GRAVITATION (MED) 78

EXERCISE - 1 : BASIC OBJECTIVE QUESTIONS

LAW OF GRAVITATION & GRAVITATIONAL FIELD

1. Newton's law of gravitation :
(a) is not applicable out side the solar system (a) (b)
(b) is used to govern the motion of satellites only
(c) control the rotational motion of satellites and planets
(d) control the rotational motion of electrons in atoms
2. Gravitational force between two masses at a distance 'd'
apart is 6N. If these masses are taken to moon and kept at
same separation, then the force between them will become: (c) (d)

1
(a) 1 N (b) N
6 8. Mars has a diameter of approximately 0.5 of that of earth,
(c) 36 N (d) 6 N and mass of 0.1 of that of earth. The surface gravitational
3. The value of universal gravitational constant G depends field strength on mars as compared to that on earth is a
upon : factor of -
(a) Nature of material of two bodies (a) 0.1 (b) 0.2
(b) Heat constant of two bodies (c) 2.0 (d) 0.4
(c) Acceleration of two bodies
9. Three equal masses of 1 kg each are placed at the vertices
(d) None of these
of an equilateral triangle PQR and a mass of 2 kg is placed
4. Four particles of masses m, 2m, 3m and 4m are kept in
at the centroid O of the triangle which is at a distance of 2
sequence at the corners of a square of side a. The magnitude
m from each of the vertices of the triangle. The force, in
of gravitational force acting on a particle of mass m placed newton, acting on the mass of 2 kg is :-
at the centre of the square will be :
(a) 2 (b) 2
24m 2 G 6m 2 G
(a) (b) (c) 1 (d) zero
a2 a2
10. The SI unit of gravitational constant G is
4 2 Gm 2
(c) (d) zero (a) Nm kg
–2
(b) Nm kg
2 –2
a2
2 –1 –1
5. During the journey of space ship from earth to moon and (c) Nm kg (d) Nm kg
back, the maximum fuel is consumed :-
11. The value of gravitational constant G depends upon
(a) Against the gravitation of earth in return journey
(a) the masses of the bodies
(b) Against the gravitation of earth in onward journey
(b) the sizes of the bodies
(c) Against the gravitation of moon while reaching the moon
(d) None of the above (c) the separation of the bodies

6. If the distance between the centres of earth and moon is D (d) none of the above quantities
and mass of earth is 81 times that of moon. At what distance 12. A rocket is fired from the earth to the moon. The distance
from the centre of earth gravitational field will be zero : between the earth and the moon is r and the mass of the
earth is 81 times the mass of the moon. The gravitational
D 2D
(a) (b) force on the rocket will be zero, when its distance from the
2 3
moon is
4D 9D
(c) (d) r r
5 10 (a) (b)
20 15
7. Following curve shows the variation of intensity of
 r r
gravitational field (I) with distance from the centre of solid (c) (d)
sphere(r) : 10 5
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13. A mass M is divided into two parts xm and (1 – x) m. For a 18. The value of 'g' reduces to half of its value at surface of
given separation, the value of x for which the gravitational earth at a height 'h', then :-
attraction between the two pieces becomes maximum is
(a) h = R (b) h = 2R
1 3
(a) (b) (c) h = ( 2 +1)R (d) h = ( 2 – 1)R
2 5
(c) 1 (d) 2 19. If the earth stops rotating suddenly,the value of g at a
place other than poles would :-
14. Three particles, each of mass m, are placed at the vertices of
an equilateral triangle of side a. The gravitational field (a) Decrease
intensity at the centroid of the triangle is (b) Remain constant
(c) Increase
Gm 2
(a) zero (b) (d) Increase or decrease depending on the position of earth
a2
in the orbit round the sun

2 Gm 2 3 Gm 2 20. Diameter and mass of a planet is double that earth. Then

(c) 2 (d) 2 time period of a pendulum at surface of planet is how much
a a
times of time period at earth surface :-
15. Infinite number of masses, each of mass m, are placed along
1
a straight line at distances of r, 2r, 4r, 8r, etc. from a reference (a) times (b) 2 times
2
point O. The gravitational field intensity at point O will be
(c) Equal (d) None of these
5 Gm 4 Gm 21. th
Gravitation on moon is 1/6 of that on earth. When a balloon
(a) (b)
4r2 3r2 filled with hydrogen is released on moon then, this :-

3 Gm 2 Gm g
(c) (d) (a) Will rise with an acceleration less then  
2 r2 r2 6

16. A mass m is placed in the cavity inside a hollow sphere of g

(b) Will rise with acceleration  
mass M as shown in the figure. What is the gravitational 6
force on mass m?
 5g 
(c) Will fall down with an acceleration less than  
 6 

g
(d) Will fall down with acceleration  
6
22. The acceleration due to gravity g and mean density of
GMm GMm earth r are related by which of the following relations ?
(a) (b)
R2 r2 [G = gravitational constant and R = radius of earth] :

4gR 2 4gR 3
GMm (a)   (b)  
(c) 2 (d) zero 3G 3G
R  r
3g 3g
ACCELERATION DUE TO GRAVITY (c)   (d)  
4GR 4GR 3
17. Acceleration due to gravity at the centre of the earth is :-
23. When you move from equator to pole, the value of
g acceleration due to gravity (g) :-
(a) g (b)
2 (a) increases (b) decreases
(c) zero (d) infinite (c) remains the same
(d) first increases then decreases

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24. When the radius of earth is reduced by 1% without

changing the mass, then the acceleration due to gravity g e R e2 g e2 R e
(c) g . 2 (d) .
will m Rm g 2m R m
(a) increase by 2% (b) decrease by 1.5% 32. Assuming that the earth is a sphere of radius R, at what
(c) increase by 1% (d) decrease by 1% altitude will the value of the acceleration due to gravity be
25. Acceleration due to gravity at earth's surface is 'g' m/s2. half its value at the surface of the earth ?
Find the effective value of acceleration due to gravity at a
R R
height of 32 km from sea level : (Re = 6400 Km) (a) h  (b) h 
2 2
(a) 0.5 g m/s2 (b) 0.99 g m/s2
(c) 1.01 g m/s2 (d) 0.90 g m/s2 (c) h   2 1 R (d) h   2 1 R 
26. Imagine a new planet having the same density as that of
33. The height of the point vertically above the earth’s surface
earth but its radius is 3 times bigger than the earth in size.
at which the acceleration due to gravity becomes 1% of its
If the acceleration due to gravity on the surface of earth is
g and that on the surface of the new planet is g', then : value at the surface is (R is the radius of the earth)
(a) 8 R (b) 9 R
(a) g' = 3g (b) g' = g/9
(c) 10 R (d) 20 R
(c) g' = 9g (d) g'=27 g
Variation of acceleration due to gravity (due to rotation of earth)
27. The change in the value of 'g' at a height 'h' above the
surface of the earth is same as at a depth 'd'. If 'd' and 'h' are 34. What must be the angular velocity of rotation of the earth
much smaller than the radius of earth, then which one of so that the effective acceleration due to gravity at the equator
4
the following is correct? is zero ? The radius of the earth = 64 × 10 m.
–3 –1 –3 –1
(a) d = h (b) d = 2h (a) 3.3 × 10 rad s (b) 3.5 × 10 rad s
–3 –1 –3 –1
(3) d = 3h/2 (d) d = h/2 (c) 3.7 × 10 rad s (d) 3.9 × 10 rad s
28. A body weighs W newton at the surface of the earth. Its 35. If a man at the equator would weigh (3/5)th of his weight,
weight at a height equal to half the radius of the earth will the angular speed of the earth is
be :
2 g g
(a) (b)
W 2W g R R
(a) (b)
2 3
R 2 R
4W W (c) (d)
g 5 g
(c) (d)
9 4
–2
GRAVITATIONAL POTENTIAL ENERGY & POTENTIAL
29. The acceleration due to gravity g on earth is 9.8 ms . What 36. Two different masses are droped from same heights. When
would the value of g for a planet whose size is the same as these just strike the ground, the following is same :
that of earth but the density in twice that of earth ?
–2 –2
(a) kinetic energy (b) potential energy
(a) 19.6 ms (b) 9.8 ms
(c) linear momentum (d) acceleration
–2 –2
(c) 4.9 ms (d) 2.45 ms 37. Which of the following curve expresses the variation of
30. If both the mass and the radius of the earth decrease by 1%, gravitational potential with distance for a hollow sphere of
the value of the acceleration due to gravity will radius R :
(a) decrease by 1% (b) increase by 1%
(c) increase by 2% (d) remain unchanged
31. The acceleration due to gravity on earth of radius Re is ge (a) (b)
and that on moon of radius Rm is gm. The ratio of the masses
of the earth and the moon is given by

ge Re ge R e
(a) g . R (b) g . R (c) (d)
m m m m

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38. If Me is the mass of earth and Mm is the mass of moon (Me gravitational attraction. Then, at a separation r, which of the
= 81 Mm). The potential energy of an object of mass m following is true ?
situated at a distance R from the centre of earth and r from (a) The total energy of the system is not zero.
the centre of moon, will be :-
(b) The force between them is not zero.
R  1  81 1  (c) The centre of mass of the system is at rest.
(a) GmM m   r  2 (b) GmM e   
 81  R  r R
(d) All the above are true.
 81 1   81 1  46. A high jumper can jump 2.0 m on earth. With the same effort
(c) GmM m    (d) GmM m    how high will he be able to jump on a planet whose density
 R r  R r
is one-third and radius one-fourth those of the earth ?
39. The gravitational potential energy is maximum at:
(a) 4 m (b) 8 m
(a) infinity
(c) 12 m (d) 24 m
(b) the earth's surface
47. A body of mass m is raised to a height h above the surface
(c) The centre of the earth
of the earth of mass M and radius R until its gravitational
(d) Twice the radius of the earth
40. A missile is launched with a velocity less than the escape 1
potential energy increases by mgR. The value of h is
velocity. Sum of its kinetic energy and potential energy is :- 3
(a) Positive
(a) R/3 (b) R/2
(b) Negative
(c) May be negative or positive depending upon its initial mR mR
(c) (d)
velocity M  m  M
(d) Zero 48. A body of mass m is placed on earth surface is taken to a
41. The gravitational potential energy of a body at a distance height of h = 3R, then change in gravitation potential energy
r from the center of the earth is U. The force at that point is: is

U U mgR 2
(a) (b) (a) (b) mgR
2 4 3
r r
(c) Ur (d) Ur2 3 mgR
(c) mgR (d)
42. A particle falls from infinity to the earth. Its velocity on 4 4
reaching the earth surface is : ESCAPE VELOCITY
(a) 2Rg (b) Rg 49. Potential energy of a 3kg body at the surface of a planet is
–54J, then escape velocity will be:
(c) Rg (d) 2 Rg
(a) 18 m/s (b) 162 m/s
43. A projectile of mass m is thrown vertically up with an initial
(c) 36 m/s (d) 6 m/s
velocity n from the surface of earth (mass of earth = M). If
it comes to rest at a height h, the change in its potential 50. Escape velocity of a 1kg body on a planet is 100 m/s.
energy is Potential energy of body at that planet is:

(a) GMmh/R(R + h) (b) GMmh2/R(R + h)2 (a) – 5000J (b) –1000J

(c) GMmhR/R(R + h) (d) GMm/hR(R+h) (c) –2400J (d) –10000J

44. An artificial satellite moving in a circular orbit around the 51. The ratio of radii of two satellites is p and the ratio of their
earth has a total (kinetic + potential) energy E0. Its potential acceleration due to gravity is q. The ratio of their escape
velocities will be :
energy is :-
(a) –E0 (b) E0 q
1/2
p
1/2

(c) –2E0 (d) 2E0 (a)   (d)  

p q
45. Two objects of masses m and 4m are at rest at infinite
separation. They move towards each other under mutual (c) pq (d) pq

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52. The escape velocity from the earth is 11.2 km/s the mass of 1/2 2
another planet is 100 times of mass of earth and its radius is  rB  R   rB  R 
4 times the radius of earth. The escape velocity for the (a)   (b)  
 rA  R   rA  R 
planet is :-
(a) 56.0 km/s (b) 280 km/s 2 1/2
 rB   rB 
(c) 112 km/s (d) 11.2 km/s (c)   (d)  
 rA   rA 
53. Body is projected vertically upward from the surface of the
earth with a velocity equal to half the escape velocity. If R 60. Two ordinary satellites are revolving round the earth in
is radius of the earth, the maximum height attained by the same elliptical orbit, then which of the following quantities
body is :- is conserved :-
R R (a) Velocity (b) Angular velocity
(a) (b)
6 3 (c) Angular momentum (d) None of above
61. Kepler's second law is a consequence of :-
2
(c) R (d) R (a) conservation of kinetic energy
3
54. The escape velocity of a body projected vertically upwards (b) conservation of linear momentum
from the surface of the earth is v. If the body is projected in (c) conservation of angular momentum
a direction making an angle  with the vertical, the escape
(d) conservation of speed
velocity would be
(a) v (b) v cos  62. One projectile after deviating from its path starts moving
round the earth in a cirular path of radius equal to nine
(c) v sin  (d) v tan 
–1
times the radius of earth R. Its time period will be :-
55. For earth the escape velocity is 11.2 kms . For a planet
whose mass and radius are twice those of the earth, the R R
(a) 2 (b) 27  2
escape velocity will be g g
–1 –1
(a) 44.8 kms (b) 22.4 kms
–1 –1
(c) 11.2 kms (d) 2.8 kms R R
(c)  (d) 0.8  3
56. A body is projected up with a velocity equal to 3/4 of the g g
escape velocity from the surface of the earth. The height it
63. In adjoining figure earth goes around the sun in elliptical
reaches is : (Radius of the earth = R)
orbit on which point the orbital speed is maximum :
10 R 9R
(a) (b)
9 7

9R 10 R
(c) (d)
8 3
57. The ratio of the escape velocity of an earth satellite to its
orbital velocity is very nearly equal to (a) On A (b) On B
(a) 2 (b) 2 (c) On C (d) On D
64. Potential energy and kinetic energy of a two particle system
(c) 1/2 (d) 1 / 2
under imaginary force field are shown by curves KE and
PLANETARY MOTION & WEIGHTLESSNESS PE. respectively in figure. This system is bound at :
58. Binding energy of moon and earth is :-
GM e M m GM e M m
(a) rem (b) 2rem

GM e M m GM e M m
(c)  rem (d)  2rem
59. Two artificial satellites A and B are at a distance rA and rB (a) only point A (b) only point D
above the earth's surface. If the radius of earth is R, then
(c) only point A, B and C (d) All points A, B, C and D
the ratio of their speed will be :-
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65. A satellite of earth of mass 'm' is taken from orbital radius magnitude of angular momentum respectively , then which
2R to 3R, then minimum work done is :- of the following statement is true :-
(a) T is conserved (b) U is always positive
GMm GMm (c) E is always negative
(a) (b)
6R 12R 
(d) L is conserved but the direction of vector L will
continuously change
GMm GMm
(c) (d) 72. What will be velocity of a satellite revolving around the
24R 3R
earth at a height h above surface of earth if radius of earth
66. If a graph is plotted between T2 and r3 for a planet then its is R :-
slope will be :-
g g
(b) R
2
(a) R
42
GM Rh (R  h) 2
(a) (b)
Gm 42
(c) 4  GM (d) Zero g Rh
(c) R (d) R
Rh g
67. A space shuttle is launched in a circular orbit near the
earth's surface. The additional velocity be given to the 73. Two artificial satellites of masses m1 and m2 are moving
space - shuttle to get free from the influence of gravitational with speeds v1 and v2 in orbits of radii r1 and r2 respectively.
force, will be : If r1 > r2 then which of the following statements in true :-
(a) 1.52 km/s (b) 2.75 km/s (a) v1 = v2 (2) v1 > v2
(c) 3.28 km/s (d) 5.18 km/s (c) v1 < v2 (d) v1/r1 = v2/r2
68. If the length of the day is T, the height of that TV satellite 74. Orbital radius of a satellite S of earth is four times that of a
above the earth's surface which always appears stationary communication satellite C. Period of revolution of S is :-
from earth, will be :
(a) 4 days (b) 8 days
1/3 1/2 (c) 16 days (d) 32 days
 42 GM   42 GM 
(a) h   2  (b) h   2  R 75. If a satellite is revolving very close to the surface of earth,
 T   T 
then its orbital velocity does not depend upon:-
1/3 1/3 (a) Mass of satellite (b) Mass of earth
 GMT 2   GMT 2 
h   R h  R (c) Radius of earth (d) Orbital radius
(c) 2  (d)  2 
 4   4  76. The minimum projection velocity of a body from the earth's
69. A planet of mass m is moving in an elliptical orbit about the surface so that it becomes the satellite of the earth (Re = 6.4
sun (mass of sun = M). The maximum and minimum × 106 m).
distances of the planet from the sun are r 1 and r 2 (a) 11 × 103 m/s (b) 8 × 103 m/s
respectively. The period of revolution of the planet will be
(c) 6.4 × 103 m/s (d) 4 × 103 m/s
proportional to :
77. The maximum and minimum distances of a comet from the
(a) r13/2 (b) r23/2 sun are 8 × 1012 m and 1.6 × 1012 m respecting. If its velocity
when it is nearest to the sun is 60 m/s then what will be its
(c) (r1  r2 )3/2 (d) (r1  r2 )3/2 velocity in m/s when it is farthest ?
(a) 12 (b) 60
70. If the satellite is stopped suddenly in its orbit which is at a
distance radius of earth from earth's surface and allowed to (c) 112 (d) 6
fall freely into the earth. The speed with which it hits the 78. Near the earth's surface time period of a satellite is 1.4 hrs.
surface of earth will be : Find its time period if it is at the distance ‘4R’ from the
(a) 7.919 m/s (b) 7.919 km/s centre of earth :-

(c) 11.2 m/s (d) 11.2 km/s  1 

(a) 32 hrs. (b)   hrs.
71. A planet is moving in an elliptical orbit. If T, U, E and L are 8 2 
its kinetic energy, potential energy, total energy and
(c) 8 2 hrs. (d) 17 hrs.
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79. Escape velocity for a projectile at earth’s surface is Ve. A 86. An object weights W newton on earth. It is suspended from
body is projected form earth's surface with velocity 2 Ve. the lower end of a spring balance whose upper end is fixed
The velocity of the body when it is at infinite distance from to the ceiling of a space capsule in a stable orbit around the
the centre of the earth is :- earth. The reading of the spring balance will be
(a) Ve (b) 2Ve
(a) W (b) less than W
(c) 2 Ve (d) 3 Ve
(c) more than W (d) zero
80. The orbital velocity of an artificial satellite in a circular
orbit just above the earth’s surface is v0. The orbital velocity 87. Two satellites of masses 3M and M orbit the earth in circular
of satellite orbiting at an altitude of half of the radius is :- orbits of radii r and 3r respectively. The ratio of their speeds is

3 2 (a) 1 : 1 (b) 3 :1
(a) v0 (b) v0
2 3
(c) 3 : 1 (d) 9 : 1
2 3
(c) v0 (d) v0 88. The gravitational force between two objects is proportional
3 2 2
to 1/R (and not as 1/R ) where R is separation between them,
81. The earth revolves around the sun in one year. If distance then a particle in circular orbit under such a force would
between them becomes double, the new time period of
have its orbital speed v proportional to
revolution will be :-
(a) 4 2 years (b) 2 2 years
1 0
(a) 4 years (d) 8 years (a) (b) R
R2
82. A satellite of mass m revolves in a circular orbit of radius R
a round a planet of mass M. Its total energy E is :-
1 1
(c) R (d)
GMm GMm R
(a)  (b) 
2R 3R
89. Two satellites of the same mass are orbiting round the earth at
GMm GMm heights of R and 4R above the earth’s surface: R being the
(c)  (d) 
R R radius of the earth. Their kinetic energies are in the ratio of
83. The mean distance of mars from sun is 1.5 times that of (a) 4 : 1 (b) 3 : 2
earth from sun. What is approximately the number of years
required by mars to make one revolution about sun ? (c) 4 : 3 (d) 5 : 2
(a) 2.35 years (b) 1.85 years 90. A satellite is orbiting the earth in a circular orbit of radius r.
(c) 3.65 years (d) 2.75 years Its period of revolution varies as
84. A satellite is moving around the earth in a stable circular
orbit. Which one of the following statements will be wrong (a) r (b) r
for such a satellite ? 3/2 2
(c) r (d) r
(a) It is moving at a constant speed.
(b) Its angular momentum remains constant. 91. A satellite is launched into a circular orbit of radius R around
(c) It is acted upon by a force directed away from the centre the earth. A second satellite is launched into an orbit of
of the earth which counter balances the gravitational radius 1.01 R. The period of the second satellite is longer
pull of the earth. than that of the first by approximately

(d) It behaves as if it were as freely falling body. (a) 0.5% (b) 1.0%
85. Astronauts in a stable orbit around the earth are said to be (c) 1.5% (d) 3.0%
in a weightless condition. The reason for this is that 92. If the distance between the earth and the sun were half its
(a) the capsule and its contents are falling freely at the same rate present value, the number of days in a year would have been
(b) there is no gravitational force acting on them (a) 64.5 (b) 129
(c) the gravitational force of the earth balances that of the sun (c) 182.5 (d) 730
(d) there is no atmosphere at the height at which they are orbiting.
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EXERCISE - 2 : PREVIOUS YEARS COMPETITION QUESTIONS

LAW OF GRAVITATION & GRAVITATIONAL FIELD 3

(c) d  km (d) d  2km
1. Two particle of equal mass go round a circle of radius R 2
under the action of their mutual gravitational attraction. 7. A body weighs 200 N on the surface of the earth. How
The speed v of each particle is : (AIIMS 2009)
much will it weigh half way down to the centre of the
 GM  1  1  earth? (2019)
(a)   (b)  
 2R  2R  GM  (a) 200 N (b) 250 N

(c) 100 N (d) 150 N

1  GM   4 GM 
(c)   (d)   8. If radius of the earth is 6347 km, then what will be difference
2R  R   R  between acceleration of free fall and acceleration due to
gravity near the earth's surface?
2. A body of mass 60 g experiences a gravitational force of
(a) 0.3400 (b) 0.0340 (2019)
3.0 N, when placed at a particular point. The magnitude
(c) 0.0034 (d) 0.24
of the gravitational field intensity at that point is :
9. Find gravitational field at a distance of 2000 km from centre
(a) 180 N/kg (b) 0.05 N/kg (NEET 2022)
of earth.(Given Rearth = 6400 km, r = 2000 km, Mearth = 6 × 1024
(c) 50 N/kg (d) 20 N/kg kg) : (2019)
ACCELERATION DUE TO GRAVITY (a) 1.53 m/s2 (b) 7.12 m/s2
3. Imagine a new planet having the same density as that of (c) 3.06 m/s2 (d) 1.8 m/s2
earth but it is 3 times bigger, than the earth in radius. If the 10. What is the depth at which the value of acceleration due
to gravity becomes 1/n times the value that the surface of
acceleration due to gravity on the surface of earth is g and
earth? (Radius of earth =R) (NEET 2020)
that on the surface of the new planet is g’, then :
(a) R/n2 (b) R(n -1) /n
(a) g’ = 3g (b) g’ = g/9 (CBSE 2005) (c) Rn / (n -1 (d) R /n
(c) g’ = 9 g (d) g’ = 27 g 11. A body weighs 72 N on the surface of the earth.What is
4. At what height above the surface of earth the value of the gravitational force on it, at a height equal to half of
radius of the earth? (NEET 2020)
acceleration due to gravity would be half of its value on
the surface of earth ? (Radius of the earth is 6400 km) (a) 32 N (b) 30 N
(c) 24 N (d) 48 N
(a) 2561 km (b) 2650 km (AIIMS 2009)
GRAVITATIONAL POTENTIAL ENERGY & POTENTIAL
(c) 3200 km (d) 9800 km
12. In a gravitational force field a particle is taken from A to B
5. The density of newly discovered planet is twice that of along different paths as shown in figure. Then
earth. The acceleration due to gravity at the surface of the (BHU 2009)
planet is equal to that at the surface of the earth. If the B
radius of the earth is R, the radius of the planet would be
(a) 2 R (b) 4 R (AFMC 2007)

I III
1 1 II
(c) R (d) R
4 2 IV

6. The acceleration due to gravity at a height 1 km above the A

earth is the same as at a depth d below the surface of (a) work done along path I will be maximum
earth. Then : (2017) (b) work done along path Ii will be maximum
1 (c) work done along path IV will be maximum
(a) d  km (b) d  1km
2 (d) work done along all the paths will be the same
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13. A particle of mass 10 g is kept on the surface of a uniform ve is its escape velocity from the surface of the earth. The
sphere of mass 100 kg and radius 10 cm. Find the work to value of f is : (CBSE 2006)
be done against the gravitational force between them, to
(a) 2 (b) 1 / 2
take the particle far away from the sphere. (you may take
–11 2 –2
G = 6.67 × 10 Nm kg ) (AIIMS 2008) (c) 1/3 (d) 1/2
–10 –10
(a) 13.34 × 10 J (b) 3.33 × 10 J 19. The ratio of the radii of the planet P1 and P2 is k. The ratio
–9 –10 of acceleration due to gravity on them is r. Then the ratio
(c) 6.67 × 10 J (d) 6.67 × 10 J
of the escape velocities from them will be :(AIIMS 1997)
14. Two bodies of masses m1 and m2 are initially at rest at
(a) r/k (b) k/r
infinite distance apart. They are then allowed to move
towards each other under mutual gravitational attraction.
(c) kr (d) kr
Their relative velocity of approach at a separation distance
r between them is : (AIIMS 2008) 20. Knowing that the mass of moon is 1/81 times that of earth
and its radius is 1/4 the radius of earth. If the escape
1/ 2 1/ 2
 m1  m 2    2G velocity at the surface of the earth is 11.2 km/s. Then the
(a) 2G  (b)  m1  m 2  value of escape velocity at the surface of the moon is :
 r   r 
(a) 2.5 km/s (b) 0.14 km/s (AIIMS 2000)
1/ 2 1/ 2 (c) 5 km/s (d) 8 km/s
 r   2G 
(c)   (d)  m1m 2  21. The velocity with which a projectile must be fired, so that
 2G m m 
1 2   r 
it escape earth’s gravitation does not depend on :
15. Two spherical bodies of mass M and 5M and radii R and (a) mass of the earth (AIIMS 2003)
2 R are released in free space with initial separation
(b) mass of the projectile
between their centres equal to 12 R. If they attract each
other due to gravitational force only, then the distance (c) radius of the projectile’s orbit
covered by the smaller body before collision is : (2015) (d) gravitational constant
(a) 1.5 R (b) 2.5 R 22. Two planets A and B have the same material density. If the
(c) 4.5 R (d) 7.5 R radius of A is twice that of B, then the ratio of escape

16. At what height from the surface of earth the gravitation vA

velocity is : (CPMT 2009)
potential and the value of g are –5.4 × 107J kg–2 and 6.0 vB
ms–2 respectively? Take the radius of earth as 6400 km : (a) 2 (b) 2
(2016)
1 1
(a) 2600 km (b) 1600 km (c) (d)
2 2
(c) 1400 km (d) 2000 km –1
23. A particle is fired with a speed of 20 kmh . The speed with
17. The work done to raise a mass m from the surface of the
earth to a height h, which is equal to the radius of the

which it will move in intersteller space is v e  8 2 kmh 1 
(CPMT 2009)
earth, is: (2019) –1 –1
(a) 16.5 kmh (b) 11.2 kmh
1 (c) 10 kmh
–1
(d) 8.8 kmh
–1
(a) 2 mgR (b) mgR
2 24. A black hole is an object whose gravitational field is so
3 strong that even light cannot escape from it. To what
(c)
2
mgR (d) mgR approximate radius would earth (mass = 5.98 × 1024kg)
have to be compressed to be a black hole ? (2014)
ESCAPE VELOCITY
(a) 10–2 m (b) 100 m
18. The earth is assumed to be a sphere of radius R. A platform
(c) 10–9 m (d) 10–6 m
is arranged at a height R from the surface of the earth. The
escape velocity of a body from this platform is fve, where
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25. The ratio of escape velocity at earth (ve) to the escape 31. The figure shows elliptical orbit of a planet m about the
velocity at a planet (vp) whose radius and mean density sun S. The shared area SCD is twice the shaded area SAB.
are twice as that of earth is : (2016)
If t1 is the time for the planet to move from C to D and t2 is
(a) 1 : 2 (b) 1: 2 2 the time to move from A to B, then (CBSE 2009)

(c) 1 : 4 (d) 1: 2
26. The escape velocity fromthe Earth’s surface is v. The
escape velocity fromthe surface of another planet having
a radius, four times that of Earth and same mass density is
(NEET 2021)
(a) v (b) 2v
(c) 3v (d) 4v (a) t1 > t2 (b) t1 = 4t2
27. A particle of massmis projected with a velocity (c) t1 = 2t2 (d) t1 = t2
v  kv3 (k  1) from the surface of the Earth. 32. A geostationary satellite is orbiting the earth at a height of
(Here, ve = escape velocity) The maximum height above 5R above the surface of the earth, R being the radius of
the surface reached by the particle is (NEET 2021) the earth. The time period of another satellite in hours at a
height of 2R from the surface of the earth is(CBSE 2012)
2 2
 k   k 
(a) R   (b) R   6
1 k  1 k  (a) (b) 5
2

R 2k Rk 2 (c) 10 (d) 6 2
(c) (d)
1 k 1 k
33. The radius vector, drawn from the sun to a planet, sweeps
PLANETARY MOTION & WEIGHTLESSNESS out equal areas in equal times. This is the statement of :
(AIIMS 1995)
28. For a satellite moving in an orbit around the earth, the
ratio of kinetic energy to potential energy is (a) Newton’s third law (b) Kepler’s third law

(CBSE 2005) (c) Kepler’s second law (d) Kepler’s first law
(a) 2 (b) 1/2 34. The earth rotates about the sun in an elliptical orbit as
shown in figure. At which point its velocity will be
1 maximum? (AIIMS 1997)
(c) (d) 2
2 B

29. Two satellites of earth, S1 and S2, are moving in the same
C Sun A
orbit. The mass of S1 is four times the mass of S2. Which
one of the following statements is true ? (CBSE 2007)
D
(a) The time period of S1 is four times that of S2 (a) At C (b) At A
(b) The potential energies of earth and satellite in the two (c) At D (d) At B
cases are equal 35. Potential energy of a satellite having mass m and rotating
(c) S1 and S2 are moving with the same speed at a height of 6.4 × 106 m from the earth surface is :
(AIIMS 2000)
(d) The kinetic energies of the two satellite are equal
(a) – 0.2 mg Re (b) – 2 mg Re
30. A geostationary satellite orbits arround the earth in a
(c) – 0.5 mg Re (d) – mg Re
circular orbit of radius 36000 km. Then, the time period of
36. If v0 be orbital velocity of a satellite in a circular orbital
satellite orbiting a few hundred kilometres above the
close to the earth’s surface and ve is escape velocity from
earth’s surface (Rearth = 6400 km) will approximately be
earth, then relation between the two is : (AIIMS 2002)
1
(a) h (b) 1 h (CBSE 2008) (a) ve = 2vo (b) v e  3 v o
2
(c) v e  2 v o (d) vo = ve
(c) 2 h (d) 4 h
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37. A satellite is launched into a circular orbit of radius R 45. An asteroid of mass m is approaching earth, initially at a
around the earth. While a second satellite launched into distance of 10 Re with speed vi. It hits the earth with a
an orbit of radius 1.01 R. The period of the second satellite speed vf (Re and Me are radius and mass of earth), then
is longer, than the first one by approximately : (AIIMS 2007)
(a) 3.0% (b) 1.5% (AIIMS 2002) 2 Gm  1 
(a) v f2  v i2  1  
(c) 0.7% (d) 1.0% M e R e  10 
38. The motion of planet in the solar system is an example of
2 2 2 Gm e  1
the conservation of : (AIIMS 2003) (b) v f  v i  1  
R e  10 
(a) mass (b) linear momentum
2 Gm  1 
(c) angular momentum (d) energy (c) v f2  v i2  1  
R e  10 
39. The radius of orbit of a planet is two times that of the
earth. The time period of planet is : (CPMT 2004) 2 Gm  1
(d) v f2  v i2  1  
(a) 4.2 T (b) 2.8 T R e  10 
(c) 5.6 T (d) 8.4 T 46. If distance between earth and sun become four times, then
40. Two satellite A and B go around a planet P in circular time period becomes CPMT 2007
orbits having radius 4 R and R respectively. If the speed of (a) 4 times (b) 8 times
satellite A is 3v, then the speed of satellite B will be : (d) 1/4 times (d) 1/8 times
(a) 6 v (b) 9 v (CPMT 2005) 47. A satellite of mass m is orbiting the earth (of radius R) at
a height h from its surface. The total energy of the satellite
(c) 3 v (d) none of these
in terms of g0, the value of acceleration due to gravity at
41. The radius of orbit of a planet is two times that of the
the earth’s surface, is (2016)
earth. The time period of planet is : (CPMT 2004)
(a) 4.2 T (b) 2.8 T mg 0 R 2 2mg 0 R 2

(a) 2 R  h (b)
(c) 5.6 T (d) 8.4 T   Rh

42. Suppose the gravitational force varies inversely as the

2mg0 R 2 mg 0 R 2
nth power of the distance. The time period of a planet in (c)  (d) 2 R  h
Rh  
circular orbit of radius R around the sun will be proportional
to : (DPMT 2006) 48. A satellite is revolving in a circular orbit at a height ‘h’
(a) R
(n – 1)/2
(b) R
(n + 1)/2 from the earth’s surface (radius of earth R; h << R). The
n–1 n +1
minimum increase in its orbital velocity required, so that
(c) R (d) R the satellite could escape from the earth’s gravitational
43. The period of revolution of an earth’s satellite close to field, is close to : (Neglect the effect of atmosphere.)
surface of earth is 90 min. The time period of another (2016)
satellite in an orbit at a distance of four times the radius of
(a) gR (b) gR / 2
earth from its surface will be : (AIIMS 2009)

(a) 90 9 min (b) 270 min

(c) gR  2 1  (d) 2gR
49. Two astronauts are floating in gravitational free space
(c) 450 5 min (d) 360 min after having lost contact with their spaceship. The two
will : (2017)
44. By what percent the energy of a satellite has to be increased
(a) move away from each other
3 (b) will become stationary
to shift it from an orbit of radius r to r ?
2 (c) keep floating at the same distance between them.
(a) 15% (b) 20.30% (CPMT 2009) (d) move towards each other.
(c) 66.7% (d) 33.33%

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50. The kinetic energies of a planet in an elliptical orbit about 51. If the mass of the Sun were ten times smaller and the
the Sun, at positions A, B and C are KA, KB and KC, universal gravitational constant were ten times larger in
respectively. AC is the major axis and SB is perpendicular magnitude, which of the following is not correct?(2018)
to AC at the position of the Sun S as shown in the figure. (a) Time period of a simple pendulum on the Earth would
Then (2018) decrease
(b) Walking on the ground would become more difficult
(c) Raindrops will fall faster
(d) ‘g’ on the Earth will not change

(a) KB < KA < KC (b) KA > KB > KC

(c) KA < KB < KC (d) KB > KA > KC

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ANSWER KEY
EXERCISE - 1 : BASIC OBJECTIVE QUESTIONS
1. (c) 2. (d) 3. (d) 4. (c) 5. (b) 6. (d) 7. (a) 8. (d) 9. (d) 10. (b)
11. (d) 12. (c) 13. (a) 14. (b) 15. (d) 16. (c) 17. (d) 18. (c) 19. (b) 20. (d)
21. (c) 22. (a) 23. (a) 24. (b) 25. (a) 26. (b) 27. (c) 28. (a) 29. (b) 30. (c)
31. (a) 32. (d) 33. (b) 34. (d) 35. (a) 36. (d) 37. (c) 38. (c) 39. (a) 40. (b)
41. (b) 42. (d) 43. (a) 44. (d) 45. (d) 46. (d) 47. (b) 48. (c) 49. (d) 50. (a)
51. (d) 52. (a) 53. (b) 54. (a) 55. (c) 56. (b) 57. (a) 58. (b) 59. (a) 60. (c)
61. (c) 62. (b) 63. (a) 64. (c) 65. (b) 66. (a) 67. (c) 68. (c) 69. (d) 70. (b)
71. (c) 72. (c) 73. (c) 74. (b) 75. (a) 76. (b) 77. (a) 78. (c) 79. (d) 80. (c)
81. (b) 82. (a) 83. (b) 84. (c) 85. (a) 86. (d) 87. (b) 88. (b) 89. (d) 90. (c)
91. (c) 92.(b)

EXERCISE - 2 : PREVIOUS YEARS COMPETITION QUESTIONS

1. (c) 2. (c) 3. (a) 4. (b) 5. (d) 6. (d) 7. (c) 8. (b) 9. (c) 10. (b)
11. (a) 12. (d) 13. (d) 14. (b) 15. (d) 16. (a) 17. (b) 18. (b) 19. (d) 20. (a)
21. (b) 22. (a) 23. (a) 24. (a) 25. (b) 26. (b) 27. (d) 28. (b) 29. (c) 30. (c)
31. (a, c) 32. (d) 33. (c) 34. (b) 35. (c) 36. (c) 37. (b) 38. (c) 39. (b) 40. (a)
41. (b) 42. (b) 43. (c) 44. (d) 45. (c) 46. (b) 47. (a) 48. (c) 49. (c) 50. (b)
51. (d)

Dream on !!
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