the
contact of ball with the plane, acceleration of plane increases to ( 3 m / s^{2} . ) Find:
(i) Initial velocity ( ^{prime} u^{prime} ) of ball.
(ii) Distance ( ^{prime} s^{prime} )
(iii) Distance between man and plane when the man catches the ball black.
( left.boldsymbol{g}=mathbf{1 0} boldsymbol{m} / boldsymbol{s}^{2}right) ) (Neglect the height of
( operatorname{man}) )
11
1068 A man crosses the river, perpendicular
to river flow in time ( t ) seconds and
travels an equal distance down the stream in ( T ) second. The ratio of man’s
speed in still water to the speed of river
water will be:
( ^{A} cdot frac{t^{2}-T^{2}}{t^{2}+T^{2}} )
в. ( frac{T^{2}-t^{2}}{T^{2}+t^{2}} )
c. ( frac{t^{2}+T^{2}}{t^{2}-T^{2}} )
D. ( frac{T^{2}+t^{2}}{T^{2}-t^{2}} )
11
1069 Two projectile ( A ) and ( B ) thrown with
speed in the ratio acquired the same heights.If A is thrown at an angle of projection of B will be.
11
1070 16. The position vectors of two balls are given by
ĩ = 2(m)i+7(m);
F = -2(m)i + 4(m);
What will be the distance between the two balls?
1.50
-1
11
1071 Two paper screens A and B are separated by 150 m.
A bullet pierces A and B. The hole in B is 15 cm below
the hole in A. If the bullet is travelling horizontally at the
time of hitting A, then the velocity of the bullet at A is
(8 = 10 ms-2)
a. 100 V3 ms -1 b. 200 V3 ms-1
c. 300 V3 ms d. 500 V3 ms -1
og of
11
1072 Linear ( & ) Angular acceleration of a particle is ( 10 mathrm{m} / mathrm{sec}^{2} ) and ( 5 mathrm{rad} / mathrm{sec}^{2} )
respectively. What is its from rotational axis :
A . ( 50 m )
B. ( 1 / 2 m )
( c .1 m )
D. ( 2 m )
11
1073 Find a unit vector in the direction of ( overrightarrow{A B} )
where ( A(1,2,3) ) and ( B(4,5,6) ) are the given points.
11
1074 The motion of a particle is described by the equation ( boldsymbol{x}=boldsymbol{a}+boldsymbol{b} boldsymbol{t}^{2} ) where ( boldsymbol{a}= )
( 15 mathrm{cm} ) and ( b=3 mathrm{cm} / mathrm{sec}^{2} . ) Its
instantaneous velocity at time 3 sec
will be:
A. ( 36 mathrm{cm} / mathrm{sec} )
B. ( 1 mathrm{cm} / mathrm{sec} )
c. ( 18 mathrm{cm} / mathrm{sec} )
D. ( 32 mathrm{cm} / mathrm{sec} )
11
1075 36. Figure 6.16 show that particle A is B
projected from point P with velocity PK
u along the plane and simultaneously
another particle B with velocity v at an
angle a with vertical. The particles collide
at point Q on the plane. Then
a. v sin (a -0.) = u b. v cos (a- .) = u
c. V = u
d. None of these
11
1076 A body is projected horizontally from a height of ( 78.4 m ) with a velocity ( 10 m s^{-1} ) Its velocity after 3 seconds is (
( boldsymbol{g}=mathbf{1 0 m s}^{-1} ) ). (Take direction of
projection on ( hat{i} ) and vertically upward direction on ( hat{j} ) ):
( mathbf{A} cdot 10 hat{i}-30 hat{j} )
B. ( 10 hat{i}+30 hat{j} )
c. ( 20 hat{i}-30 hat{j} )
D. ( 10 hat{i}+10 sqrt{30} hat{j} )
11
1077 A uniform disk rotating with constant
angular acceleration covers 50
revolutions in the first five seconds
after the start. Calculate the angular
acceleration and the angular velocity at the end of five seconds.
11
1078 If ( vec{A}=vec{B}+vec{C}, ) and the magnitudes of ( vec{A} ) ( vec{B}, vec{C} ) are ( 5,4, ) and 3 units, then the angle between ( vec{A} ) and ( vec{C} ) is
A ( cdot cos ^{-1}left(frac{3}{5}right) )
B. ( cos ^{-1}left(frac{4}{5}right) )
( ^{c} cdot sin ^{-1}left(frac{3}{4}right) )
D. ( frac{pi}{2} )
11
1079 A body of mass m is projected horizontally with a velocity
from the top of a tower of height h and it reaches the
sround at a distance x from the foot of the tower. If a
second body of mass 2 m is projected horizontally from
the top of a tower of height 2 h, it reaches the ground at
a distance 2x from the foot of the tower. The horizontal
velocity of the second body is
a. v b. 2v in c. /2v d. vl2
.
1.
conto11-
1-
11
1080 The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are ( v ) and respectively.The density of air is ( mathrm{p} ) and surface area of wings is A.The dynamic lift on the wing is- 11
1081 A cannon fires successively two shells
with velocity ( v_{0}=250 m / s ; ) the first at
the angle ( theta_{1}=60^{circ} ) and the second at
the angle ( theta_{2}=45^{circ} ) to the horizontal, the
azimuth being the same. Neglecting the air drag, the time interval(in seconds) between firings leading to the collision of the shells is ( (10+x) ). Find the value of
x. (Take ( g=10 m / s^{2} ) and round-off your
answer to the nearest integer.)
11
1082 17. Two boats bo
passengers in it
o boats both having a mass of 150 kg including
engers in it are at rest. A sack of mass 50 kg makes
+ boat having total mass of 200 kg. It is thrown to the
rond boat with a velocity whose horizontal component
ms-1. relative to water. Calculate the distance (in m)
hetween the boat 8.5 s. after the throw if the sack spent
0.5 s. in air. Neglect the resistance of air and water.
11
1083 car is moving horizontally along a straight line with
uniform velocity of 25 ms. A projectile is to be fired
from this car in such a way that it will return to it after it
has moved 100 m. The speed of the projection must be
10 ms b. 20 ms c. 15 ms’ d. 25 ms
10 ondamn:
11
1084 Two bodies move uniformly towards each other. They become ( 4 m ) nearer in
every 1 second. After crossing each
other they get ( 4 m ) farther every 10
second. If their speeds are constant,
their values would be
A . ( 1.8 m s^{-1}, 1.8 m s^{-1} )
B . ( 2.2 m s^{-1}, 2.0 m s^{-1} )
c. ( 2.2 m s^{-1}, 1.8 m s^{-1} )
D. ( 1.5 m s^{-1}, 2.5 m s^{-1} )
11
1085 Show that the area of the triangle
contained between the vectors a and b
is one half of the magnitude of ( a times b )
11
1086 Illustration 4.2 A particle moves in x-y plane such
that its position vector varies with time as ř= (2 sin 3t)i
+2(1-сos 3t)j. Find the equation of the trajectory of the
particle.
11
1087 Co-efficient of restitution is defined as
the ratio of
A. Velocity of separation and approach
B. Velocity of approach and separation
c. Ratio of velocity of objects
D. None
11
1088 A particle is moving along a circular path with a constant speed of ( 10 m s^{1} ) What is the magnitude of the change is velocity of the particle, when it moves
through an angle of 60 around the centre of the circle?
A .
в. ( 10 mathrm{m} / mathrm{s} )
( mathbf{c} cdot 10 sqrt{3} m / s )
D. ( 10 sqrt{2} mathrm{m} / mathrm{s} )
11
1089 Fig. 5.66
Illustration 5.35 Two roads one, along the y-axis and anoth
along a direction at angle with x-axis, are as shown in F
5.68. Two cars A and B are moving along the roads. Consid
the situation of the diagram. Draw the direction of
VR
Road
Car A
Car B
Fig. 5.68
a. Car B as seen from car A.
b. Car A as seen from car B.
11
1090 If ( vec{a}=2 hat{i}+4 hat{j}-5 hat{k}, vec{b}=hat{i}+ )
( hat{boldsymbol{j}}+hat{boldsymbol{k}}, overrightarrow{boldsymbol{c}}=hat{boldsymbol{j}}+2 hat{boldsymbol{k}}, ) then the unit vectors
parallel to ( overrightarrow{boldsymbol{a}}+overrightarrow{boldsymbol{b}}+overrightarrow{boldsymbol{c}} ) is
A ( cdot pm frac{1}{7}(3 hat{i}+6 hat{j}-2 hat{k}) )
в. ( (3 hat{i}+6 hat{j}-2 hat{k}) )
( ^{mathrm{C}} pm frac{1}{7}(3 hat{i}+6 hat{j}+2 hat{k}) )
D. ( (3 hat{i}+6 hat{j}+2 hat{k}) )
11
1091 Illustration 5.28 A body is thrown at an angle e, with the
horizontal such that it attains a speed equal to
times the
speed of projection when the body is at half of its maximum
height. Find the angle 8.
11
1092 Q Type your question.
moving horizontally with a speed ( u )
perpendicular to the direction of ( v )
enters through a hole at an upper corner
( A ) and strikes the diagonally opposite
corner ( B ). Assume ( g=10 m / s^{2} . ) Which
of the following values of ( u ) and ( v ) is(are)
correct?
This question has multiple correct options
A. ( v=20 mathrm{m} / mathrm{s} )
в. ( u=3 mathrm{m} / mathrm{s} )
c. ( v=15 mathrm{m} / mathrm{s} )
D. ( u=2 m / s )
11
1093 4. The trajectory of a projectile in a vertical plane is y = ax –
bx’. where a, b are constants, and x and y are, respectively,
the horizontal and vertical distances of the projectile from
the point of projection. The maximum height attained is
and the angle of projection from the horizontal
(IIT JEE, 1997)
11
1094 A drunkard is walking along a straight
road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 ( mathrm{m} ) long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit
after:
A . 21 s
B. 29 s
c. ( 31 s )
D. 37 s
11
1095 13. The time taken by the block to move from A to B is 11
1096 Billy jogs ( 2.5 k m ) east in 45 minutes,
takes a water break for 12 minutes, and
then walks west at a rate of ( 0.65 k m / h ) for 30 min. What is Billy’s average
velocity? (Answer units: km/hr)
A . 1.52
B. 1.96
( c cdot 2 )
D. 1.45
11
1097 Which physical quantities remain constant in U.C.M? 11
1098 31. The maximum range of a projectile is 500 m. If the particle
is thrown up a plane, which is inclined at an angle of 30°
with the same speed, the distance covered by it along the
inclined plane will be
a. 250 m b. 500 m c. 750 m d. 1000 m
connamundant: no chain
11
1099 A car travelling at ( 60 mathrm{km} / mathrm{h} ) overtake
another car traveling at ( 42 mathrm{km} / mathrm{h} )
Assuming each car to be ( 5.0 m ) long,
find the time taken during the overtaking and the total road distance
used for the overtake.
11
1100 – U+al, When a is constant
20. Forces X, Y, and Z have magnitudes 10 N 5
and 5(13+1) N, respectively. The to
the same direction as shown in Fig. 3.73. The te
of X and Y and the resultant of X and Z have
magnitude. Find 0, the angle between X and I.
nd Z h
11
1101 At the uppermost point of a projectile its velocity and acceleration are at an angle of :-
A ( cdot 180^{circ} )
B. ( 90^{circ} )
( c cdot 60^{circ} )
D. ( 45^{circ} )
11
1102 A ball is dropped from a great height and the velocity of the ball as a function of time is given ( boldsymbol{v}=frac{boldsymbol{m} boldsymbol{g}}{boldsymbol{K}}left(boldsymbol{1}-boldsymbol{e}^{-(boldsymbol{K} / boldsymbol{m}) t}right) )
where ( m ) is mass of ball, ( K ) is a
constant and ( g ) is the acceleration due to gravity. Then, at a time when ( t gg ) ( (boldsymbol{m} / boldsymbol{K}), ) the velocity of the ball becomes
A. ( v=g t )
в. ( _{v}=frac{m g}{K} )
c. ( v=frac{m g}{K} )
D. ( v=0 )
11
1103 A shell is fired from point 0 on the level ground with velocity ( 50 m / s ) at angle
( 53^{circ} . A ) hill of uniform slope ( 37^{circ} ) starts
from point ( A ) that is ( 100 m ) away from the point 0 as shown in the figure. Calculate the time of flight (in seconds)
11
1104 A projectile is thrown in the upward direction making an angle of 60 with the horizontal direction with a velocity
of 47 Then the time after which its
inclination with the horizontal is 45
11
1105 If the system is in equilibrium ( left(cos 53^{0}=right. )
( mathbf{3} / mathbf{5}), ) then the value of ( ^{prime} boldsymbol{P}^{prime} ) is
( mathbf{A} cdot 16 N )
B. ( 4 N )
( mathbf{c} cdot sqrt{208} N )
D. ( sqrt{232} N )
11
1106 What is the distance travelled by a point during the time t. if it moves in ( x ) Y plane according to relation.
[
begin{array}{l}
boldsymbol{X}=boldsymbol{a} boldsymbol{s} boldsymbol{i} boldsymbol{n} boldsymbol{omega} boldsymbol{t} \
boldsymbol{Y}=boldsymbol{a}(1-boldsymbol{c o s} boldsymbol{omega} boldsymbol{t})
end{array}
]
11
1107 19. A particle has an initial velocity of 3i +4j and an
acceleration of 0.4 +0.3j. Find speed after 10 s. (Hint:
v =ū+ āt, when ã is constant]
11
1108 If ( vec{a}+vec{b}+vec{c}=0,|vec{a}|=3,|vec{b}|=5,|vec{c}|=7 )
then the angle between ( vec{a} & vec{b} ) is?
A ( cdot frac{pi}{6} )
в. ( frac{2 pi}{3} )
( c cdot frac{5 pi}{3} )
D.
11
1109 1. A train is moving along a straight line with a constant
acceleration a. A boy standing in the train throws a bal
forward with a speed of 10 ms, at an angle of 60° to
the horizontal. The body has to move forward by 1.15 m
inside the train to catch the ball back to the initial height.
The acceleration of the train, in ms, is
(IIT JEE, 2011)
11
1110 If the magnitude of the cross product of two vector is ( sqrt{3} ) times to the
magnitude of their scalar product the angle between two vector will be :
( A )
B.
c.
D.
11
1111 A man throws a packet from a tower directly aiming at his friend who is standing at a certain distance from the base which is same as a height of the tower. If packet is thrown with a speed of ( 4 m / s ) and it hits the ground midway between the tower base ( & ) his friend.
Find the height of the tower. (Take ( g= ) ( 9.8 m / s^{2} )
A. 3.8
в. 4.4
( c .3 .2 )
D. 2.2
11
1112 70. A body is projected with velocity v, from the point A as
shown in Fig. 5.203. At the same
AV2
time, another body is projected 30)
vertically upwards from B with
velocity V2. The point B lies
vertically below the highest point of first particle. For both
the bodies to collide, valv, should be
a. 2 b. c. 0.5 d. 1
Fig.5.203
11
1113 A cyclist moves in such a way that he
takes ( 72^{circ} ) turn towards left after
travelling ( 200 mathrm{m} ) in straight line. What is the displacement when he takes just takes fourth turn?
A. zero
B. 600 ( m )
c. ( 400 mathrm{m} )
D. 200 ( mathrm{m} )
11
1114 Speed ( v ) of a particle moving along a
straight line, when it is at a distance ( x )
from a fixed point on the line is given by ( v^{2}=108-9 x^{2} ) (assuming mean
position to have zero phase constant)
(all quantities in are in ( c g s ) unit):
A. The motion is uniformly accelerated along the straight line
B. The magnitude of the acceleration at a distance ( 3 mathrm{cm} ) from the fixed point is ( 27 mathrm{cm} / mathrm{s}^{2} )
C. The motion is simple harmonic about ( x=sqrt{12} mathrm{m} )
D. The maximum displacement from the fixed point is ( 4 mathrm{cm} )
11
1115 4. Rain is falling vertically with a velocity of 25 ms.
woman rides a bicycle with a speed of 10 ms in the
north to south direction. What is the direction (angle with
vertical) in which she should hold her umbrella to safe
herself from rain?
a. tan-‘(0.4)
b. tan- (1)
c. tan-(13)
d. tan-(2.6)
mouing on a highway with a speed of
11
1116 A man wearing a wingsuit glides through the air with a constant velocity
of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the
horizontal. The path of the man is shown
n Fig
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point ( A ) to
point ( boldsymbol{B} )
The pressure of the still air at ( A ) is
( 63 k P a ) and at ( B ) is ( 92 k P a . ) Assume the
density of the air in constant between ( boldsymbol{A} )
and ( B )
Determine the density of the air between ( A ) and ( B )
density ( = )
11
1117 (110Biciul Cun).
5. Statement I: A body with constant acceleration always
moves along a straight line.
Statement II: A body with constant magnitude of
acceleration may not speed up.
11
1118 33. The speed of a projectile at its highest point is v, and at
nen
the point half the maximum height is v2. If
find the angle of projection.
a. 45° b. 30° c . 37° d. 60°
12V5′
11
1119 Two particles ( A ) and ( B ) are projected with same speed so that ratio of their
maximum heights reached is ( 3: 1 . ) If
the speed of ( A ) is doubled without
altering other parameters, the ratio of horizontal ranges attained by A and B is?
11
1120 Equation of trajectory of a projectile is
given by ( y=-x^{2}+10 x ) where ( x ) and ( y )
are in meters and ( x ) is along horizontal
and y is vertically upward and particle is projected from origin. Then which of the following options is/are correct.
( left(g=10 m / s^{2}right) )
A. Initial velocity of particle is ( sqrt{505} mathrm{m} / mathrm{s} )
B. Horizontal range is ( 10 mathrm{m} )
c. Maximum height is 25 m
D. Angle of projection with horizontal is ( tan ^{-1}(5) )
11
1121 A man projects a coin upwards from the gate of a uniform moving train. The path of coin for the man will be 11
1122 In uniform circular motion
A. acceleration is variable.
B. acceleration is uniform.
C. the direction and magnitude of acceleration both vary.
D. if force applied is doubled in circular motion, then angular velocity becomes double.
11
1123 is at a height equal
17. The velocity of the projectile when it is at a height
to half of the maximum height is
sin²e
a. v/cos +
b. √2 v cose
c. √2vsine
d. v tan 8 sec
11
1124 A farmer has to go ( 500 m ) due north,
( 400 m ) due east and ( 200 m ) due south to
reach his field. If he takes 20 minutes to
reach the field. What is the average
velocity of farmer during the walk?
A. ( 25 m / min )
в. ( 50 m / min )
c. ( 55 m / min )
D. ( 110 mathrm{m} / mathrm{min} )
11
1125 2. Statement I: The time of flight of a body becomes n
times the original value if its speed is made n times.
Statement II: This due to the range of the projectile which
becomes n times.
11
1126 A car moving along a circular path of radius R with uniform speed covers an
angle ( theta ) during a given time t. What is
its average velocity?
A ( cdot frac{2 R sin (theta / 2)}{t} )
B. ( frac{2 R cos (theta / 2)}{t} )
c. ( frac{2 R sin (theta)}{t} )
D. ( frac{R sin (theta / 2)}{t} )
11
1127 A small sphere of mass ( boldsymbol{m}=mathbf{1} boldsymbol{k} boldsymbol{g} ) is
moving with a velocity ( (4 hat{i}-hat{j}) m / s . ) It
hits fixed smooth wall and rebounds with velocity ( (hat{mathbf{i}}+mathbf{3} hat{mathbf{j}}) boldsymbol{m} / boldsymbol{s} . ) The
coefficient of restitution between the
sphere and the wall is ( n / 16 . ) Find the
value of ( n )
11
1128 Assertion
A body with constant acceleration
always moves along a straight line.
Reason
A body with constant acceleration may not speed up.
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. Reason is correct but assertion is incorrect
11
1129 A particle moves in a way such that its
position can be expressed with ( boldsymbol{x}(boldsymbol{t})= ) ( t^{2}+t-3 ) and with ( y(t)=t^{3}-frac{1}{t-1} )
with being time in seconds. ( x(t) ) and
( boldsymbol{y}(t) ) are both in meters.
Initially, how far away is the particle from the origin?
A. ( 0.00 m )
в. ( 1.00 m )
c. ( 1.56 m )
D. ( 2.83 m )
E. ( 3.16 m )
11
1130 What remains constant in uniform
circular motion?
A. Velocity
B. Speedd
c. Displacement
D. Direction
11
1131 If ( vec{a} ) and ( vec{b} ) are two vectors then the value of ( (vec{a}+vec{b}) times(vec{a}-vec{b}) ) is:
A ( cdot 2(vec{b} times vec{a}) )
B. ( -2(vec{b} times vec{a}) )
c. ( vec{b} times vec{a} )
D. ( vec{a} times vec{b} )
11
1132 • Find the drift of the boat when it is in the middle of the
river.
1/3
71/3
b.
u
+1
d. None of these
11
1133 A man wearing a wingsuit glides through the air with a constant velocity
of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown n Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point ( A ) to
point ( boldsymbol{B} )

Show that the difference in height ( h )
between points ( A ) and ( B ) is ( 3200 m )

11
1134 4. The trajecto
The trajectories of the motion of three particles are shown
A 40. Match the entries of Column I with the entries
of Column II.
VA
Fig. A.40
Column I
Column II
i Time of flight is least for a.
ii. Vertical component of the b.
velocity is greatest for
i. Horizontal component of
the velocity is greatest for
liv. Launch speed is least for d. No appropriate
match given
5 The nath of nroiectile is represented by y = Px – Ox?.
11
1135 A man rows upstream a distance of
( 9 k m ) or downstream a distance of
( 18 k m ) taking 3 hours each time. The
speed of the boat in still water is
A ( cdot 7 frac{1}{2} k m / h )
В ( cdot 6 frac{1}{2} k m / h )
c. ( _{5} frac{1}{2} k m / h )
D. ( 4 frac{1}{2} k m / h )
11
1136 If ( overline{boldsymbol{A}}=mathbf{2} hat{mathbf{i}}+mathbf{3} hat{boldsymbol{j}}-hat{boldsymbol{k}} ) and ( overline{boldsymbol{B}}=-hat{boldsymbol{i}}+mathbf{3} hat{boldsymbol{j}}+ )
( 4 hat{k}, ) then projection of ( bar{A} ) on ( bar{B} ) will be:
A ( cdot frac{3}{sqrt{13}} )
в. ( frac{3}{sqrt{26}} )
c. ( sqrt{frac{3}{26}} )
D. ( sqrt{frac{3}{13}} )
11
1137 w
50. A man is riding on a horse. He is
trying to jump the gap between two
symmetrical ramps of snow separated
by a distance W as shown in Fig. A.26.
He launches off the first ramp with a Fig. A.26
speed V. The man and the horse have a total mass m. and
their size is small as compared to W The value of initial
launch speed V, which will put the horse exactly at the peak
of the second ramp is
– Wg
Wg
** Vsin o x cose
V sin(0/2)* cos(0/2)
1 2Wg
C. V2 sin cos 0
sin cos e
b.
Wg
11
1138 Two locomotives approach each other on the parallel tracks. Each has speed of ( 95 k m / h ) with respect to the ground. If they are initially ( 8.5 k m ) apart, how long will it be before they reach each other? (in hours)
( mathbf{A} cdot 0.045 )
B. 0.065
c. 0.025
D. 0.078
11
1139 A thin circular ring of mass ( mathrm{M} ) and radius R is rotating about its axis with a constant angular velocity ( omega . ) Two objects, each of mass ( mathrm{m}, ) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:
A. ( frac{M omega}{(M+m)} )
в. ( frac{omega(M-2 m)}{(M+2 m)} )
c. ( frac{M omega}{M+2 m} )
D. ( frac{omega(M+2 m)}{M} )
11
1140 A particle moves in such a manner that
( boldsymbol{x}=boldsymbol{A t}, boldsymbol{y}=boldsymbol{B} boldsymbol{t}^{3}-boldsymbol{2 t}, boldsymbol{z}=boldsymbol{c} boldsymbol{t}^{2}-boldsymbol{4} boldsymbol{t} )
where ( x, y ) and ( z ) are measured in
metres and ( t ) is measured in seconds,
and ( A, B ) and ( C ) are unknown constants.
Given that the velocity of the particle at ( boldsymbol{t}=2 boldsymbol{s} ) is ( overrightarrow{boldsymbol{v}}=left(frac{boldsymbol{d} overrightarrow{boldsymbol{r}}}{boldsymbol{d} boldsymbol{t}}right)=boldsymbol{3} hat{boldsymbol{i}}+2 boldsymbol{2} hat{boldsymbol{j}} boldsymbol{m} / boldsymbol{s} )
determine the velocity of the particle at
( boldsymbol{t}=mathbf{4} boldsymbol{s} )
( mathbf{A} cdot 8 hat{i}+94 hat{j}+4 hat{k} m / s )
B. ( 6 hat{i}+94 hat{j}+6 hat{k} m / s )
( mathbf{c} cdot 3 hat{i}+94 hat{j}+4 hat{k} m / s )
D ( .3 hat{i}+92 hat{j}+4 hat{k} m / s )
11
1141 15. The horizontal distance x travelled by the block in moving
from A to C is
a. (1+13) b. (1 – 13)m
c. (13 + 3)m
d. g meter
11
1142 U
O
VJ 1115
A projectile can have same range R for two angles of
projection. It t, and t2 are the times of flight in the two
cases, then what is the product of two times of flight?
a. tytz & R²
b. tt2 «R
c. tit oc
al
d. tt . –
11
1143 usuvuvi
wauns.
30. During the motion the magnitude of velocity of ram with
respect to Shyam is
a. 1 ms b. 4 ms- c. 5 ms 1 d. 7 ms!
11
1144 The minimum number of vectors of
unequal magnitude required to produce a zero resultant is :
A .2
B. 3
( c cdot 4 )
D. more than 4
11
1145 A man wearing a wingsuit glides through the air with a constant velocity
of ( 47 ~ m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point ( A ) to
point ( boldsymbol{B} )

For the movement of the man from ( A ) to
( B, ) determine:
the magnitude of the force on the man
due to air resistance.

11
1146 A stone projected at an angle ( theta ) with horizontal from the roof of a tall
building falls on the ground after three seconds. Two seconds after the
projection it was again at the level of projection. Then the height of the building is:
A . ( 15 mathrm{m} )
в. ( 5 m )
( c .25 m )
D. ( 20 m )
11
1147 The relation between the acceleration
and time for an object is given below. Calculate the velocity with which the object is moving at ( boldsymbol{t}=mathbf{1}(mathbf{A t} boldsymbol{t}=mathbf{0}, boldsymbol{v}= )
( mathbf{0} )
( boldsymbol{a}=boldsymbol{3} boldsymbol{t}-boldsymbol{4} boldsymbol{t}^{2} )
11
1148 The roadway bridge over a canal is in the form of an arc of a circle of radius
( 20 m . ) What is the maximum speed with
which a car can cross the bridge without leaving the ground at the highest point.
A ( cdot 10 mathrm{ms}^{-1} )
B. ( 12 mathrm{ms}^{-1} )
( mathrm{c} cdot 14 mathrm{ms}^{-1} )
D. ( 16 mathrm{ms}^{-1} )
11
1149 Fill in the blank.
In uniform circular motion
remains constant.
A. Acceleration
B. Time
c. speed
D. Direction
11
1150 If ( |boldsymbol{v}|= ) const; circular motion place
then
A ( cdot alpha= ) angular accl” ( = ) const
B ( cdot a_{t}= ) const
( mathbf{c} cdot a_{c}= )const
D. All are false
11
1151 12. An object may have
a. varying speed without having varying velocity.
b. varying velocity without having varying speed.
c. non-zero acceleration without having varvin
velocity.
d. non-zero acceleration without having varying speed
11
1152 The minimum number of vectors having different planes which can be added to give zero resultant is
A .2
B. 3
( c cdot 4 )
D. 5
11
1153 Let ( vec{a} ) and ( vec{b} ) be unit vectors inclined at
an variable angle ( boldsymbol{theta}left(boldsymbol{theta epsilon}left(mathbf{0}, frac{pi}{2}right)left(frac{pi}{2}, boldsymbol{pi}right)right) )
( operatorname{Let} g(theta)=int_{-(vec{alpha} . vec{b})^{2}}^{-lambda} f^{2}(x) d x+ )
( int_{lambda}^{|vec{a} times vec{b}|^{2}} f^{2}(x) d x-frac{2}{lambda}, w h e r e lambda>0, ) is
function satisfying ( boldsymbol{f}(boldsymbol{x})+boldsymbol{f}(boldsymbol{y})= )
( frac{boldsymbol{x}+boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}, boldsymbol{x}, boldsymbol{y} epsilon boldsymbol{R}-[mathbf{0}] boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{h}(boldsymbol{theta})= )
( -g(theta)+|vec{a} times vec{b}|^{2} cdotleft(vec{a} cdot vec{b}_{1}right)^{2}, vec{b}_{1}=2 vec{b} )
( mathbf{f}|boldsymbol{g}(boldsymbol{theta})| ) is attaining its minimum value, then minimum distance between origin and the point of intersection of lines ( vec{r} times vec{a}=vec{a} times vec{b} ) and ( vec{r} times vec{b}=vec{b} times vec{a} )
is
A. ( sqrt{2-sqrt{2}} )
в. ( sqrt{2+sqrt{2}} )
c. ( sqrt{sqrt{2}+1} )
D. ( sqrt{sqrt{2}-1} )
11
1154 Which force is required to maintain a body in uniform circular motion? 11
1155 17. The direction (angle) with horizontal at which В will
appear to move as seen from A is
a. 37° b. 53° c. 15° d. 90°
11
1156 A river ( 400 m ) wide is flowing at a rate of
( 2.0 m / s . A ) boat is sailing at a velocity of ( 10 m / s ) with respect to the water, in a direction perpendicular to the river. ( (boldsymbol{a}) ) Find the time taken by the boat to reach the opposite bank.
(b) How far from the
point directly opposite to the starting point does the boat reach the opposite bank?
11
1157 Passengers in the jet transport ( boldsymbol{A} ) flying east at a speed of ( 800 k m / h ) observe a
second jet plane ( B ) that passes under
the transport in horizontal flight

Although the nose of ( B ) is pointed in the
( 45^{circ} ) northeast direction, plan ( B ) appears
to the passengers in ( A ) to be moving
away from the transport at the ( 60^{circ} )
angle as shown in the fig. The true
velocity of ( boldsymbol{B} ) is
A. ( 586 k m / h )
в. ( 400 sqrt{2} k m / h )
c. ( 717 k m / h )
D. ( 400 k m / h )

11
1158 A man wearing a wingsuit glides through the air with a constant velocity
of ( 47 m s^{-1} ) at an angle of ( 24^{circ} ) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is ( 85 k g . ) The man takes a time
of 2.8 minutes to glide from point ( A ) to
point ( boldsymbol{B} )

For the movement of the man from ( A ) to
( B, ) determine:
the decrease in gravitational potential energy decrease in gravitational potential energy ( = )

11
1159 A motor car is traveling at ( 30 m s^{-1} ) on a circular road of radius ( 500 mathrm{m} ). It is
increasing speed at the rate of ( 2 m s^{-2} ) The acceleration of car is :
A ( .2 m s^{-2} )
В. 2.7 ( m s^{-2} )
( c cdot 3 m s^{-2} )
D. 3.7 ( m s^{-2} )
11
1160 18. What is the angle of projectile with the vertical if
velocity at the highest point is V2/5 times the velo
when it is at a height equal to half of the maxim
height?
a. 150 b. 30° c. 450 d. 60°
11
1161 Find the change in velocity of the tip of the minute hand (radius ( =10 mathrm{cm} ) ) of a
clock in 45 minutes. ( (text { in } mathrm{cm} / mathrm{min}) )
A ( cdot frac{sqrt{2}}{3} )
B. ( pi frac{sqrt{2}}{2} )
c. ( pi frac{sqrt{3}}{3} )
D. ( pi frac{2}{3} )
11
1162 Two particles ( A ) and ( B ) start
simultaneously from the same point
and move in a horizontal plane. ( A ) has
an initial velocity ( u_{1} ) due east and
acceleration ( a_{1} ) due north. ( B ) has an
initial velocity ( u_{2} ) due north and
acceleration ( a_{2} ) due east. Which of the
following statements is(are) correct? This question has multiple correct options
A. Their paths must intersect at some point
B. They must collide at some point.
C. They will collide only if ( a_{1} u_{1}=a_{2} u_{2} )
D. If ( u_{1}>u_{2} ) and ( a_{1}<a_{2} ), the particles will have the same speed at some point of time.
11
1163 A smooth block loosely fits in a circular tube placed on a horizontal surface. The
block moves in a uniform circular
motion along the tube. Which wall (inner or outer) will exert a non-zero
normal contact force on the block?
11
1164 Enter 1 if true else 0 ( frac{1}{sqrt{3}}(hat{i}+hat{j}+hat{k}) ) is the unit vector in the
direction of vector ( overrightarrow{P Q} )
where ( P ) and ( Q ) are the point (1,2,3)
and (4,5,6)
11
1165 Vectors ( vec{a} ) and ( vec{b} ) make an angle ( theta=frac{2 pi}{3} ) If ( |vec{a}|=1,|vec{b}|=2 ) then
( {(vec{a}+3 vec{b}) times(3 vec{a}-vec{b})}^{2}= )
A . 225
B. 250
c. 275
D. 300
11
1166 The displacement of a particle is given by ( sqrt{x}=t+1 . ) Which of the following
statements about its velocity is true?
A. It is zero
B. It is constant but not zer
c. It increases with time
D. It decreases with time
11
1167 Two forces are such that the sum of
their magnitude is ( 18 N ) and their
resultant is ( 12 N ) and it is
also perpendicular to the smaller force.Then the magnitude of the forces
are
A ( .12 N, 6 N )
B . ( 13 N, 5 N )
c. ( 10 N, 8 N )
D. ( 16 N, 2 N )
11
1168 A particle ( P ) is sliding down a frictionless hemispherical bowl. It
passes the point ( A ) at ( t=0 . ) At this
instant of time, the horizontal
component of its velocity is ( v . A ) bead ( Q ) of the same mass as ( P ) is ejected from
( A ) at ( t=0 ) along the horizontal string
( A B, ) with the speed ( v . ) Friction between
the bead and the string may be
neglected. Let ( t_{p} ) and ( t_{q} ) be the respective times taken by ( P ) and ( Q ) to reach the
point ( boldsymbol{B} ). Then
( mathbf{A} cdot t_{p}t_{q} )
D. ( _{t_{p} / t_{q}}=frac{text {length of are } A C D}{text {length of cord } A B} )
11
1169 The direction cosines of ( hat{i}+hat{j}+hat{k} ) are
( mathbf{A} cdot 1,1,1 )
B. 2,2,2
c. ( 1 / sqrt{2}, 1 / sqrt{2}, 1 / sqrt{2} )
D. ( 1 / sqrt{3}, 1 / sqrt{3}, 1 / sqrt{3} )
11
1170 Fill in the blank.
In circular motion, force is always
to the displacement.
A. Perpendicular
B. Parallel
c. opposite
D. None
11
1171 Which of the following represent circular motion
A. Ball sliding down an inclined plane
B. Motion of a simple pendulum
c. A freely falling body
D. A stone tied to a thread and whirled
11
1172 5. 100 coplanar forces each equal to 10 N act on a body. Each
force makes angle tu/50 with the preceding force. What is
the resultant of the forces
(a) 1000 N
(b) 500 N
(c) 250 N
(d) Zero
11
1173 2. A projectile fired from the ground follows a parabolic
path. The speed of the projectile is minimum at the top
of its path
(UIT JEE, 1984)
11
1174 In the projectile motion, if air resistance is ignored, the horizontal motion is at
A. constant acceleration
B. variable acceleration
C. constant velocity
D. constant retardation
11
1175 fu) v3
9. Maximum and minimum magnitudes of the resultant of
two vectors of magnitudes P and Q are in the ratio 3:1.
Which of the following relations is true?
(a) P=2Q
(b) P=Q
(c) PQ = 1
(d) None of these
11
1176 4. A golfer standing on level ground hits a ball with a
velocity of 52 ms at an angle above the horizontal.
tan O= 5/12, then find the time for which the ball is atleast
15 m above the ground (take g = 10 ms).
at an angle of A to
11
1177 Rain is falling vertically with ( 3 m s^{-1} ) and a man is moving due North with ( 4 m s^{-1} . ) In which direction he should
hold the umbrella to protect himself from rains?
A ( cdot 37^{circ} ) North of vertical
B. ( 37^{circ} ) South of vertical
C. ( 53^{circ} ) North of vertical
D. ( 53^{circ} ) South of vertical
11
1178 In circular motion, the
A. Direction of motion is fixed
B. Direction of motion changes continuously
C. Acceleration is zero
D. Velocity is constant
11
1179 A projectile is thrown in the upward
direction making an angle of ( 60^{circ} ) with the horizontal direction with a velocity
of ( 147 m s^{-1} . ) Then the time after which
its inclination with the horizontal is ( 45^{circ} )
is (Take ( boldsymbol{g}=mathbf{9 . 8} boldsymbol{m} / boldsymbol{s}^{2} ) )
A . ( 15 s )
B. ( 10.98 s )
c. ( 5.49 s )
D. 2.745 ( s )
11
1180 The two adjacent sides ( boldsymbol{O A}, boldsymbol{O B} ) of parallelogram are ( 2 hat{i}+4 hat{j}-5 hat{k} ) and ( hat{i}+ ) ( 2 hat{j}+3 hat{k} . ) The unit vectors along the
diagonals of the parallelogram are given by
A ( cdot frac{(3 hat{i}+6 hat{j}-2 hat{k})}{7} )
B. ( frac{(-hat{i}-2 hat{j}+8 hat{k})}{sqrt{69}} )
( frac{(-3 hat{i}-6 hat{j}+2 hat{k})}{7} )
D. ( frac{(hat{i}+2 hat{j}-8 hat{k})}{sqrt{69}} )
11
1181 A man walks 12 steps in Northern direction and turns left to walk 5 steps, then returns to the initial point by the
shortest path. Find the distance
travelled given each step is ( 0.3 mathrm{m} )
A . ( 5.1 mathrm{m} )
B. ( 9 mathrm{m} )
( c cdot o m )
D. 3.6 m
11
1182 Illustration 5.71 A fan is rotating with angular velocity
100 revs-‘. Then it is switched off. It takes 5 min to stop.
a. Find the total number of revolution made before the fan
stops. (assume uniform angular retardation).
b. Find the value of angular retardation.
c. Find the average angular velocity during this interval.
11
1183 Two particles are projected under
gravity with speed ( 4 mathrm{m} / mathrm{s} ) and ( 3 mathrm{m} / mathrm{s} ) simultaneously from same point and at
angles ( 53^{circ} ) and ( 37^{circ} ) with the horizontal
surface respectively as shown in figure.
Then:
This question has multiple correct options
A. Their relative velocity is along vertical direction.
B. Their relative acceleration is non-zero and it is along vertical direction.
C. They will hit the surface simultaneously
D. Their relative velocity is constant and has magnitude ( 1.4 mathrm{m} / mathrm{s} )
11
1184 A river is flowing from west to east at a speed of ( 5 mathrm{m} / mathrm{min}^{-1} ). A man on the south
bank of the river, capable of swimming at ( 10 m / m i n^{-1} ) in still waters wants to swim
the river in the shortest time. In which
direction should swim in a direction
A ( .30^{circ} ) west of north
B. ( 60^{circ} ) east of north
( mathbf{c} cdot 30^{circ} ) east of north
D. due north
11
1185 A man of mass ( 62 mathrm{kg} ) is standing on a stationary boat of mass 238 kg. The man is carrying a sphere of mass ( 0.5 mathrm{kg} ) in his hands. If the man throws the
sphere horizontally with a velocity of
( 12 m s-1, ) find the velocity with which the boat will move (in magnitude)
A ( .0 .02 m s^{-1} )
B. ( 0.5 m s^{-1} )
C. ( 0.04 m s^{-1} )
D. ( 0.06 m s^{-1} )
11
1186 At what angle should a body be projected with a velocity ( 24 frac{m}{s} ) just to
pass over the obstacle ( 14 mathrm{m} ) high of a distance of ( left.24 m . text { (Take } g=10 m / s^{2}right) )
( mathbf{A} cdot tan theta=3.8 )
B. ( tan theta=1 )
( mathbf{c} cdot tan theta=3.2 )
D. ( tan theta=2 )
11
1187 Two towns ( T_{1} ) and ( T_{2} ) are connected by
a regular bus service. A
scooterist moving from ( boldsymbol{T}_{1} ) to ( boldsymbol{T}_{2} ) with
speed of ( 20 k m h^{-1} ) notices that a bus
goes past it every 21 minutes in the
direction of his motion and every 7
minutes in the opposite direction. If a
bus leaves in either direction every ( t )
minutes, the period ( t ) is
A . 1.5 minute
B. 9.5 minute
c. 6 minute
D. 10.5 minute
11
1188 When a particle moves in a circle with a
uniform speed
A. its velocity and acceleration are both constant
B. its velocity is constant but the acceleration changes
C. its acceleration is constant but the velocity changes
D. its velocity and acceleration both change
11
1189 The distance covered by a particle in ( t )
second is given by ( boldsymbol{x}=mathbf{3}+mathbf{8} boldsymbol{t}-mathbf{4} boldsymbol{t}^{2} )
After ( 1 s ) its velocity will be
A. 0 unit ( / ) s
B. 3unit/
c. ( 4 u n i t / s )
D. ( 7 u n i t / s )
11
1190 A particle of mass ( mathrm{m} ) is tied to a string of length L. The free end of the string is fixed and the particle is whirled in a circular path. The speed of the particle increases from ( 5 mathrm{m} / mathrm{s} ) to ( 10 mathrm{m} / mathrm{s} ) for 5
secs. The motion is
A. Uniform circular motion
B. Non-uniform circular motion
c. Non uniformly accelerated motion
D. Non of these
11
1191 A pendulum is suspended from the roof of a rail road car. When the car is
moving on a circular track the pendulum inclines.
A. Forward
B. Rearward
c. Towards the centre of the path
D. Away from the centre of the path
11
1192 3. A policeman moving on a highway with a speed of
30 km h-‘fires a bullet at thief’s car speeding away in the
same direction with a speed of 192 kmh. If the muzzle
speed of the bullet is 150 ms, with what speed does the
bullet hit the thief’s car?
a. 120 ms?
b. 90 ms -1
c. 125 ms -1
d. 105 ms
11
1193 A frog sits on the end of a long board of length ( L=10 c m . ) The board rests on
frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is minimum take of speed
( v ) in ( m s^{-1} ) relative to the ground that the frog follows to do the tricks?
[Assume that the board and frog have equal masses?]
A ( cdot 2 sqrt{5} m s^{-1} )
B. ( 5 m s^{-1} )
D. ( 10 sqrt{2} mathrm{ms}^{-1} )
11
1194 16. The angle o which the velocity vector of stone makes wi
horizontal just before hitting the ground is given by:
(a) tan o = 2 tane (b) tan o = 2 cot 0
(c) tan $ = V2 tan 0 (d) tan º = 12 cos 0
11
1195 If a line makes angles ( 90^{0}, 135^{0}, 45^{0} )
with ( X, Y ) and ( Z ) axes respectively, then find its direction cosines.
11
1196 The direction of which of the following vectors is along the line of axis of
rotation?
A. Angular velocity, angular acceleration only
B. Angular velocity, angular momenturm only
c. Angular velocity, angular acceleration, angular momentum only
D. Angular velocity, angular acceleration, angular momentum and torque
11
1197 A particle is projected at an angle ( boldsymbol{theta}= )
( 30^{circ} ) with the horizontal, with a velocity
of ( 10 m s^{-1} . ) Then
This question has multiple correct options
A. After ( 2 s ), the velocity of particle makes an angle of ( 60^{circ} ) with initial velocity vector.
B. After ( 1 s ), the velocity of particle makes an angle of ( 60^{circ} ) with initial velocity vector
c. The magnitude of velocity of particle after 1 s is ( 10 mathrm{ms}^{-1} )
D. The magnitude of velocity of particle after 1 s is ( 5 m s^{-1} )
11
1198 A police van moving on a highway with a speed of ( 30 mathrm{km} / mathrm{hr} ) fires a bullet at a
thief’s car speeding away in the same
direction with a speed of ( 192 k m / h r ) If the muzzle speed of the bullet is ( 150 m / s, ) with what speed does the bullet hit the thief’s car? (Note:Obtain
that speed which is relevant for
damaging the thief’s car)
11
1199 36. The vector sum of two forces is perpendicular to their
vector difference. The forces are
a. Equal to each other
b. Equal to each other in magnitude
C. Not equal to each other in magnitude
d. Cannot be predicted
37 If none111
11
1200 A gramophone disc is rotating at 78 rotations per minute. Due to power cut,
it comes to rest after ( 30 s ). The angular retardation of the disc will be :
A. 0.27 radians ( / sec ^{2} )
B. 0.127 radians ( / ) sec ( ^{2} )
c. 12.7 radians ( / mathrm{secc}^{2} )
D. zero.
11
1201 The resultant of ( vec{A} times overrightarrow{0} ) will be equal to:
A . zero
в. ( A )
c. zero vector
D. unit vector
11
1202 23. A particle has been projected with a speed of 20 ms at
an angle of 30° with the horizontal. The time taken when
the velocity vector becomes perpendicular to the initial
velocity vector is
a. 4s
b. 2 s
c. 3s
d. Not possible in this case
11
1203 SULVEW LAAIPLES
Example 5.1 Two towers AB and CD are situated at distance
d apart as shown in Fig. 5.168. AB is 20 m high and CD is
30 m high from the ground. An obiect of mass m is thrown
from the top of AB horizontally with a velocity of 10 ms
towards CD. Simultaneously, another object of mass amis
thrown from the top of CD at an angle 60° to the horizontal
towards AB with the same magnitude of initial velocity as that
of the first object. The two objects move in the same vertical
plane, collide in mid-air, and stick to each other.
30 m
20 m
Fig. 5.168
a. Calculate the distance d between the towers.
b. Find the position where the objects hit the ground.
11
1204 o alue Lal ! (cs)
7. A staircase contains three steps
staircase contains three steps each 10 cm high and
20 cm wide. What should be the minimum hori-
zontal velocity of the ball rolling off the upper-
most plane so as to hit directly the lowest plane?
(in ms-
Fig. 5.210
11
1205 A particle is moving with velocity ( vec{v}= ) ( K(y hat{i}+x hat{j}), ) where ( K ) is a constant. The
general equation for its path is
A ( cdot y^{2}=x^{2}+ ) contant
B . ( y=x^{2}+ ) contant
C ( cdot y^{2}=x+ ) contant
D. ( x y= ) contant
11
1206 48. A body is projected horizontally from the top of a tower
with initial velocity 18 ms. It hits the ground at angie
45°. What is the vertical component of velocity when
strikes the ground?
a. 9 ms -1
b. 9/2 ms-1
c. 18 m s-1
d. 18/2 ms-1
11
1207 Two particle move in a uniform gravitational field with an acceleration
( g . ) At the initial moment the particles
were located over a tower at one point
and moved with velocities ( boldsymbol{v}_{1}=mathbf{3} boldsymbol{m} / s )
and ( v_{2}=4 m / s ) horizontally opposite
directions. Find the distance between
the particles at the moment when their velocity vectors become mutually perpendicular.
11
1208 48. Jai is standing on the top of a building of height 25 m
he wants to throw his gun to Veeru who stands on top of
another building of height 20 m at distance 15 m from
first building. For which horizontal speed of projection,
it is possible?
a. 5 ms b. 10 ms? c. 15 ms 1 d. 20 ms?
101112
11
1209 A projectile aimed at a mark which is in
the horizontal plane through the point of projection falls a cm short of it when the
elevation is ( alpha ) and goes ( b c m ) too far
when the elevation is ( beta . ) Show that if the
velocity of projection is same in all the case, the proper elevation is ( frac{1}{2} sin ^{-1}left[frac{b sin 2 alpha+a sin 2 beta}{a+b}right] )
11
1210 In uniform circular motion the velocity
is
A. Constant
B. Variable
( c cdot>1 )
D. None
11
1211 A particle moves in a circle of radius
1.0 ( c m ) with a speed given by ( v=2 t )
where ( v ) is in ( c m / s ) and ( t ) in
seconds. Find the radial acceleration of
the particle at ( t=1 s: )
( mathbf{A} cdot 2.0 mathrm{cms}^{-2} )
B. ( 3.0 mathrm{cms}^{-2} )
c. ( 4.0 mathrm{cms}^{-2} )
D. ( 5.0 mathrm{cms}^{-2} )
11
1212 What happens to the centripetal acceleration of a revolving body if you
double the orbital speed ( v ) and half
angular velocity ( omega )
A. It remains unchanged
B. It is halvedd
c. It is doubleo
D. It is quadrupled
11
1213 A ball is thrown at angle ( theta ) and another
ball is thrown at an angle ( (90-theta) ) with
the horizontal direction from the same
point with the same speed ( 40 m s^{-1} ). The
second ball reaches ( 50 m ) higher than the first ball. Find their individual
heights.
A. ( 20 m, 70 m )
B . ( 25 m, 75 m )
( mathbf{c} cdot 15 m, 65 m )
D. ( 10 m, 60 m )
11
1214 A boat takes 2 hours to travel ( 8 k m ) and
back in still water lake. With water
velocity of ( 4 k m / h, ) the time taken for going upstream of ( 8 k m ) and coming back is
A. 160 minutes
B. 80 minutes
c. 100 minutes
D. 120 minutes
11
1215 Consider two vectors ( vec{A} ) and ( vec{B} ). Let
these two vectors represent two
adjacent sides of a parallelogram. We construct a parallelogram OACB as shown in the diagram. Which of the following represent the resultant
vector?
( A cdot O A )
в. ( O C )
( c . O B )
D. None
11
1216 Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in ( 3^{r d} ) second is twice the
distance covered by it in 5th second. (Take ( left.g=10 mathrm{m} s^{-2}right) )
A. ( 85 mathrm{m} s^{-1} )
B. 75 ( mathrm{m} s^{-1} )
c. ( 65 mathrm{m} s^{-1} )
D. ( 95 mathrm{m} s^{-1} )
11
1217 For a projectile, the physical quantities which remain constant are:
A. vertical component of velocity and kinetic energy
B. potential energy and kinetic energy
c. acceleration and horizontal component of velocity
D. potential energy and acceleration
11
1218 A body of mass ( 50 mathrm{kg} ) revolves in a circle of diameter ( 0.40 mathrm{m}, ) making 500 revolutions per minute. Calculate linear
velocity and centripetal acceleration
11
1219 62. Two balls A and
balls A and B are thrown with speeds u and u/2,
spectively. Both the balls cover the same horizontal
Distance before returning to the plane of projection. If the
angle of projection of ball B is 15° with the horizontal.
then the angle of projection of A is
su
a.
sin -1
11
1220 The important characteristic that
distinguishes uniform from non
uniform circular motion are
A. Uniform circular motion has radial acceleration and radial velocity, while non uniform motion lacks it
B. Uniform circular motion has radial acceleration and tangential velocity, while non uniform motion lacks it
C. Non uniform circular motion has tangential acceleration, while uniform circular motion lacks it
D. Non uniform circular motion has tangential acceleration and radial velocity, while uniform circular motion lacks it
11
1221 A body is projected vertically upwards. The times corresponding to height ( h ) while ascending and while descending
are ( t_{1} ) and ( t_{2} ) respectively. Then the
velocity of projection is ( (g ) is acceleration due to gravity)
A. ( g sqrt{t_{1} t_{2}} )
an ( t_{2} )
в. ( frac{g t_{1} t_{2}}{t_{1}+t_{2}} )
c. ( frac{g sqrt{t_{1} t_{2}}}{2} )
D. ( frac{gleft(t_{1}+t_{2}right)}{2} )
11
1222 A stone is dropped into water from a bridge ( 44.1 mathrm{m} ) above the water. Another
stone is thrown vertically downward one second later. Both strike the water
simultaneously, then the initial speed of the second stone is
A ( cdot 12.25 mathrm{ms}^{-1} )
B . ( 14.75 mathrm{ms}^{-1} )
c. ( 16.23 m s^{-1} )
D. ( 17.15 mathrm{ms}^{-1} )
11
1223 32. The time t when they are at shortest distance from each
other subsequently, is –
a. 8.8 s b. 12 s c. 15 d. 44 s
11
1224
V. – Wall
(R
)
Illustration 5.69 A particle moves in a circular path such
that its speed v varies with distance s as v = Vs, where is
a positive constant. Find the acceleration of the particle after
traversing a distance s.
11
1225 A car moving with a speed of ( 40 mathrm{km} / mathrm{h} ) can be stopped by applying brakes at least after ( 2 mathrm{m} ). If the same car is moving with a speed of ( 80 mathrm{km} / mathrm{h} ), what is the minimum stopping distance?
( A cdot 8 c m )
B. ( 6 m )
( c .4 m )
D. ( 2.6 m )
11
1226 15. Rain, driven by the wind, falls on a railway compartment
with a velocity of 20 ms, at an angle of 30° to the
vertical. The train moves, along the direction of wind flow,
at a speed of 108 km h . Determine the apparent velocity
of rain for a person sitting in the train.
a. 20/7 ms
b. 1077 ms -1
c. 1577 ms-
t d . 1077 km h —
11
1227




2. A ball is projected upwards from a height h above the
surface of the earth with velocity v. The time at which the
ball strikes the ground is
h
(a)
+ 2hg
60
8
11
1228 What is rotatory motion? 11
1229 A body is projected horizontally from the top of a tower with initial velocity
( 18 m s^{-1} . ) It hits the ground at angle ( 45^{circ} )
What is the vertical component of velocity when strikes the ground?
B. ( 18 m s^{-1} )
( mathrm{D} cdot 9 mathrm{ms}^{-1} )
11
1230 27. A projectile has a time of flight T and range R. If the time
of flight is doubled, keeping the angle of projection same
what happens to the range?
a. R/4 b. R/2 c. 2 d. 4R
11
1231 Figure shows three vectors ( vec{a}, vec{b} ) and ( vec{c} ) where ( R ) is the midpoint of ( P Q ). Then
which of the following relations is
correct?
A. ( vec{a}+vec{b}=2 vec{c} )
в. ( vec{a}+vec{b}=vec{c} )
c. ( vec{a}-vec{b}=2 vec{c} )
D. ( vec{a}-vec{b}=vec{c} )
11
1232 shell fired from the ground is just able to cross
horizontally the top of a wall 90 m away and 45 m high.
The direction of projection of the shell will be
2 250 b. 30° C. 60° do 45°.
11
1233 Six particles are situated at the corners
of a regular hexagon of side ( a ), they
move at a constant speed ( v ). Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet
each other:
A ( cdot 2 ) a/v
B. 3 a/v
( c cdot 5 a / v )
D. 6 a/v
11
1234 When a vector of magnitude 12 units is added to a vector of magnitude 8 units, the magnitude of the resultant vector will be:
A. exactly 4 units
B. exactly 20 unit
c. exactly 2 unitt
D. O units, 10 units, or some value between them
E. 4 units, 20 units, or some value between them
11
1235 Circular motion is a example of
A. ( 1- ) D motion
B. 2-D motion
c. 3-D motion
D. None
11
1236 A particle moves with a uniform speed of ( 5 mathrm{m} / mathrm{s} ) in a circular path. If the speed increases to ( 8 mathrm{m} / mathrm{s} ) in the 20 th second
The motion of the particle in the 22 nd second will be
A. Uniform circular motion
B. Non uniform circular motion
c. Linear motion, since the particle flies off from the circular path
D. Non linear motion, since velocity has increased
11
1237 3. A particle at a height ‘h’ from the ground is projected with
an angle 30° from the horizontal, it strikes the ground
making angle 45° with horizontal. It is again projected
from the same point with the same speed but with an angle
of 60° with horizontal. Find the angle it makes with the
horizontal when it strikes the ground:
(a) tan-1 (4)
(b) tan-1 (5)
(c) tan-1 (15)
(d) tan-1 (13)
11
1238 A ball is projected from level ground with a velocity of ( 40 mathrm{m} / mathrm{s} ) at an angle of
( 30^{circ} ) from the ground. Calculate the vertical component of the projectile’s velocityjust before it strikes the ground?
(Take ( left.sin 30^{circ}=0.5, cos 30^{circ}=0.87right) )
( A cdot 10 mathrm{m} / mathrm{s} )
B. 20 ( mathrm{m} / mathrm{s} )
( c .30 mathrm{m} / mathrm{s} )
D. 35 m/s
E. ( 40 mathrm{m} / mathrm{s} )
11
1239 Define following:
Position vector
11
1240 2. Velocity of a stone projected, 2 second before it reaches
the maximum height, makes angle 53° with the horizontal
then the velocity at highest point will be
(a) 20 m/s
(b) 15 m/s
(c) 25 m/s
(d) 80/3 m/s
11
1241 13. A body is projected at angle of 30° and 60° with the
same velocity. Their horizontal ranges are R, and R, and
maximum heights are H, and H2, respectively, then
11
1242 Starting from rest, the acceleration of a
particle is ( a=2(t-1) . ) The velocity of
the particle at ( t=5 s ) is:
A. ( 15 mathrm{m} / mathrm{s} )
B. ( 25 mathrm{m} / mathrm{s} )
( mathbf{c} cdot 5 m / s )
D. None of these
11
1243 A plane is flying horizontally at ( 98 m s^{-1} ) and releases an object which reaches the ground in ( 10 s . ) The angle made by it while hitting the ground is:
A . 55
B . 45
c. 60
D. 75
11
1244 Three particles ( A, B ) and ( C ) are situated at the vertices of an equilateral triangle
of side ( r ) at ( t=0 . ) The particle ( A ) heads
towards ( B, B ) towards ( C, C ) towards ( A )
with constant speeds ( v . ) Find the time of their meeting.
11
1245 P
O5ound.
19. A bomber plane moves due east at 100 kmh over a
town T at a certain instant of time. Six minutes later, an
interceptor plane sets off flying due north-east from the
station S which is 40 km south of T. If both maintain their
courses, find the velocity with which the interceptor plane
must fly in order to just overtake the bomber.
11
1246 A particle moves according to the equation ( x=a sin omega t ) and ( y=a(1- )
( cos omega t) . ) The path of the particle is
A . circle
B. parabola
c. hyperbola
D. cycloid
E . ellipse
11
1247 A player kicks a ball at a speed of 20 ( m s^{-1} ) so that its horizontal range is
maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant
of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to (Take ( g=10 ) ( m s-2) )
A ( cdot 2 sqrt{2} mathrm{ms}^{-1} )
B. ( 4 sqrt{2} mathrm{ms}^{-1} )
( c cdot 6 sqrt{2} m s^{-1} )
D. ( 10 sqrt{2} mathrm{ms}^{-1} )
11
1248 The motion of a body is given by the equation ( frac{d v}{d t}=6-3 v ) where v is the speed in ( m s^{-1} ) and ( t ) is time in s. The
body is at rest at ( t=0 . ) The speed varies with time as
A ( cdot v=left(1-e^{-3 t}right) )
B . ( v=2left(1-e^{-3 t}right) )
c. ( v=left(1+e^{-2 t}right) )
D ( cdot v=2left(1+e^{-2 t}right) )
11
1249 a. 5, 10, 20
37. A particle slides from rest from the topmost po
I rest from the topmost point of a
ucal circle of radius r along a smooth chord making
an angle with the vertical. The time of descent is
a. Least for O=0
b. Maximum for O=0
c. Least for 0 = 45º d . Independent of e
11
1250 Illustration 5.32 An inclined plane makes an angle o = 30
with the horizontal. A particle is projected from this plane
with a speed of 5 ms’ at an angle of elevation ß= 30° with
the horizontal as shown in Fig. 5.53.
5 ms-
Fig. 5.53
a. Find the range of the particle on the plane when it strikes
the plane.
b. Find the range of the particle for B= 120°.
11
1251 A particle moving along ( x- ) axis whose position is given by ( boldsymbol{x}=mathbf{4}-mathbf{9} boldsymbol{t}+frac{boldsymbol{t}^{mathbf{3}}}{mathbf{3}} )
then choose the correct statement(s)
for this motion-
This question has multiple correct options
A. Direction of motion is not changing at any of the instants
B. For ( 0<t<3 s ), the particle is slowing down
c. Direction of motion is changing at ( t=3 )sec
D. For ( 0<t<3 s ) the particle is speeding up
11

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