1.

In an experiment, four quantities a, b, c and d The error in kinetic energy obtained by

are measured with percentage error 1%, 2%, 3% measuring mass and speed, will be
and 4% respectively. Quantity P is calculated as (a) 12% (b) 10%
follows (c) 8% (d) 2%
𝑎3 𝑏2 10. Which of the following is a dimensional
P = 𝑐𝑑 %. Error in P is
constant ?
(a) 14% (b) 10% (a) Refractive index
(c) 7% (d) 4% (b) Poisson's ratio
2. If the error in the measurement of radius of a (c) Relative density
sphere is 2%, then the error in the determination (d) Gravitational constant
of volume of the sphere will be 11. In a vernier callipers N divisions of vernier scale
(a) 4% (b) 6% coincide with N–1 divisions of main scale (in
(c) 8% (d) 2% which length of one division is 1 mm). The least
3. The velocity v of a particle at time t is given by v count of the instrument should be
𝑏
= at + 𝑡 + 𝑐, where a,b and c are constants. The (a) N (b) N– 1
1 1
dimensions of a,b and c are respectively (c) 10𝑁 (d) (𝑁 − 1)
(a) [LT–2], [L] and [T] (b) [L2], [T] and [LT2]
2 12. The dimensions of gravitational constant Gare
(c) [LT ], [LT] and [L] (d) [L], [LT] and [T2]
(a) [MLT–2] (b)[ML3T2]
4. The dimensions of universal gravitational –1 3 –2
(c) [M L T ] (d)[M–1L2T–3]
constant are
13. According to Newton, the viscous forceacting
(a) [M–1L3T–2] (b) [ML2T–1]
between liquid layers of area A andvelocity
(c) [M–2L3T–2] (d) [M–2L2T–1] 𝑣 𝑑𝑣
5. A pair of physical quantities having same gradient 𝑧 is given by F = –A 𝑑𝑧 ,where  is
dimensional formula is constant called coefficient ofviscosity. The
(a) force and torque dimensional formula of  is
(b) work and energy (a) [ML–2T–2] (b)[M0L0T0]
2 –2
(c) force and impulse (c) [ML T ] (d)[ML–1T–1]
(d) linear momentum and angular momentum 14. The dimensional formula of pressure is
6. The force F on a sphere of radius r moving in a (a) [MLT–2] (b)[ML–1T2]
medium with velocity v is given by F = 6rv. (c) [ML–1T–2] (d) [MLT–2]
The dimensions of  are 15. The dimensional formula of torque is
(a) [ML–3] (b) [MLT–2] (a) [ML2T–2] (b)[MLT–2]
–1 –2
(c) [MT ]–1
(d) [ML–1T–1] (c) [ML T ] (d) [ML–2T–2]
7. The density of a cube is measured by measuring 16. If x=at + bt2, where x is the distance travelled by
its mass and length of its sides. If the maximum the body in kilometer while t isthe time in
error in the measurement of mass and length are second, then the unit of b is
4% and 3% respectively, the maximum error in (a) km/s (b) km-s
the measurement of density will be (c) km/s2 (d) km-s2
(a) 7% (b) 9% 17. The dimensional formula for angular
(c) 12% (d) 13% momentum is
𝑎 
8. An equation is given as (𝑝 + 𝑉 2 )=b𝑉, where p = (a) [M0L2T–2] (b)[ML2T–1]
–1
(c) [MLT ] (d)[ML2T–2]
pressure, V = volume and =absolute 18. A stone falls freely under gravity. It covers
temperature. If a and b are constants, then distances h1, h2 and h3 in the first 5s, the next 5s
dimensions of a will be and the next 5s respectively. The relation
(a) [ML5T–2] (b) [M–1L5T2] between h1, h2 and h3 is
–5 –1
(c) [ML T ] (d) [ML5T] ℎ ℎ
(a) h1 =2h2 = 3h3 (b)h1 = 2 = 3
9. The percentage errors in the measurement of 3 5
mass and speed are 2% and 3% respectively. (c) h2 = 3h1 and h3 = 3h2 (d) h1 = h2 = h3

1
19. A boy standing, at the top of a tower of 20 respectively. The ratio of the time taken by them
mheight drops a stone. Assuming, g = 10 ms–2, to reach the ground is
the velocity with which it hits the ground is (a) –5/4 (b) 12 /5
(a) 20 m/s (b) 40 m/S (c) 5/12 (d) 4/5
(c) 5 m/s (d) 10 m/s 27. If a ball is thrown vertically upwards with speed
20. A body is moving with velocity 30 m/s towards u, the distance covered during the last t sec of its
East. After 10s, its velocity becomes 40 m/s ascent is
towards North. The average acceleration of the 1
(a) ut – 2gt2 (b) (u + gt)t
body is 1
(c) ut (d)2gt2
(a) 7 m/s2 (b) √7 m/s2
(c) 5m/s 2
(d) 1 m/s2 28. A stone is thrown vertically upwards. When
21. A particle starts its motion from rest underthe stone is at a height half of its maximum height,
action of a constant force. If the distancecovered its speed is 10 m/s, then the maximum height
in first 10 s is s1 and that covered inthe first 20 s attained by the stone is (g =10 m/s2)
is s2, then (a) 8 m (b) 10 m
(a) s2 = 2 s1 (b) s2 = 3 s1 (c) 15 m (d) 20 m
(c) s2 = 4 s1 (d) s2 = s1 29. A particle moves along a straight line such that
22. A particle moves in a straight line with a its displacement at any time t is given by s= 3t3
constant acceleration. It changes its velocity + 7t2 + 14t + 5.The acceleration of the particle at
from 10 ms–1 to 20 ms–1 while passing through a t = 1 s is
distance 135 m in t sec. The value of it is (a) 18 m/s2 (b) 32 m/s2
2
(a) 10 (b) 1.8 (c) 29 m/s (d) 24 m/s2
(c) 12 (d) 9 30. A car moving with a speed of 40 km/h can be
23. A particle shows distance-time curve as given in stopped after 2m by applying brakes. If the
this figure. The maximum instantaneous same car is moving with a speed of 80 km/h,
velocity of the particle is around the point what is the minimum stopping distance?
(a) 8 m (b) 2 m
(c) 4 m (d) 6 m
31. If a car at rest, accelerates uniformly to a speed
of 144 km/h in 20s, it covers a distance of
(a) 2880 m (b) 1440 m
(c) 400 m (d) 20 m
(a) B (b) C 32. If a ball is thrown vertically upwards with a
(c) D (d) A velocity of 40 m/s, then velocity of the ball after
24. The distance travelled by a particle starting from 2s will be (g =10 m/s2)
4 (a) 15 m/s (b) 20 m/s
rest and moving with an acceleration ms–2, in
3 (c) 25 m/s (d) 28 m/s
the third-second is 33. Three different objects of masses m1, m2 and m3
(a) 6 m (b) 4 m are allowed to fall from rest and from the same
10 19
(c) 3 m (d) 3 m point O along three different frictionless paths.
25. A car moves from X to Y with a uniform speed The speeds of the three objects on reaching the
vu and returns to X with a uniform speed vd. The ground will be in the ratio of
average speed for this round trip is (a) m1 : m2 : m3 (b) m1 : 2m2 : 3m3
2𝑣 𝑣 1 1 1
(a) 𝑣 +𝑑 𝑣𝑢 (b) √𝑣𝑑 𝑣𝑢 (c) 1 : 1 : 1 (d) 𝑚 : 𝑚 : 𝑚
1 2 3
𝑑 𝑢
𝑣𝑑 𝑣𝑢 𝑣𝑢 + 𝑣𝑑 34. A body is thrown vertically upwards from the
(c) (d)
𝑣𝑑 + 𝑣𝑢 2 ground. It reaches a maximum height of 20 m in
5 s. After what time it will reach the ground
26. Two bodies A (of mass 1 kg) and B (of mass 3 from its maximum height position ?
kg) are dropped from heights of 16 m and 25 m, (a) 2.5 s (b) 5 s
2
(c) 10 s (d) 25 s (a) 60 m (b) 45 m
35. A stone released with zero velocity from the top (c) 80 m (d) 50 m
of a tower, reaches the ground in 4 s. The height 42. What will be the ratio of the distance moved by
of the tower is (g =10 m/s2) a freely falling body from rest in 4th and 5th
(a) 20 m (b) 40 m second of journey?
(c) 80 m (d) 160 m (a) 4 : 5 (b) 7 : 9
36. The displacement-time graph of moving particle (c) 16 : 25 (d) 1 : 1
is shown below. 43. A particle is moving such that its position co-
ordinates (x, y) are (2m, 3m) at time t = 0, (6m,
7m) at time t = 2 s and (13m, 14m) at time t =
5s.Average velocity vector (vav) from t = 0 to t
=5 s is
1 7
(a) 5 (13î + 14ĵ) (b) 3 (î +ĵ)
11
The instantaneous velocity of the particle is (c) 2(î +ĵ) (d) 5 (î +ĵ)
negative at the point
44. The velocity of a projectile at the initial point A
(a) D (b) F
is (2î + 3ĵ) m/s. Its velocity (in m/s) at point B is
(c) C (d) E
37. A body starts from rest, what is the ratio of the
distance travelled by the body during the 4th
and 3rd s?
7 5
(a) 5 (b) 7
7 3
(c) 3 (d) 7
(a) –2î– 3ĵ (b) –2î + 3ĵ
38. A train of 150 m length is going towards North
(c) 2î– 3ĵ (d) 2î + 3ĵ
direction at a speed of 10 m/s. A parrot flies at
45. The horizontal range and the maximum height
the speed of 5 m/s towards South direction
of a projectile are equal. The angle of projection
parallel to the railways track. The time taken by
of the projectile is
the parrot to cross the train is 1
(a) 12 s (b) 8 s (a)  = tan–1(4) (b) = tan–1(4)
(c) 15 s (d) 10 s (c)  = tan–1(2) (d)  = 45°
39. Which of the following curves does not 46. A missile is fired for maximum range with an
represent motion in one dimension? initial velocity of 20 m/s. If g =10 m/s2, the
range of the missile is
(a) (b) (a) 50 m (b) 60 m
(c) 20 m (d) 40 m
47. A particle has initial velocity (3î + 4ĵ) and has
acceleration (0.4î + 0.3ĵ).Its speed after 10s is
(c) (d) (a) 7 unit (b) 7√2 unit
(c) 8.5 unit (d) 10 unit
48. Six vectors a tof have the magnitudes and
40. A car moves a distance of 200 m. It covers the directions indicated in the figure. Which of the
first-half of the distance at speed 40 km/h and following statements is true?
the second-half of distance at speed v km /h The
average speed is 48 km/h. Find the value of v.
(a) 56 km/h (b) 60 km/h
(c) 50 km/h (d) 48 km/h
41. A body dropped from top of a tower fall through
40 m during the last two seconds of its fall. The
(a) b + c=f (b) d + c = f
height of tower is (g = 10 m/s2)
(c) d + e = f (d) b + e = f
3
49. A particle of mass m is projected with velocity v 56. The vector sum of two forces is perpendicular to
making an angle of 45° with the horizontal. their vector differences. In that case, the forces
When the particle lands on the level ground, the (a) are not equal to each other in magnitude
magnitude of the change in its momentum will (b) cannot be predicted
be (c) are equal to each other
𝑚𝑣
(a) 2mv (b) (d) are equal to each other in magnitude
√2
57. P is the point of contact of a wheel and the
(c) mv√2 (d) zero ground. The radius of wheel is 1m. The wheel
50. A and B are two vectors and 0 is the angle rolls on the ground without slipping. The
between them. If |AB|=√3(AB), then the value displacement of point P when wheel completes
of  is half rotation is
(a) 60° (b) 45° (a) 2 m (b)√2 + 4m
(c)30° (d) 90°
(c)  m (d) √2 + 2m
51. A car runs at a constant speed on a circular track
58. A stone is attached to one end of a string and
of radius 100 m, taking 62.8 s for every circular
rotated in a vertical circle. If string breaks at the
lap. The average velocity and for each circular
position of maximum tension, it will break at
lapaverage speed respectively is
(a) 0, 0 (b) 0,10 m/s
(c) 10 m/s, 10 m/s (d) 10 m/s, 0
52. For angles of projection of a projectile at angles
(45° – ) and (45°+ ), the horizontal ranges
described by the projectile are in the ratio of
(a) 1: 1 (b) 2 : 3
(c) 1: 2 (d) 2 : 1 (a) A (b)B
53. A stone tied to the end of a string of 1 m long is (c) C (d) D
whirled in a horizontal circle with a constant 59. Two particles are projected with same initial
speed. If the stone makes 22 revolutions in 44 s, velocities at an angle 300 and 600 with the
what is the magnitude and direction of horizontal. Then
acceleration of the stone? (a) their heights will be equal
2 (b) their ranges will be equal
(a) ms–2 and direction along the radius 4 towards (c) their time of flights will be equal
4
the centre (d) their ranges will be different
(b) 2 ms–2 and direction along the radiusaway from 60. A person swims in a river aiming to reach
centre exactly opposite point on the bank of a river.
(c) 2 ms–2 and direction along the radius towards His speed of swimming is 0.5 m/s at an angle
the centre 120° with the direction of flow of water. The
(d) 2 ms–2 and direction along the tangent to the speed of water in stream is
circle (a) 1.0 m/s (b) 0.5 m/s
54. If a vector 2𝐢̂ + 3𝐣̂ + 8𝐤 ̂ is perpendicular to the (c) 0.25 m/s (d) 0.43 m/s
vector 4𝐣̂– 4𝐢̂ + 𝐤
̂ , then the value of α is 61. If a unit vector is represented by 0.5𝐢̂ + 0.8𝐣̂ +
1 ̂ , then the value of c is
c𝐤
(a) –1 (b) 2
1 (a) 1 (b)√0.11
(c) − 2 (d) 1
(c) √0.01 (d) 0.39
55. The circular motion of a particle with constant 62. The speed of a boat is 5 km/h in still water. It
speed is crosses a river of width 1.0 km along the
(a) simple harmonic but not periodic shortest possible path in 15 min. The velocity of
(b) periodic and simple harmonic the river water is (in km/h)
(c) neither periodic nor simple harmonic (a) 5 (b) 1
(d) periodic but not simple harmonic (c) 3 (d) 4

4
63. Find the torque of a force F = –3î+ ĵ + 5k̂ acting respectively. The ratio of their horizontal ranges
at the point r =7 î + 3 ĵ + k̂ will be
(a) –21î + 3ĵ + 5k̂ (b)–14î + 0.8ĵ + ck̂ (a) 1 : 1 (b) 1 : 2
(c) 4î + 4ĵ + 6k̂ (d)14î + 38ĵ + 16k̂ (c) 1 : 3 (d) 2 : √2
64. A body is whirled in a horizontal circle of radius 74. The maximum range of a gun of horizontal
20 cm. It has an angular velocity of 10 rad/s. terrain is 16 km. If g = 10 ms–2, then muzzle
What is its linear velocity at any point on velocity of a shell must be
circular path? (a) 160 ms–1 (b) 200 √2 ms–1
(a) √2 m/s (b) 2 m/s (c) 400 ms–1 (d) 800 ms–1
(c) 10 m/s (d) 20 m/s 75. The angle between A and B is . The value of
65. The position vector of a particle is r = ( cos the triple product A (BA) is
t)𝐢̂+ ( sin t)𝐣̂. The velocity of the particle is (a) A2B (b) zero
(a) directed towards the origin (c) A2B sin (d) A2B cos 
(b) directed away from the origin 76. The magnitudes of vectors A, B and C are 3, 4
(c) parallel to the position vector and 5 units respectively. If A + B the angle
(d) perpendicular to the position vector between A and B is

66. Which of the following is not a vector (a) 2 (b) cos–1(0.6)
(a) Speed (b) Velocity 7 
(c) tan–1(5) (d)4
(c) Torque (d) Displacement
67. The angle between the two vectorsA = 3𝐢̂ + 4𝐣̂ + 77. Three blocks with masses m, 2m and
5𝐤̂ and B = 3𝐢̂ + 4𝐣̂– 5𝐤
̂ will be 3m are connected by strings, as
(a) 0° (b) 45° shown in the figure. After an
(c) 90° (d) 180° upward force F is applied on block
68. A boat is sent across a river with a velocity of 8 m, the masses move upward at
km h–1. If the resultant velocity of boat is 10 km constant speed v. What is the net
h–1, then velocity of river is force on the block of mass 2m? (g is
(a) 12.8 km h–1 (b) 6 km h–1 the acceleration due to gravity)
(c) 8 km h –1
(d) 10 km h–1 (a) Zero (b) 2 mg
(c) 3 mg (d) 6 mg
69. The resultant of A 0 will be equal to
78. A car of mass 1000 kg negotiates a banked
(a) zero (b) A
curve of radius 90 m on a frictionless road. If
(c) zero vector (d) unit vector
the banking angle is 45°, the speed of the car is
70. When milk is churned, cream gets separated due
(a) 20 ms–1 (b) 30 ms–1
to –1
(c) 5 ms (d) 10 ms–1
(a) centripetal force (b)centrifugal force
79. A ball moving with velocity 2 ms–1 collides
(c) frictional force (d)gravitational force
head on with another stationary ball of double
71. The vectors A and B are such that angle
the mass. If the coefficient of restitution is 0.5,
between the | A + B | = | A – B|, then angle
then their velocities (in ms–1) after collision will
between the two vectors will be
be
(a) 45° (b) 60°
(a) 0,1 (b) 1, 1
(c) 75° (d) 90°
(c) 1, 0.5 (d) 0, 2
72. An electric fan has blades of length 30 cm
80. A man of 50 kg mass is standing in a gravity
measured from the axis of rotation. If the fan is
free space at a height of 10 m above the floor.
rotating at 120 rev/min, the acceleration of a
He throws a stone of 0.5 kg mass downwards
point on the tip of the blade is
with a speed 2 ms–1. When the stone reaches the
(a) 1600 ms–2 (b) 47.4 ms–2
–2 floor, the distance of the man above the floor
(c) 23.7 ms (d) 50.55 ms–2
will be
73. Two bodies of same mass are projected with the
(a) 9.9 m (b) 10.1 m
same velocity at an angle 30° and 60°
(c) 10 m (d) 20 m

5
81. A body, under the action of a force F = 6𝐢̂– 8𝐣̂+ 88. Two masses M1 = 5 kg, M2 =10 kg are
10𝐤̂ , acquires an acceleration of 1 ms–2. The connected at the ends of an inextensible string
mass of this body must be passing over a frictionless pulley as shown.
(a) 2√10 kg (b) 10 kg When masses are released, then acceleration of
(c) 20 kg (d) 10√2 kg masses will be
82. The mass of a lift is 2000 kg. When the tension
in the supporting cable is 28000 N, then its
acceleration is
(a) 30 ms–2downwards (b) 4 ms–2 upwards
(c) 4 ms–2 downwards (d) 14 ms–2 upwards
𝑔
83. A block B is pushed momentarily along a (a) g (b) 2
horizontal surface with an initial velocity v. If , 𝑔 𝑔
(c) 3 (d) 4
is the coefficient of sliding friction between B
and the surface,block B will come to rest after a 89. The force on a rocket moving with
time [2007] a velocity 300 m/s is 210 N. The
rate of consumption of fuel of
rocket is
(a) 0.7 kg/s (b) 1.4 kg/s
𝑣 𝑔 (c) 0.07 kg/s (d) 10.7 kg/s
(a) (b)
𝑔 𝑣 90. A 5000 kg rocket is set for vertical
g 𝑣
(c) 𝑣
(d) 𝑔 firing. The exhaust speed is 800 ms–1.To give an
84. An object of mass 3 kg is at rest. If a initial upward acceleration of 20 m/s2, the
forceF = (6t2𝐢̂ + 4t𝐣̂) N is applied on the amount of gas ejected per second to supply the
object, then the velocity of the object at needed thrust will be (g = 10 ms–2)
t = 3 s is (a) 127.5 kg s–1 (b) 187.5 kg s–1
–1
(a) 18𝐢̂ + 3𝐣̂ (b)18𝐢̂ + 6𝐣̂ (c) 185.5 kg s (d) 137.5 kg s–1
(c) 3𝐢̂ + 18𝐣̂ (d) 18𝐢̂ + 4𝐣̂
85. A player takes 0.1 s in catching a ball of 91. A 10 N force is applied on a body produces an
mass 150 g moving with velocity of 20 acceleration of 1 m/s2. The mass of the body is
m/s. The force imparted by the ball on the hands (a) 5 kg (b) 10 kg
of the player is (c) 15 kg (d) 20 kg
(a) 0.3 N (b) 3 N 92. A ball of mass 150 g moving with an
(c) 30 N (d) 300 N acceleration 20 m/s2 is hit by a force, which acts
86. 1 kg body explodes into three fragments. The on it for 0.1 s. The impulsive force is
ratio of their masses is 1 : 1 : 3.The fragments of (a) 0.5 N-s (b) 0.1 N-s
same mass move perpendicular to each other (c) 0.3 N-s (d) 1.2 N-s
with speeds 30 m/s, while the heavier part 93. What will be the maximum speed of a car on a
remains in the initial direction. The speed of road turn of radius 30 m, if the coefficient of
heavier part is friction between the tyres and the road is 0.4?
10 (Take g= 9.8 m/s2)
(a) 2 m/s (b) 10√2 m/s
√ (a) 10.84 m/s (b) 9.84 m/s
(c) 20√2 m/s (d) 30√2 m/s (c) 8.84 m/s (d) 6.84 m/s
87. A particle of mass 1 kg is thrown vertically 94. If the force on a rocket moving with a velocity
upwards with speed 100 m/s. After 5s,it of 300 m/s is 345 N, then the rate ofcombustion
explodes into two parts. One part of mass 400 g of the fuel is
comes back with speed 25 m/s, what is the (a) 0.55 kg/s (b) 0.75 kg/s
speed of other part just after explosion? (c) 1.15 kg/s (d) 2.25 kg/s
(a) 100 m/s upwards (b) 600 m/s upwards 95. A shell is fired from a cannon, it explodes in
(c) 100 m/s downwards (d) 300 m/s upwards mid air, its total
(a) momentum increases
6
(b) momentum decreases a ceiling and has force constant value k. The
(c) KE increases mass is released from rest with the spring
(d) KE decreases initially unstretched. The maximum extension
96. A satellite in a force free space sweeps produced in the length of the spring will be
𝑑𝑀 (a) Mg/k (b) 2 Mg/k
stationary interplanetary dust at a rate. ( 𝑑𝑡 )=
(c) 4 Mg/k (d) Mg/2k
v. The acceleration of satellite is 104. A body of mass 3 kg is under a constant
2 v2 v2
(a) − (b)− force, which causes a displacement s in metre in
M M 1
v2 it, given by the relation s = 3 t2, where t is in
(c) − 2M (d) –v 2
97. A block has been placed on an inclined plane second. Work done by the force in 2s is
5 3
with the slope angle , block slides down the (a) 19 J (b) 8 J
plane at constant speed. The coefficient of 8 19
(c) 3 J (d) 5 J
kinetic friction is equal to
105. A force F acting on an object varies with
(a) sin  (b) cos  distance x as shown here. The force is in newton
(c) g (d) tan  and x is in metre. The work done by the force in
98. Physical independence of force is a consequence moving the object from x = 0 to x = 6 m is
of
(a) third law of motion
(b) second law of motion
(c) first law of motion
(d) All of these
99. A particle of mass m is moving with a uniform
velocity v1. It is given an impulse such that its
velocity becomes v2. The impulse is equal to (a) 4.5 J (b) 13.5 J
1
(a) m [ | v2 | – |v1 |] (b) 2m (𝑣22 –𝑣12 ) (c) 9.0 J (d) 18.0 J
(c) m (v1 + v2) (d)m (v2 – v1) 106. A bomb of mass 30 kg at rest explodes into
two pieces of masses 10 kg and 12 kg. The
100. A uniform force of (3 𝐢̂ + 𝐣̂ )N acts on a
velocity of 18 kg mass is 6 ms–1. The kinetic
particle of mass 2 kg. Hence, the particle is
̂ )m to position (4𝐢̂ energy of the other mass is
displaced from position (2𝐢̂ +𝐤
(a) 256 J (b) 486 J
+3𝐣̂– 𝐤̂ )m. The work done by the force on the
(c) 524 J (d) 324 J
particle is 107. A particle of mass m1 is moving with a
(a) 9 J (b) 6 J velocity v1, and another particle of mass m2 is
(c) 13 J (d) 15 J moving with a velocity v2. Both of them have
101. The potential energy of a particle in a force the same momentum, but their different kinetic
𝐴 𝐵
field is U =𝑟 2 − 𝑟 , where A and B are positive energies are E1 and E2 respectively. If m1>m2,
constants and r is the distance of particle from then
𝐸 𝑚
the centre of the field. For stable equilibrium, (a) E1<E2 (b) 𝐸1 = 𝑚1
2 2
the distance of the particle is
(c) E1>E2 (d) E1 = E2
(a) B/2A (b) 2A/B
108. A stationary particle explodes into two
(c) A/B (d) B/A
particles of masses m1 and m2, which move in
102. The potential energy of a system increases,
opposite directions with velocities v1 and v2. The
if work is done
ratio of their kinetic energies E1/E2 is
(a) by the system against a conservative force 𝑚 𝑣
(b) by the system against a non-conservative force (a) 1 (b) 𝑚1 𝑣2
2 1
𝑚2 𝑚1
(c) upon the system by a conservative force (c) (d)
𝑚1 𝑚2
(d) upon the system by a non-conservativeforce
103. A block of mass M is attached to the lower
end of a vertical spring. The spring is hung from
7
109. If kinetic energy of a body is increased by (b) –0.3 m/s and +0.5 m/s
300%, then percentage change in momentum (c) +0.3 m/s and 0.5 m/s
will be (d) –0.5 m/s and +0.3 m/s
(a) 100% (b) 150% 118. How much water a pump of 2 kW can raise
(c) 265% (d) 73.2% in one minute to a height of 10 m?
110. A stone is thrown at an angle of 45° to the (Take g = 10 m/s2)
horizontal with kinetic energy K. The kinetic (a) 1000 L (b) 1200 L
energy at the highest point is (c) 100 L (d) 2000 L
𝐾 𝐾 119. The coefficient of restitution e for a
(a) 2 (b) 2
√ perfectly elastic collision is
(c) K (d) zero
(a) 1 (b) zero
111. Two bodies with kinetic energies in the ratio
(c) infinite (d) –1
4 : 1 are moving with equal linear momentum.
120. The ratio of the accelerations for a solid
The ratio of their masses is
sphere (mass m and radius R) rolling down an
(a) 1 : 2 (b) 1 : 1
incline of angle  without slipping and slipping
(c) 4 : 1 (d) 1 : 4
down the incline without rolling is
112. A metal ball of mass 2 kg moving with a
(a) 5 : 7 (b) 2 : 3
velocity of 36 km/h has a head on collision with
(c) 2 : 5 (d) 7 : 5
a stationary ball of mass 3 kg. If after the
121. A rod PQ of mass M
collision, the two balls move together, the loss
and length L is hinged at
in kinetic energy due to collision is
end P. The rod is kept
(a) 140 J (b) 100 J
horizontal by a massless
(c) 60 J (d) 40 J
string tied to a point Q as
113. A body of mass m moving with velocity 3
shown in figure. When
km/h collides with a body of mass 2 m at rest.
string is cut, the initial angular acceleration of
Now, the coalesced mass starts to move with a
the rod is
velocity 3𝑔 𝑔
(a) 1 km/h (b) 2 km/h (a) 2𝐿 (b) 𝐿
(c) 3 km/h (d) 4 km/h 2𝑔 2𝑔
(c) 𝐿 (d)3𝐿
114. If the momentum of a body is increased by
122. A small object of uniform density rolls up a
50%, then the percentage increase in its kinetic
curved surface with an initial velocity v. It
energy is 3𝑣 2
(a) 50% (b) 100% reaches upto a maximum height of with
4𝑔
(c) 125% (d) 200% respect to the initial position. The object is
115. Two masses 1 g and 9 g are moving with (a) ring (b) solid sphere
equal kinetic energies. The ratio of the (c) hollow sphere (d) disc
magnitudes of their respective linear momenta is 123. When a mass is rotating in a plane about a
(a) 1 : 9 (b) 9 : 1 fixed point, its angular momentum is directed
(c) 1 : 3 (d) 3 : 1 along
116. A position dependent force (a) a line perpendicular to the plane of rotation
F = (7 – 2x + 3x2)N, (b) the line making an angle of 45° to theplane of
acts on a small body of mass 2 kg and displaces it rotation
from x = 0 to x = 5m. What done in joule is (c) the radius
(a) 35 (b) 70 (d) the tangent to the orbit
(c) 135 (d) 270 124. Two persons of masses 55 kg and 65 kg
117. Two identical balls A and B moving with respectively, are at the opposite ends of a boat.
velocities +0.5 m/s and –0.3 m/s respectively, The length of the boat is 3 m and weights 100
collide head on elastically. The velocity of the kg. The 55 kg man walks upto the 65 kg man
balls A and B after collision will be respectively and sits with him. If the boat is in still water the
(a) +0.5 m/s and +0.3 m/s centre of mass of the system shifts by
8
(a) 3 m (b) 2.3 m 130. A gramophone record is revolving with an
(c) zero (d) 0.75 m angular velocity . A coin is placed at a
125. ABC is an equilateral triangle with O as its distance r from the centre of the record. The
centre. F1, F2 and F3 represent three forces static coefficient of friction is . The coin will
acting along the sides AB, BC and AC, revolve with the record if
respectively. If the total torque about O is zero, 2
(a) r = 𝑔2 (b) r<
then the magnitude of F3 is 𝑔
𝑔 𝑔
(c) r≤ 2 (d) r≥2
131. Two bodies of masses 1kg and 3 kg have
position vectors 𝐢̂ + 2 𝐣̂ + 𝐤 ̂ and –3 𝐢̂ – 2 𝐣̂ +
̂ ,respectively. The centre of mass of this
𝐤
system has a position vector
[2009]
(a) F1 + F2 (b) F1–F2 (a) –2𝐢̂ +2𝐤 ̂ (b)–2𝐢̂–𝐣̂ + 𝐤̂
𝐹1 + 𝐹2
(c) 2 (d) 2(F1 + F2) (c) 2𝐢̂–𝐣̂– 2𝐤̂ ̂
(d) –𝐢̂ + 𝐣̂ + 𝐤
126. A particle moves in a circle of radius 5 cm 132. A thin circular ring of mass M and radius
with constant speed and time period 0.2s. The Ris rotating in a horizontal plane about an axis
acceleration of the particle is vertical to its plane with a constant angular
(a) 25 m/s2 (b) 36 m/s2 velocity . If two objects each of mass m be
(c) 5 m/s2 (d) 15 m/s2 attached gently to the opposite ends of a
diameter of the ring, the ring will then rotate
127. The moment of inertia of a thin uniform rod with an angular velocity
(𝑀 − 2𝑚) 𝑀
of mass M and length L about an axis passing (a) 𝑀 + 2𝑚 (b)𝑀 + 2𝑚
through its mid-point and perpendicular to its (𝑀 + 2𝑚) 𝑀
length is I0. Its moment of inertia about an axis (c) (d) 𝑀 + 𝑚
𝑀
passing through one of its ends and 133. If F is the force acting on a particle having
perpendicular to its length is position vector r and  be the torque of this
(a) I0 + ML2/4 (b) I0 + 2ML2 force about the origin, then
(c) I0 + ML2 (d) I0 + ML2/2 (a) r≠ 0 and F = 0
128. A circular disc of moment of inertia It is (b) r> 0 and F< 0
rotating in a horizontal plane, about its (c) r= 0 and F = 0
symmetry axis, with a constant angular speed (d) r = 0 and F≠ 0
i. Another disc of moment of inertia Ib is 134. A thin rod of length L and mass M is bent at
dropped coaxially onto the rotating disc. its mid-point into two halves so that the angle
Initially the second disk has zero angular speed. between them is 90°. The moment of inertia of
Eventually both the discs rotate with a constant the bent rod about an axis passing through the
angular speed f The energy lost by initially bending point and perpendicular to the plane
rotating disc due to friction is defined by the two halves of the rod is
1 𝐼𝑏2 1 𝐼𝑡2 ML2 ML2
(a) 2
) 𝑖
(b)2 (𝐼 2
) 𝑖
(a) 24
(b) 12
2 (𝐼𝑡 + 𝐼𝑏 𝑡 + 𝐼𝑏
1 𝐼𝑏 − 𝐼𝑡 1 𝐼𝑏 𝐼𝑡 ML2 √2ML2
(c) 2 (d)2 (𝐼 + 𝐼 ) 2𝑖 (c) 6 (d) 24
2 (𝐼𝑡 + 𝐼𝑏 ) 𝑖 𝑡 𝑏
129. Two particles which are initially atrest, 135. The ratio of the radii of gyration of a
move towards each other under the action of circular disc to that of a circular ring, each of
their internal attraction. If their speeds are v and same mass and radius, around their respective
2v at any instant, then the speed of centre of axes is
mass of the system will be (a) √3 : √2 (b) 1 : √2
(a) 2v (b) 0 (c) √2 : 1 (d) √2 : √3
(c) 1.5v (d) v

9
136. A particle of mass m 141. Consider a system of two particles having
in the XY-plane with a masses m1 and m2. If the particle of mass m1 is
velocity v along the pushed towards the centre of mass of particles
straight line AB. If the through a distance d, by what distance would
angular momentum of the particle of mass m2 move so as to keep the
the particle with respect mass centre of particles at the original position?
𝑚 𝑚
to origin O is LA when it is at A and LB when it (a) 𝑚 +1𝑚 d (b)𝑚1 d
1 2 2
is at B, then 𝑚2
(a) LA>LB (c) d (d) d
𝑚1
(b) LA = LB 142. A round disc of moment of inertia I2 about
(c) the relationship between LA and LBdepends upon its axis perpendicular to its plane and passing
the slope of the line AB through its centre is placed over another disc of
(d) LA<LB moment of inertia I1 rotating with an angular
137. A tube of length L is filled completely with velocity  about the same axis. The final
an incompressible liquid of mass M and closed angular velocity of the combination of discs is
at both the ends. The tube is then rotated in a 𝐼 
(a) 𝐼 2+ 𝐼 (b) 
horizontal plane about one of its ends with a 1 2
𝐼1  (𝐼1 + 𝐼2)
uniform angular velocity . The force exerted (c) 𝐼1 + 𝐼2
(d) 𝐼1
by the liquid at the other end is 143. The ratio of the radii of gyration of a
𝑀𝐿2 𝑀𝐿2 
(a) (b) circular disc about a tangential axis in the plane
2 2
2 𝑀𝐿2 2 of the disc and of a circular ring of the same
(c) 𝑀𝐿 (d) 2 radius about a tangential axis in the plane of the
138. The moment of inertia of a uniform circular ring is
disc of radius R and mass M about an axis (a) 2 : 3 (b) 2 : 1
passing from the edge of the disc and normal to (c) √5 : √6 (d) 1: √2
the disc is 144. A ball rolls without slipping. The radius of
1
(a) 2MR2 (b) MR2 gyration of the ball about an axis passing
7 3 through its centre of mass is k. If radius of the
(c) 2MR2 (d)2MR2
ball be R, then the fraction of total energy
139. Two bodies have their moments of inertia I associated with its rotational energy will be
and 2I respectively about their axis of rotation. 𝑘2 𝑅2
If their kinetic energies of rotation are equal, (a) (b) 𝑘 2 + 𝑅2
𝑘2 + 𝑅2
their angular momenta will be in the ratio 𝑘2 + 𝑅2 𝑘2
(c) 𝑅2 (d) 𝑅2
(a) 1 : 2 (b) √2 : 1 145. A thin circular ring of mass M and radius r
(c) 2 : 1 (d) 1 : √2 is rotating about its axis with a constant angular
140. Three particles, each of mass m grams velocity . Four objects each of mass m, are
situated at the vertices of an equilateral ABC of kept gently to the opposite ends of two
side l cm (as shown in the figure). The moment perpendicular diameters of the ring. The angular
of inertia of the system about a line AX velocity of the ring will be
perpendicular to AB and in the plane of ABC in (𝑀 + 4𝑚) (𝑀 + 4𝑚)
(a) (b) 𝑀 + 4𝑚
g-cm2 units will be 𝑀
𝑀 𝑀
(c) (d)
4𝑚 𝑀 + 4𝑚
146. A solid sphere of radius Ris placed on a
smooth horizontal surface. A horizontal force F
is applied at height h from the lowest point. For
the maximum acceleration of the centre of mass
3 (a) h = R
(a) (4)ml2 (b) 2ml2
5 3
(b) h = 2R
(c) (4)ml2 (d) (2)ml2 (c) h = 0
10
(d) the acceleration will be same whatever hmay be
147. A circular disc is to be made using iron and
aluminium. To keep its moment of inertia
maximum about a geometrical axis, it should be
so prepared that
(a) aluminium is at the interior and ironsurrounds it
(b) iron is at the interior and aluminium surrounds it (a) I1 = I2 = I3 (b)I2>I1>I3
(c) aluminium and iron layers are inalternate order (c) I3<I2<I1 (d) I3>I1>I2
(d) sheet of iron is used at both externalsurfaces and 152. Three identical metal balls each of radius
aluminium sheet as innermaterial rare placed touching each other on a horizontal
148. A disc is rotating with angular velocity .If surface such that an equilateral triangle formed
a child sits on it, what is conserved? with centres of three balls joined. The centre of
(a) Linear momentum mass of the system is located at
(b) Angular momentum (a) horizontal surface
(c) Kinetic energy (b) centre of one of the balls
(d) Moment of inertia (c) line joining the centres of any two balls
149. A wheel of bicycle is rolling without (d) point of intersection of the medians
slipping on a level road. The velocity of the 153. The moment of inertia of a disc of mass M
centre of mass is vCM, then true statement is and radius R about a tangent to its rim in
itsplane is
2 3
(a) 3MR2 (b) 2MR2
4 5
(c) 5MR2 (d)4MR2
154. A thin circular ring of mass M and radius R
is rotating about its axis with a constant angular
velocity .Two objects each of mass mare
(a) The velocity of point A is 2vCM and velocity of attached gently to the opposite ends of diameter
point B is zero of the ring. The ring will now rotate with an
(b) The velocity of point A is zero andvelocity of angular velocity
point B is 2vCM (𝑀 − 2𝑚) (𝑀 − 2𝑚)
(a) (𝑀 + 2𝑚) (b) (𝑀 + 2𝑚)
(c) The velocity of point A is 2vCM and velocity of
𝑀 (𝑀 + 2𝑚)
point B is –vCM (c) (d)
(𝑀 + 𝑚) 𝑀
(d) The velocities of both A and B are vCM
150. A particle of mass M is revolving along a 155. O is the centre of an equilateral ABC. F1,
circle of radius R and another particle of mass m F2 and F3 are three forces acting along the sides
is revolving in a circle of radius r. If time AB, BC and AC as shown in figure. What should
periods of both particles are same, then the ratio be the magnitude of F3, so that the total torque
of their angular velocities is about O is zero?
𝑅
(a) 1 (b) 𝑟
𝑟 𝑅
(c) (d) √ 𝑟
𝑅
151. ABC is a right angled triangular plate of
uniform thickness. The sides are such that
(𝐹 + 𝐹 )
AB>BC as shown in figure. I1, I2, I3 are (a) 1 2 2 (b) (F1 – F2)
moments of inertia about AB, BC and AC (c) (F1 + F2) (d) 2(F1 + F2)
respectively. Then, which of the following 156. A ball of mass 0.25 kg attached to the end of
relations is correct? a string of length 1.96 m is moving in a
horizontal circle. The string will break if the

11
 tension is more than 25N. What is the maximum (a) 1.5  rad/s (b) 3 rad/s
speed with which the ball can be moved? (c) 4.5  rad/s (d) 6 rad/s
(a) 14 m/s (b) 3 m/s 164. Two racing cars of masses m and 4m are
(c) 3.92 m/s (d) 5 m/s moving in circles of radii r and 2r respectively.
157. A couple produces If their speeds are such that each makes a
(a) no motion complete circle in the same time, then the ratio
(b) linear and rotational motion of the angular speeds of the first to the second
(c) purely rotational motion car is
(d) purely linear motion (a) 8: 1 (b) 4: 1
158. A cart of mass M is tied to one end of a (c) 2: 1 (d) 1: 1
massless rope of length 10 m. The other end of 165. A spherical ball rolls on a table without
the rope is in the hands of a man of mass M. The slipping. Then, the fraction of its total energy
entire system is on a smooth horizontal surface. associated with rotation is
The man is at x =0 and the cart at x =10 m. If the 2 2
(a) 5 (b)7
man pulls the cart by the rope, the man and the 3 3
cart will meet at the point (c) 5 (d) 7
(a) they will never meet (b)x =10 m 166. A thin uniform circular ring is rolling down
(c) x= 5 m (d)x= 0 an inclined plane of inclination 30° without
159. In a carbon monoxide molecule, the carbon slipping. Its linear acceleration along the
and the oxygen atoms are separated by a inclined plane will be
distance 1.12 × 10–10m. The distance of the 𝑔
(a) 2
𝑔
(b) 3
centre of mass from the carbon atom is 𝑔 2𝑔
(a) 0.64 10–10 m (b) 0.56 10–10 m (c) 4 (d) 3
(c) 0.51 10–10 m (d) 0.48 10–10 m 167. Angular momentum is
160. If a flywheel makes 120 rev/min, then its (a) vector (axial) (b) vector (polar)
angular speed will be (c) scalar (d) None of these
(a) 8 rad/s (b) 6 rad/s 168. In a rectangle ABCD (BC = 2AB). The
(c) 4 rad/s (d) 2rad/s moment of inertia is minimum along axis
161. The angular momentum of a body with mass through [1993]
(m) moment of inertia (I) and angular velocity
() rad/s is equal to
(a) I (b) I2
𝐼 𝐼
(c)  (d) 2
162. ABC is a triangular plate of uniform (a) BC (b) BD
thickness. The sides are in the ratio shown in the (c) HF (d)EG
figure. IAB,IBC and ICA are the moments of inertia 169. A solid sphere, disc and solid cylinder all of
of the plate about AB, BC and CA as axes the same mass and made of the same material
respectively. Which one of the following are allowed to roll down (from rest) on the
relations is correct? inclined plane, then
(a) solid sphere reaches the bottom first
(b) solid sphere reaches the bottom last
(c) disc will reach the bottom first
(d) all reach the bottom at the same time
170. The speed of a homogeneous solid sphere
(a) IAB>IBC (b)IBC>IAC after rolling down an inclined plane of vertical
(c) IAB + IBC = ICA (d) ICA is maximum height h from rest without sliding is
163. The angular speed of an engine wheel 10
(a) √ 𝑔ℎ (b) √𝑔ℎ
making 90 rev/min is 7

12
 6 4 177. Dependence of intensity of gravitational
(c) √5 𝑔ℎ (d) √3 𝑔ℎ field (E) of the earth with distance (r) from
171. If a sphere is rolling, the ratio of the centre of the earth is correctly represented by
translational energy to total kinetic energy is
given by (a) (b)
(a) 7 : 10 (b) 2 : 5
(c) 10 : 7 (d) 5 : 7
(c) (d)
172. At any instant, a rolling body may be
considered to be in pure rotation about an axis
through the point of contact. This axis is 178. The height at which the weight of a body
translating forward with speed becomes 1/16th, its weight on the surface of the
(a) equal to centre of mass earth (radius R), is
(b) zero (a) 5R (b)15R
(c) twice of centre of mass (c) 3R (d)4R
(d) None of the above 179. A spherical planet has a mass Mpand
173. A solid cylinder of mass M and radius R diameter Dp. A particle of mass m falling freely
rolls down an inclined plane of height h without near the surface of this planet will experience an
slipping. The speed of its centre of mass when it acceleration due to gravity, equal to
reaches the bottom is (a) 4GMp / 𝐷𝑝2 (b) GMpm / 𝐷𝑝2
4𝑔ℎ (c) GMp / 𝐷𝑝2 (d) 4GMpm / 𝐷𝑝2
(a) √2𝑔ℎ (b)√ 3 180. A geostationary satellite is orbiting the earth
3𝑔ℎ 4𝑔 at a height of 5R above that surface of the earth,
(c) √ (d) √ ℎ R being the radius of the earth. The time period
4
174. A ring of mass m and radius r rotates about of another satellite in hour at a height of 2R
an axis passing through its centre and from the surface of the earth is
perpendicular to its plane with angular velocity (a) 5 (b) 10
. Its kinetic energy is (c) 6√2 (d) 6/√2
1
(a) 2mr2 2 (b) mr2 181. A planet moving along an elliptical orbit is
1 closest to the sun at a distance r1 and farthest
(c) mr2 2 (d)3mr2 2 away at a distance of r2. If v1 and v2 are the
175. A solid homogeneous sphere of mass M and linear velocities at these points respectively,
𝑣
radius R is moving on a rough horizontal then the ratio 𝑣1 is
2
surface, partly rolling and partly sliding. During
(a) r2 / r1 (b) (r2 / r1)2
this kind of motion of the sphere
(c) r1 / r2 (d) (r1 / r2)2
(a) total kinetic energy is conserved
182. A body projected vertically from the earth
(b) the angular momentum of the sphereabout the
reaches a height equal to earth's radius before
point of contact with the plane is conserved
returning to the earth. The power exerted by the
(c) only the rotational kinetic energy aboutthe
gravitational force is greatest
centre of mass is conserved
(a) at the instant just before the body hits theearth
(d) angular momentum about the centre ofmass is
(b) it remains constant all through
conserved
(c) at the instant just after the body is projected
176. A black hole is an object whose
(d) at the highest position of the body it
gravitational field is so strong that even light
183. A particle of mass M is situated at the centre
cannot escape from it. To what approximate
of a spherical shell of same mass and radius a.
radius would earth (mass =5.98 × 1024 kg) have
The gravitational potential at a point situated at
to be compressed to be a black hole?
a/2 distance from the centre, will be
(a) 10–9 m (b) 10–6 m 3𝐺𝑀 2𝐺𝑀
–2
(c) 10 m (d) 100 m (a) − 𝑎 (b) − 𝑎

13
 𝐺𝑀 4𝐺𝑀 2
(c) − 𝑎 (d) − 𝑎 (a) 6 m (b) 3 m
184. The figure shows elliptical orbit of a planet 2
(c) 9 m (d) 18 m
mabout the sun S. The shaded area SCD is twice
190. A body of mass m is placed on the earth's
the shaded area SAB. If t1 is the time for the
surface. It is then taken from the earth's surface
planet to move from C to D and t2 is the time to
to a height h = 3R, then the change in
move from A to B, then
gravitational potential energy is
𝑚𝑔ℎ 2
(a) 𝑅 (b) 3mgR
3 𝑚𝑔𝑅
(c) 4mgR (d) 2
191. Escape velocity from the earth is 11.2 km/s.
(a) t1>t2 (b)t1 = 4t2 Another planet of same mass has radius 1/4
(c) t1 = 2t2 (d)t1 = t2 times that of the earth. What is the escape
185. Two satellites of the earth, S1 andS2 are velocity from another planet?
moving in the same orbit. The mass of S1 is four (a) 11.2 km/s (b) 44.8 km/s
times the mass of S2. Which one of the (c) 22.4 km/s (d) 5.6 km/s
following statements is true? 192. The escape velocity of a sphere of mass m is
(a) The time period of S1 is four times that of S2 given by (G = universal gravitational constant,
(b) The potential energies of the earth and satellite Me = mass of the earth and Re= radius of the
in the two cases are equal earth)
(c) S1 and S2 are moving with the samespeed 𝐺𝑀𝑒 2𝐺𝑀𝑒
(a) √ (b)√
(d) The kinetic energies of the two satellitesare 𝑅𝑒 𝑅𝑒
equal 2𝐺𝑚 𝐺𝑀𝑒
186. For a satellite moving in an orbit around the (c) √ (d)
𝑅𝑒 𝑅𝑒2
earth, the ratio of kinetic energy to 193. The escape velocity of a body on the surface
potentialenergy is of the earth is 11.2 km/s. If the earth’s mass
(a) 2 (b) 1/2 increases to twice its present value and the
1
(c) 2 (d) √2 radius of the earth becomes half, the escape
√
187. Imagine a new planet having the same velocity would become
density as that of the earth but it is 3 times (a) 44.8 km/s
bigger than the earth in size. If the acceleration (b) 22.4 km/s
due to gravity on the surface of the earth is g (c) 11.2 km/s (remain unchanged)
and that on the surface of the new planet is g', (d) 5.6 km/s
then 194. A ball is dropped from a satellite revolving
𝑔 around the earth at a height of 120 km. The ball
(a) g = 3g (b) g = 9
will
(c) g = 9g (d) g = 27g (a) continue to move with same speed along a
188. Two spheres of masses m and M are situated straight line tangentially to the satellite at that
in air and the gravitational force between them time
is F. The space around the masses is now filled (b) continue to move with the same speed along the
with a liquid of specific gravity 3. The original orbit of satellite
gravitational force will now be (c) fall down to the earth gradually
𝐹 𝐹
(a) 3 (b) 9 (d) go far away in space
(c) 3F (d)F 195. What will be the formula of the mass in
189. The acceleration due to gravity on the planet terms of g, R and G? (R = radius of the earth)
𝑅 𝑅2
A is 9 times the acceleration due to gravity on (a) g2𝐺 (b) G 𝑔
the planet B. A man jumps to a height of 2m on 𝑅 𝑅2
the surface of A. What is the height of jump by (c) G 𝑔 (d)g 𝐺
the same person on the planet B?

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196. The escape velocity from the surface of the
earth is ve. The escape velocity from the surface
of a planet whose mass and radius are three
times those of the earth, will be
(a) ve (b) 3ve
1
(c) 9ve (d)
3𝑣𝑒
197. The escape velocity from the earth is 11.2
km/s. If a body is to be projected in a direction
making an angle 45° to the vertical, then the
escape velocity is
(a) 11.2  2 km/s (b) 11.2 km/s
11.2
(c) 2 km/s (d) 11.2√2 km/s
√
198. The satellite of mass m is orbiting around
the earth in a circular orbit with a velocity v.
What will be its total energy?
3 1
(a) 4mv2 (b) 2mv2
1
(c) mv2 (d)− (2)mv2
199. A planet is moving in an elliptical orbit
around the sun. If T, U, E and L stand for its
kinetic energy, gravitational potential energy,
total energy and magnitude of angular
momentum about the centre of force, which of
the following is correct?
(a) T is conserved
(b) U is always positives
(c) F is always negative
(d) L is conserved but direction of vector Lchanges
continuously
200. For a satellite escape velocity is 11 km/s. If
the satellite is launched at an angle of 60o with
the vertical, then escape velocity will be
(a) 11 km/s (b) 11√3 km/s
11
(c) 3 km/s (d) 33 km/s
√

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