1

GRAVITATION
1. The radius of the earth shrinks by 1%. The acceleration 10. A body is projected with escape velocity 11.2 km/s from
due to gravity on the earth's surface would (mass earth's surface. If the body is projected in a direction 30º
remaining constant). angle to the vertical, its escape velocity in this case will
(a) increase by 2% (b) increase by 1% be :
(c) decrease by 1% (d) decrease by 0.5%
1
2. If F1 is the magnitude of the force exerted on earth by (a) 11.2 km/s (b) 11.2 × km/s
2
moon and F2 is the magnitude of force exerted on moon
by earth then :  3
(c) 11.2 
(a) F1 > F2 (b) F1 = F2  2  km/s (d) None of these
(c) F1 < F2 (d) None of these  
3. The gravitational force of attraction between two spheri- 11. A planet is moving in an elliptical orbit. If T, V, E and L
cal bodies, each of mass 100 kg, if the distance between are respectively the kinetic energy, potential energy,
their centres is 100m, is : total energy & the magnitude of the angular momentum
(G = 6.67 × 10–11 Nm2 kg–2) of the planet then the true statement out of the following
(a) 6.67 × 10–11 N (b) 6.67 × 10–9 N is :
(c) 6.67 N (d) None of these (a) T is conserved (b) V is always positive
4. A particle is fired vertically upwards with a speed of v = (c) E is always negative

(d) L is conserved but the direction vector L
0.8 . ve. If the radius of the earth is Re then the maximum
height attained by the particle will be : continuously changes.
(a) Re (b) 2Re (c) 3Re (d) 4Re 12. The gravitational field in a region is given by E = (5 i +
5. A planet has radius and mass, both half of those of the
12 j ) N/kg then the magnitude of the gravitational force
earth, then the value of g on that planet will be :
(a) 4.9 m/s2 (b) 9.8 m/s2 (c) 19.6 m/s2 (d) 13.8 m/s2 acting on a particle of mass 2 kg placed at the origin, will
6. A body is projected vertically from the earth's surface be :
with velocity equal to half of the escape velocity. (a) zero (b) 13 N (c) 26 N (d) 75 N
Maximum height reached by the body is : 13. The minimum energy required to launch a 'm' kg satellite
from earth's surface in a circular orbit at an altitude of 2R
5R R 2R R
(a) (b) (c) (d) which is the radius of each, will be :
3 3 3 2
5 1
7. If the radius of the earth reduces by 4% density remain- (a) 3mgR (b) mgR (c) 2mgR (d) mgR
ing the same, then the escape velocity will : 6 5
(a) increase by 4% (b) increase by 2% 14. The gravitational potential difference between the
(c) decrease by 4% (d) decrease by 2% surface of a planet and a point 20m above it is 16 J/kg.
8. The time period of artificial satellite in a circular orbit of Then the work done in moving a 2kg mass by 8m on a
radius R is T. The radius of the orbit in which time period slope 60º from the horizontal, is :
is 8T is : (a) 11.1 J (b) 5.55 J (c) 16 J (d) 27.7 J
–2
(a) 2R (b) 3R (c) 4R (d) 5R 15. Three particles, each of mass 10 kg are brought from
9. A satellite is orbiting very close to planet. Its time infinity to the vertices of an equilateral triangle of side
period depends only upon : 0.1m, the work done is :
(a) density of the planet (b) mass of the planet (a) 2 × 10–8 J (b) 2 × 10–11 J (c) 2 × 10–12 J (d) 2 × 10–13 J
(c) radius of the planet (d) mass of the satellite 16. The gravitational force of attraction between two spherical
bodies, each of mass 1 kg placed at 10m apart
(G = 6.67 × 10–11 Nm2/kg2) is :
(a) 6.67 × 10–13 N (b) 6.67 × 10–11 N
(c) 6.67 × 10–7 N (d) None of these

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17. If the distance between the two particles is increased poles
by 2%, then the force of attraction between them will : (b) decrease at the equator but remain unchanged at
(a) decrease 6% (b) decrease 4% the poles.
(c) increase 4% (d) increase 6% (c) remain unchanged at the equator but decrease at
18. How the gravitational constant will change if a brass the poles
plate is introduced between two bodies ? (d) remain unchanged at the equator but increase at
(a) No change (b) Decreases the poles
(c) Increases (d) No sufficient data 26. If the earth stops rotating about its axis, the acceleration
19. Six particles each of mass m are placed at the corners of due to gravity will remain unchanged at :
a regular hexagon of edge length a. If a point mass m0 is (a) equator (b) latitude 45º
placed at the centre of the hexagon, then the net (c) latitude 60º (d) poles
gravitational force on the point mass m0 is : 27. The work done in shifting a particle of mass m from
centre of earth to the surface of earth is :
6Gm2 6Gmm0
(a) (b) mgR
a2 a2 (a) – mgR (b) + (c) zero (d) None
(c) zero (d) None of these 2
20. Suppose the gravitational force varies inversely as the 28. If a rocket is fired with a speed v = 2 gR near the
nth power of the distance. Then the time period of a
earth's surface and coasts upwards, its speed in the inter-
planet in circular orbit of radius R around the sun will be
steller space is :
proportioanl to :
(a) Rn (b) R(n+1)/2 (c) R(n–1)/2 (d) R–n (a) 4 gR (b) 2gR (c) gR (d) 4gR
21. The mass of the moon is about 1.2% of the mass of the 29. In the above question, if the satellite is stopped sud-
earth. The gravitational force exerted by moon on earth denly in its orbit and allowed to fall freely onto the earth,
as compared to the gravitational force exerted by earth the speed with which it hits the surface of the earth is :
on moon : (a) 4 km/sec (b) 8 km/sec (c) 2 km/sec (d) 6 km/sec
(a) is the same (b) is smaller 30. A satellite is orbiting a planet at a constant height in
(c) is greater (d) varies with its phase circular orbit. If the mass of the planet is reduced to half,
22. The time period of a simple pendulum at the centre of the satellite would :
earth is : (a) fall on the planet
(a) zero (b) infinite (b) go to an orbit of smaller radius
(c) less than zero (d) None of these (c) go to an orbit of higher radius
23. At the surface of a certain planet acceleration due to (d) escape from the planet
gravity is one-quarter of that on the earth. If a brass ball 31. A satellite is launched into a circular orbit of radius R
is transported to this planet, then which one of the around the earth. A second satellite is launched into an
following statements is not correct ? orbit of radius 1.01R. The time period of the second
(a) The mass of the brass ball on this planet is quarter satellite is larger than that of the first one by approxi-
of its mass as measured on the earth. mately :
(b) The brass ball has same mass on the other planet as (a) 0.5% (b) 1.5% (c) 1% (d) 3.0%
on the earth. 32. The period of a satellite in a circular orbit of radius R is
(c) The brass ball has same volume on the other planet T. What is the period of another satellite in a circular
as on the earth. (d) None of the above orbit of radius 4R ?
24. If the radius of earth decreases by 10%, the mass remaining
T T
unchanged, what will happen to the acceleration due to (a) 4T (b) (c) (d) 8T
8 4
gravity ?
33. Two satellites S & S' revolve around the earth at distances
(a) Decreases by 19% (b) Increases by 19%
3R and 6R from the centre of earth. Their periods of
(c) Decreases by more than 19%
revolution will be in the ratio :
(d) Increase by more than 19%
(a) 1 : 2 (b) 2 : 1 (c) 1 : 21.5 (d) 1 : 0.67
25. If earth were to rotate faster than its present speed, the
34. An artificial satellite of the earth releases a packet. If air
weight of an object will :
resistance is neglected, the point where the packet will
(a) increase at the equator but remain unchanged at
hit, will be :
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(a) ahead (b) exactly below (a) 5.6 km/sec (b) 11.2 km/sec
(c) behind (d) it will never reach the earth (c) 22.4 km/sec (d) 44.8 km/sec
35. If the universal constant of gravitation is decreasing 43. The mass of a planet is twice the mass of the earth and
uniformly with time, then a satellite in orbit would still diameter of the planet is thrice the diameter of the earth,
maintain its : then the acceleration due to gravity on the planet's
(a) radius (b) tangential speed surface :
(c) angular momentum (d) period of revolution 3g
g 2g
36. A satellite of mass ms revolving in a circular orbit of (a) (b) 2g (c) (d)
2 9 2
radius rs around the earth of mass M has a total energy
E. Then its angular momentum will be : 44. If radius of the earth is R, then the height h, at which the
value of g becomes one-fourth, is :
E E (a) 2R (b) 3R (c) R (d) 4R
(a) (b)
ms rs2 2ms rs2 45. Weight of a body is maximum at
(a) poles (b) equator
(c) 2 Ems rs2 (d) 2 Ems rs (c) centre of the earth (d) at latitude 45º
37. Mark correct option or options : 46. The depth d, at which the value of acceleration due to
(a) Only equatorial orbits are stable for a satellite 1
gravity becomes times the value at the surface, is
(b) Escape velocity does not depend upon angle of n
projection (R = radius of the earth)
(c) A communication satellite rotates in a direction
from west to east
R  n 1 
(a) (b) R  
(d) All the above n  n 
38. Two bodies each of mass 1 kg are at a distance of 1m.
R  n 
(d) R 
 n  1 
The escape velocity of a body of mass 1 kg which is (c)
n2
midway between them is :
(a) 8 × 10–5 m/s (b) 2.31 × 10–5 m/s 47. If a planet consists of a satellite, whose mass and radius
were both half that of the earth, the acceleration due to
(c) 4.2 × 10–5 m/s (d) zero
gravity at its surface would be
39. If an artificial satellite is moving in a circular orbit around
the earth with a speed equal to half the magnitude of the (a) 4.9 m/s2 (b) 9.8 m/s2 (c) 19.6 m/s2 (d) 29.4 m/s2
48. Two points masses each equal to 1 kg attract one another
escape velocity from the earth, the height of the satellite
with a force of 10–9 kg wt. The distance between the two
above the surface of the earth is :
point masses is approximately
R R (G = 6.6 × 10–11 MKS units)
(a) 2R (b) (c) R (d)
2 4 (a) 8 cm (b) 0.8 cm (c) 80 cm (d) 0.08 cm
40. The ratio of the radii of the planets P1 and P2 is k. The 49. A body has a weight 72 N. Whe it is taken to a height h
ratio of acceleration due to gravity is r. The ratio of the = R = radius of the earth, it would weight
escape velocities from them will be : (a) 72 N (b) 36 N (c) 18 N (d) zero
50. The angular speed of the earth in rad's so that the ob-
(a) kr (b) (c)
k (d)
r
kr     ject on equator may appear weightlessness, is (radius
r k of earth = 6400 km).
41. The escape velocity on the surface of the earth is 11.2 (a) 1.23 × 10–3 (b) 6.20 × 10–3
km/sec. If mass and radius of a planet are 4 and 2 times (c) 1.56 (d) 1.23 × 10–5
respectively than that of earth. The escape velocity from 51. The weight of a body at the centre of the earth is
the planet will be : (a) zero (b) infinite
(a) 11.2 km/sec (b) 1.112 km/sec (c) same as on the surface of the earth
(c) 15.8 km/sec (d) 22.4 km/sec (d) None of the above
42. The escape velocity of a body on the surface of the 52. If the change in the value of g at a height h above the
earth is 11.2 km/sec. If the earth's mass increases to surface of earth is the same as at a depth d below it
twice its present value and radius of the earth becomes (both h and d are much smaller than the radius of the
half, the escape velocity becomes : earth), then

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h constant is :
2
(a) d = h (b) d = 2h (c) d = (d) d = h
2 R2 M M
(a) (b) (c) MR2 (d)
53. The rotation of the earth having radius R about its axis M R2 R
speeds up to a value such that a man at latitude angle 63. A mass M is split into two parts, m and (M – m), which
60º feels weightlessness. The duration of the day in are then separated by a certain distance. What ratio of
such a case is
m
  maximizes the gravitational force between the two
R R R g M
(a)  (b) (c) (d) 
g 2 g 3 g R parts ?
54. Gravitational force between a point mass m & M separated 1 1 1 1
(a) (b) (c) (d)
by a distance is F. Now, if a point mass 2m is placed next 3 2 4 5
to m in contact with it, the force on M due to m and the 64. The height above the surface of the earth, where accel-
total force on M are
1
(a) 2F, F (b) F, 2F (c) F, 3F (d) F, F eration due to gravity is of its value at surface of the
55. The weights of an object in a coal mine, at sea level and
64
at top of mountains are w1, w2 and w3 respectively, then earth is approximately.
(a) w1 < w2 > w3 (b) w1 = w2 = w3 (a) 45× 106 m (b) 54 × 106 m
(c) w1 < w2 < w3 (d) w1 > w2 > w3 (c) 102 × 106 m (d) 72 × 106 m
56. When a body is taken from the equator to the poles, its 65. The angular velocity of rotation of a star (of mass M
weight and radius R) at which the matter will start escaping
(a) remains constant (b) increases from its equator is
(c) decreases 2GR GM GR 2GM 2
(d) increases at N-pole and decreases at S-pole (a) (b) (c) (d)
M R3 M R
57. If the earth suddenly shrinks (without changing mass)
66. At what depth below the surface of the earth accelera-
to half of its present radius, the acceleration due to gravity
tion due to gravity will be half its value 1600 km above
will be
the surface of the earth ?
g g (a) 4.8 × 106 m (b) 2.4 × 106 m
(a) (b) 4g (c) (d) 2g
2 4 6
(c) 3.2 × 10 m (d) 1.6 × 106 m
58. The diameters of two planets are in the ratio 4 : 1 and 67. Unit of gravitational potential is
their mean densities in the ratio 1 : 2. The acceleration (a) Joule (b) Joule/kilogram
due to gravity on the planets will be in ratio (c) Joule kilogram (d) None of these
(a) 1 : 2 (b) 2 : 3 (c) 2 : 1 (d) 4 : 1 68. For a uniform ring of mass M and radius R at its centre
59. If density of the earth increased 4 times and its radius (a) field and potential both are zero
become half of what it is, our weight will ?
GM
(a) Be four times its present value (b) field is zero but potential is
R
(b) Be doubled (c) Remain same
(d) Be halved GM
(c) field is zero but potential is –
60. The acceleration due to gravity near the surface of a R
planet of radius R and density d is proportional to
GM GM
d d (d) magnitude of field is 2 and potential –
(a) 2 (b) dR2 (c) dR (d)
R R
R R 69. Inside a uniform shell
61. If earth is supposed to the sphere of radius R, if g 30º is (a) potential energy is zero
value of acceleration due to gravity at latitude of 30º (b) potential is zero (c) potential is constant
and g at the equator, the value of g – g 30º is (d) All of these
1 2 3 2 1 2 70. In a gravitational field, if a body is bound with the earth,
(a) R (b) R (c) 2R (d) R then total mechanical energy has
4 4 2
(a) positive (b) zero (c) negative
62. If M is the mass of the earth and R its radius, the ratio of
(d) may be positive, negative or zero
the gravitational acceleration and the gravitational
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71. The velocity with which a projectile must be fired to (c) fall downward with increasing velocity
escape from the earth does not depend upon (d) ultimately come to rest somewhere on the original
(a) mass of the earth (b) mass of the projectile orbit
(c) radius of the earth (d) None of the above 81. A body is projected from earth's surface to become its
72. Escape velocity is given by satellite, its time period of revolution will not depend
upon
(a) 2gR (b) gR (c) 2g R (d) 2 gR
(a) mass of the earth (b) its own mass
73. Escape velocity on the earth is 11.2 km/s. What would
(c) gravitational constant (d) radius of orbit
be the escape velocity on a planet whose mass is 1000
82. For a satellite in elliptical orbit which of the following
times and radius is 10 times that of the earth ?
quantities does not remain constant ?
(a) 112 km/s (b) 11.2 km/s (c) 1.12 km/s (d) 3.7 km/s
(a) Angular momentum (b) Momentum
74. The escape velocity from the earth is ve. A body is
(c) Areal velocity (d) Total energy
projected with velocity 2ve. With what constant velocity
83. In case of an orbiting satellite, if the radius of orbit is
will it move in the inter planetary space ?
decreased
(a) ve (b) 2 ve (c) 3 ve (d) 5 ve (a) its kinetic energy decreases
75. When escape velocity is given to a particle on surface (b) its potential energy increases
of the earth, its total energy is (c) Both (a) and (b) are correct
(a) zero (b) greater than zero (d) Both (a) and (b) are wrong
84. Kepler's second law is based on
(c) less than zero (d) – GMm (a) newton's first law (b) newton's second law
2R (c) special theory of relativity
76. The escape velocity of a particle of mass m varies as (d) conservation of angular momentum
(a) m2 (b) m (c) m0 (d) m–1 85. An artificial satellite moving in a circular orbit around
77. At what angle with the horizontal should a projectile be the earth has total mechanical energy E0. Its potential
fired with the escape velocity to enable it escape from energy is :
gravitational pull of the earth ? (a) – 2E0 (b) 1.5E0 (c) 2E0 (d) E0
(a) Less than 45º (b) 45º 86. When a planet moves around sun, its
(c) More than 45º (d) Any angle (a) areal velocity is constant
78. Energy required in moving a body of mass m from a (b) linear velocity is constant
distance 2R to 3R from centre of the earth of mass M is (c) angular velocity is constant
GMm GMm GMm GMm (d) All of the above
(a) 2 (b) (c) (d) 87. The orbital velocity of a body close to the earth's surface
12 R 3R 2 8R 6R
is :
79. Gas escapes from the surface of a planet, because it
(a) 8 km/s (b) 11.2 km/s
acquires an escape velocity. The escape velocity will 8
(c) 3 × 10 m/s (d) 2.2 × 103 m/s
depend on which of the following factors :
88. For a satellite orbiting very close to earth's surface, total
I. Mass of the planet
energy is :
II. Mass of the particle escaping
III. Temperature of the planet GMm GMm GMm
(a) zero (b) (c) – (d) –
IV. Radius of the planet R R 2R
Select the correct answer from the codes given below : 89. Two identical satellites are orbiting at distances R and
(a) I and II (b) II and IV 7R from the surface of the earth, R being the radius of
(c) I and IV (d) I, III and IV the earth. The ratio of their
80. A satellite of the earth is revolving in a circular orbit (a) kinetic energies is 4 (b) potential energies is 4
with a uniform speed v. If gravitational force suddenly (c) total energies is 4 (d) All of these
disappears, the satellite will 90. The distance of two planets from the sun are 1011 and
(a) continue to move with speed v along the original 1012 m respectively. The ratio of the periods of the planet
orbit is :
(b) move with the velocity v tangentially to the original
1
orbit (a) 100 (b) (c) 10 (d) 10 10
10
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91. The period of a satellite in a circular orbit around a planet 99. For a geostationary satellite orbiting around the earth
is independent of identify the condition which is not necessary ?
(a) the mass of the planet (b) the radius of the planet (a) It must lie in the equatorial plane of the earth
(c) the mass of the satellite (b) Its height from the surface of the earth must be
(d) All the three parameters (a), (b) and (c) 36000 km
92. A satellite moves round the earth in a circular orbit is
R
radius R making one revolution per day. A second satellite (c) Its period of revolution must be 2 , where R is
moving in a circular orbit, moves round the earth once g
in 8 days. The radius of the orbit of the second satellite the radius of the earth
is : (d) Its period of revolution must be 24h.
(a) 8 R (b) 4 R (c) 2 R (d) R 100. A satellite is revolving round the earth in circular orbit
93. Kepler discovered (a) if mass of the earth is made four times, keeping other
(a) laws of motion (b) laws of rotational motion factors constant, orbital speed of satellite will become
(c) laws of planetary motion two times
(d) laws of curvilinear motion (b) corresponding to change in part (a), times period of
94. What is not conserved in case of celestial bodies satellite will remain half
revolving around sun all the time ? (c) when value of G is made two times orbital speed
(a) Kinetic energy (b) Mass increases and time period decreases
(c) Angular momentum (d) None of these (d) Both (a) and (b)
95. If G is universal gravitational constant & g is acceleration 101. If the sun and the planets carried huge amounts of
opposite charges, which of the following is incorrect ?
G
due to gravity, then the unit of the quantity is : (a) all three of Kepler's laws would still be valid
g
(b) only the third law will be valid
(a) kg-m2 (b) kg/m (c) kg/m2 (d) m2/kg (c) the second law will not change
96. Reason of weightlessness in a satellite is (d) the first law will still be valid
(a) zero gravity (b) no atmosphere 102. What happens to the acceleration due to gravity with
(c) zero reaction force by satellite surface the increase in altitude from the surface of the earth ?
(d) None of the above (a) Increases (b) Decreases
97. If orbital velocity of planet is given by v = Ga MbRc, then (c) First decreases and then increases
1 1 1 1 1 1 (d) Remains same
(a) a = ,b= ,c=– (b) a = , b = , c = –
3 3 3 2 2 2 103. At what depth below the surface of the earth, the value
of g is the same as that at a height of 5 km ?
1 1 1 1 1 1
(c) a = , b = – , c = (d) a = , b = – , c = – (a) 1.25 km (b) 10 km (c) 5 km (d) 7.5 km
2 2 2 2 2 2 104. A body is at rest on the surface of the earth. Which of
98. Earth orbiting satellite will escape, if the following statement is correct ?
(a) its speed is increased by 41% (a) No force is acting on the body
(b) its KE is doubled (b) Only weight of the body acts on it
(c) Both (a) and (b) are correct (c) Net downward force is equal to the net upward force
(d) Both (a) and (b) are wrong (d) None of the above statement is correct
105. In a satellite, if the time of revolution is T, then KE is
proportional to
1 1 1
(a) (b) (c) (d) T–2/3
T T2 T3

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