Gravitation

Exercise - I
NEWTON'S LAW OF GRAVITATION & 6. Four particles of masses m, 2m, 3m and 4m
GRAVITATIONAL FIELD are kept in sequence at the corners of a square
of side a. The magnitude of gravitational force
1. Newton's law of gravitation : acting on a particle of mass m placed at the
(1) is not applicable outside the solar system centre of the square will be :
(2) is used to govern the motion of satellites 24m2G 6m2G
only (1) (2)
a2 a2
(3) control the rotational motion of satellites 4 2Gm2
(3) (4) Zero
and planets a2
(4) control the rotational motion of electrons 7. The tidal waves in the seas are primarily due
in atoms to :
2. Mass particles of 1 kg each are placed along (1) The gravitational effect of the sun on the
x-axis at x = 1, 2, 4, 8,..... Then gravitational earth
force on a mass of 3kg placed at origin is (2) The gravitational effect of the moon on the
(G = universal gravitational constant) :- earth
(3) The rotation of the earth
4G
(1) 4G (2) (3) 2G (4)  (4) The atmospheric effect of the earth itself
3
8. During the journey of space ship from earth
3. Gravitational force between two masses at a to moon and back, the maximum fuel is
distance 'd' apart is 6N. If these masses are consumed :-
taken to moon and kept at same separation, (1) Against the gravitation of earth in return
then the force between them will become : journey
1 (2) Against the gravitation of earth in onward
(1) 1 N (2) N
6 journey
(3) 36 N (4) 6 N (3) Against the gravitation of moon while
4. The value of universal gravitational constant reaching the moon
(4) None of the above
G depends upon :
9. If the distance between the centres of earth
(1) Nature of material of two bodies
and moon is D and mass of earth is 81 times
(2) Heat constant of two bodies
that of moon. At what distance from the
(3) Acceleration of two bodies centre of earth gravitational field will be zero :
(4) None of these D 2D 4D 9D
5. Three identical bodies (each mass M) are (1) (2) (3) (4)
2 3 5 10
placed at vertices of an equilateral triangle of 10. An earth's satellite is moving in a circular
arm L, keeping the triangle as such by which orbit with a uniform speed v. If the
angular speed the bodies should be rotated in gravitational force of the earth suddenly
their gravitational fields so that the triangle disappears, the satellite will:-
moves along circumference of circular orbit : (1) vanish into outer space
3GM GM (2) continue to move with velocity v in
(1) (2) original orbit
L3 L3
(3) fall down with increasing velocity
GM GM
(3) (4) 3 (4) fly off tangentially from the orbit with
3L3 L3
velocity v

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 NEET : Physics
11. Following curve shows the variation of 13. Assume that a tunnel is dug through earth
intensity of gravitational field (I) with from North pole to south pole and that the
distance from the centre of solid sphere(r) : earth is a non-rotating, uniform sphere of
density . The gravitational force on a particle
of mass m dropped into the tunnel when it
I
reaches a distance r from the centre of earth is
R r
(1) O 3 4
(1)  mG  r (2)  mG  r
4
   3 
4 4
(3)  mG  r2 (4)  m2G  r
 3   3 
14. Mars has a diameter of approximately 0.5 of
I that of earth, and mass of 0.1 of that of earth.
(2) O The surface gravitational field strength on
R r
mars as compared to that on earth is a factor
of –
(1) 0.1 (2) 0.2 (3) 2.0 (4) 0.4
15. Three equal masses of 1 kg each are placed at
I the vertices of an equilateral triangle PQR and
R r a mass of 2 kg is placed at the centroid O of
(3) O
the triangle which is at a distance of 2 m
from each of the vertices of the triangle. The
force, in newton, acting on the mass of 2 kg is :-
(1) 2 (2) 2 (3) 1 (4) zero
16. One can easily “weigh the earth” by calculating
I
the mass of earth using the formula (in usual
(4) O notation)
R r
G g g G
(1) R 2E (2) R 2E (3) R E (4) R 3E
g G G g

12. Suppose the acceleration due to gravity at the

ACCELERATION DUE TO GRAVITY
earth's surface is 10m/s2 and at the surface of
17. Acceleration due to gravity at the centre of
mars it is 4.0 m/s2. A 60kg passenger goes
from the earth to the mars in a spaceship the earth is :-
moving with a constant velocity. Neglect all g
(1) g (2)
other objects in the sky. Which part of figure 2
best represent the weight (Net gravitational (3) zero (4) infinite
force) of the passenger as a function of time : 18. The value of 'g' on earth surface depends :-
Weight (N) (1) only an earth's structure
600 (2) only an earth's rotational motion
A (3) on above both
400 (4) on none these and is same
B
240 19. The value of 'g' reduces to half of its value at
200 C
surface of earth at a height 'h', then :-
D (1) h = R (2) h = 2R
Time
(1) A (2) B (3) C (4) D (3) h = ( 2 + 1)R (4) h = ( 2 − 1)R

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Gravitation
20. At some planet 'g' is 1.96 m/sec2. If it is safe 26. When you move from equator to pole, the
to jump from a height of 2m on earth, then value of acceleration due to gravity (g) :-
what should be corresponding safe height for (1) increases
jumping on that planet:- (2) decreases
(1) 5m (2) 2m (3) 10m (4) 20m (3) remains the same
21. If the earth stops rotating suddenly, the value (4) first increases then decreases
of g at a place other than poles would :- 27. When the radius of earth is reduced by 1%
(1) Decrease without changing the mass, then the
(2) Remain constant acceleration due to gravity will
(3) Increase (1) increase by 2% (2) decrease by 1.5%
(4) Increase or decrease depending on the (3) increase by 1% (4) decrease by 1%
position of earth in the orbit round the sun 28. Weight of a body of mass m decreases by 1%
22. Diameter and mass of a planet is double that when it is raised to height h above the earth's
earth. Then time period of a pendulum at surface. If the body is taken to a depth h in a
surface of planet is how much times of time mine, then in its weight will
period at earth surface :-
(1) decrease by 0.5% (2) decrease by 2%
1
(1) times (2) 2 times (3) increase by 0.5% (4) increase by 1%
2 29. Acceleration due to gravity at earth's surface
(3) Equal (4) None of these is 'g' m/s2. Find the effective value of
23. Gravitation on moon is 1/6th of that on earth. acceleration due to gravity at a height of
When a balloon filled with hydrogen is 32 km from sea level : (Re = 6400 Km)
released on moon then, this :- (1) 0.5g m/s2 (2) 0.99g m/s2
(1) Will rise with an acceleration less then (3) 1.01g m/s2 (4) 0.90g m/s2
g 30. The mass of the moon is 1% of mass of the
6
  earth. The ratio of gravitational pull of earth
g
(2) Will rise with acceleration   on moon to that of moon on earth will be :
6
  (1) 1 : 1 (2) 1 : 10 (3) 1 : 100 (4) 2 : 1
(3) Will fall down with an acceleration less 31. Imagine a new planet having the same density
5g
than   as that of earth but its radius is 3 times bigger
 6  than the earth in size. If the acceleration due
g to gravity on the surface of earth is g and that
(4) Will fall down with acceleration  
6  on the surface of the new planet is g', then :
24. The acceleration due to gravity g and mean (1) g' = 3g (2) g' = g/9
density of earth  are related by which of the (3) g' = 9g (4) g'=27 g
following relations ? [G = gravitational constant 32. The change in the value of 'g' at a height 'h'
and R = radius of earth] : above the surface of the earth is same as at a
4gR 2 4gR 3 depth 'd'. If 'd' and 'h' are much smaller than
(1)  = (2)  = the radius of earth, then which one of the
3G 3G
3g 3g following is correct?
(3)  = (4)  = (1) d = h (2) d = 2h
4gR 4gR 3
3h
25. More amount of sugar is obtained in 1kg (3) d = (4) d = h/2
weight: 2
(1) At North pole 33. If the rotational speed of earth is increased
(2) At equator then weight of a body at the equator
(3) Between pole and equator (1) increases (2) decreases
(4) At South pole (3) becomes double (4) does not changes

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 NEET : Physics
34. A body weighs W newton at the surface of the 39. If Me is the mass of earth and Mm is the mass
earth. Its weight at a height equal to half the of moon (Me = 81 Mm). The potential energy of
radius of the earth will be : an object of mass m situated at a distance R
W 2W 4W W from the centre of earth and r from the centre
(1) (2) (3) (4) of moon, will be :-
2 3 9 4
R 81 1 
35. The imaginary angular velocity of the earth (1) −GmMm  
+r (2) −GmMe  + 
for which the effective acceleration due to  81   r R
81 1  81 1
gravity at the equator shall be zero is equal to (3) −GmMm  +  (4) GmMm  − 
(1) 1.25 × 10–3 rad/s (2) 2.50 × 10–3 rad/s  r R  r R
(3) 3.75 × 10 rad/s
–3 (4) 5.0 × 10–3 rad/s 40. The gravitational potential energy is maximum
[Take g = 10m/s2 for the acceleration due to at:
gravity if the earth were at rest and radius of (1) infinity
earth equal to 6400 km.] (2) the earth's surface
(3) The centre of the earth
GRAVITATIONAL POTENTIAL ENERGY & (4) Twice the radius of the earth
POTENTIAL 41. A missile is launched with a velocity less than
36. Two different masses are dropped from same the escape velocity. Sum of its kinetic energy
heights. When these just strike the ground, and potential energy is :-
the following is same : (1) Positive
(1) kinetic energy (2) potential energy (2) Negative
(3) linear momentum (4) acceleration (3) May be negative or positive depending
37. Which of the following curve expresses the upon its initial velocity
variation of gravitational potential with (4) Zero
distance for a hollow sphere of radius R : 42. A body attains a height equal to the radius of
R the earth when projected from earth' surface.
(1) The velocity of the body with which it was
V projected is :
r GM 2GM
(1) (2)
R r R R
(2)
5 GM 3GM
(3) (4)
V 4 R R
43. The gravitational potential energy of a body
R r at a distance r from the center of the earth is
(3)
U. The force at that point is :
V
U U
(1) 2 (2) (3) Ur (4) Ur2
r r
R
(4) 44. A particle falls from infinity to the earth. Its
V r velocity on reaching the earth surface is :
(1) 2Rg (2) Rg (3) Rg (4) 2Rg
38. Gravitational potential difference between 45. A projectile of mass m is thrown vertically up
surface of a planet and a point situated at a with an initial velocity  from the surface of
height of 20m above its surface is 2 J/kg. If earth (mass of earth = M). If it comes to rest
gravitational field is uniform, then the work at a height h, the change in its potential
done in taking a 5kg body upto height 4 meter energy is
above surface will be : (1) GMmh/R(R + h) (2) GMmh2/R(R + h)2
(1) 2 J (2) 20 J (3) 40 J (4) 10 J (3) GMmhR/R(R + h) (4) GMm/hR(R+h)

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Gravitation
46. Two small and heavy spheres, each of mass M, 53. The escape velocity from the earth is 11.2 km/s
are placed a distance r apart on a horizontal the mass of another planet is 100 times of
surface. The gravitational potential at the mass of earth and its radius is 4 times the
mid-point on the line joining the centre of the radius of earth. The escape velocity for the
spheres is :- planet is :-
GM
(1) Zero (2) − (1) 56.0 km/s (2) 280 km/s
r (3) 112 km/s (4) 11.2 km/s
2GM 4GM
(3) − (4) − 54. Body is projected vertically upward from the
r r surface of the earth with a velocity equal to
47. An artificial satellite moving in a circular orbit
half the escape velocity. If R is radius of the
around the earth has a total (kinetic +
earth, the maximum height attained by the
potential) energy E0. Its potential energy is :-
(1) –E0 (2) E0 body is :-
(3) –2E0 (4) 2E0 R R 2
(1) (2) (3) R (4) R
48. A particle of mass m is moving in a horizontal 6 3 3
circle of radius R under a centripetal force
A PLANETARY MOTION & WEIGHTLESSNESS
equal to − 2 (A = constant). The total energy
r 55. Binding energy of moon and earth is :-
of the particle is :- GMe M m GMe M m
(1) (2)
(Potential energy at very large distance is rem 2rem
zero) GMe M m GMe M m
A A A A (3) − (4) −
(1) (2) − (3) (4) − rem 2rem
R R 2R 2R
56. Two artificial satellites A and B are at a
ESCAPE VELOCITY distance rA and rB above the earth's surface. If
49. Potential energy of a 3kg body at the surface the radius of earth is R, then the ratio of their
of a planet is – 54J, then escape velocity will speed will be :-
be:  r +R 
1/2
 r +R 
2

(1) 18 m/s (2) 162 m/s (1)  B  (2)  B 

 rA + R   rA + R 
(3) 36 m/s (4) 6 m/s
2 1/2
50. Escape velocity of a 1kg body on a planet is r  r 
100 m/s. Potential energy of body at that (3)  B  (4)  B 
 rA   rA 
planet is:
(1) – 5000J (2) –1000J 57. The average radii of orbits of mercury and
(3) –2400J (4) –10000J earth around the sun are 6 × 107 km and
51. The ratio of radii of two satellites is p and the 1.5 × 108 km respectively. The ratio of their
ratio of their acceleration due to gravity is q. orbital speeds will be :-
The ratio of their escape velocities will be : (1) 5: 2 (2) 2: 5
1/2 1/2
q p (3) 2.5 : 1 (4) 1 : 25
(1)   (2)  
p q 58. A body is dropped by a satellite in its geo-
(3) pq (4) pq stationary orbit :
(1) it will burn on entering in to the atmosphere
52. Escape velocity of a body from earth is
(2) it will remain in the same place with respect
11.2 km/s. Escape velocity, when thrown at
an angle of 45° from horizontal will be :- to the earth
(1) 11.2 km/s (2) 22.4 km/s (3) it will reach the earth is 24 hours
2 (3) (4) 11.2 2 km/s (4) it will perform uncertain motion
11.2/ km/s
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 NEET : Physics
59. Two ordinary satellites are revolving round 64. A satellite of earth of mass 'm' is taken from
the earth in same elliptical orbit, then which orbital radius 2R to 3R, then minimum work
of the following quantities is conserved :- done is :-
(1) Velocity GMm GMm
(1) (2)
(2) Angular velocity 6R 12R
(3) Angular momentum GMm GMm
(4) None of above (3) (4)
24R 3R
60. Kepler's second law is a consequence of :- 65. If a graph is plotted between T2 and r3 for a
(1) conservation of kinetic energy planet then its slope will be :-
(2) conservation of linear momentum
42 GM
(3) conservation of angular momentum (1) (2) (3) 4 GM (4) Zero
GM 42
(4) conservation of speed
66. A planet is revolving round the sun. Its
61. One projectile after deviating from its path
distance from the sun at Apogee is rA and that
starts moving round the earth in a circular
at Perigee is rp. The mass of planet and sun is
path of radius equal to nine times the radius
m and M respectively, A and P is the velocity
of earth R. Its time period will be :-
of planet at Apogee and Perigee respectively
R R
(1) 2 (2) 27  2 and T is the time period of revolution of
g g planet round the sun.
R R 2
(3)  (4) 0.8  3 (a) T2 = (rA + rP )2
g g 2Gm
62. In adjoining figure earth goes around the sun 2
(b) T2 = (rA + rP )3
in elliptical orbit on which point the orbital 2GM
speed is maximum : (c) vArA = vPrP
B (d) vA < vP , rA > rP
(1) a, b, c (2) a, b, d
(3) b, c, d (4) all
A C
67. A satellite launching station should be :
(1) near the equatorial region
D (2) near the polar region
(3) on the polar axis
(1) On A (2) On B (3) On C (4) On D
(4) all locations are equally good
63. Potential energy and kinetic energy of a two
68. A space shuttle is launched in a circular orbit
particles system under imaginary force field
near the earth's surface. The additional
are shown by curves KE and PE respectively
velocity be given to the space - shuttle to get
in figure. This system is bound at :
free from the influence of gravitational force,
will be :
(1) 1.52 km/s (2) 2.75 km/s
Energy

KE Distance
→
(3) 3.28 km/s (4) 5.18 km/s
A B C
D 69. A satellite is moving in a circular orbit around
PE earth with a speed v. If its mass is m, then its
total energy will be :
(1) only point A 3
(1) mv 2 (2) mv2
(2) only point D 4
(3) only point A, B, and C 1 1
(3) mv 2 (4) – mv 2
(4) All 2 2
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Gravitation
70. If the length of the day is T, the height of that 74. The relay satellite transmits the television
TV satellite above the earth's surface which programme continuously from one part of the
always appears stationary from earth, will be : world to another because its :
1/3 (1) Period is greater than the period of
 42GM 
(1) h =  2  rotation of the earth about its axis
 T  (2) Period is less than the period of rotation
1/2
 42GM  of the earth about its axis
(2) h =  2  −R (3) Period is equal to the period of rotation of
 T 
the earth about its axis
1/3
 GMT2  (4) Mass is less than the mass of earth
(3) h =  2 
−R
 4  75. If the satellite is stopped suddenly in its orbit
1/3
which is at a distance radius of earth from
 GMT2  earth's surface and allowed to fall freely into
(4) h =  2 
+R
 4  the earth. The speed with which it hits the
71. If two bodies of mass M and m are revolving surface of earth will be :
around the centre of mass of the system in (1) 7.919 m/s (2) 7.919 km/s
circular orbit of radii R and r respectively due (3) 11.2 m/s (4) 11.2 km/s
to mutual interaction. Which of the following 76. A planet is moving in an elliptical orbit. If T, U,
formula is applicable :- E and L are its kinetic energy, potential
GMm energy, total energy and magnitude of
(1) = m2r angular momentum respectively, then which
(R + r)2
of the following statement is true :-
GMm (1) T is conserved
(2) 2
= m2r
R (2) U is always positive
GMm (3) E is always negative
(3) = m2r
r2 (4) L is conserved but the direction of vector
GMm L will continuously change
(4) 2 2 = m2r
R +r 77. The gravitational force between two bodies is
72. Two satellites of same mass m are revolving 1 1
directly proportional to (not 2 ), where
round of earth (mass M) in the same orbit of R R
radius r. Rotational directions of the two are 'R' is the distance between the bodies. Then
opposite therefore, they can collide. Total the orbital speed for this force in circular
mechanical energy of the system (both orbit is proportional to :-
satellites and earths) is (m << M) :- (1) 1/R2 (2) R° (3) R (4) 1/R
GMm 2GMm 78. What will be velocity of a satellite revolving
(1) − (2) −
r r around the earth at a height h above surface
GMm of earth if radius of earth is R :-
(3) − (4) Zero g g
2r (1) R2 (2) R
73. A planet of mass m is moving in an elliptical R+h (R + h)2
orbit about the sun (mass of sun = M). The g R+h
(3) R (4) R
maximum and minimum distances of the R+h g
planet from the sun are r1 and r2 respectively. 79. Two artificial satellites of masses m1 and m2
The period of revolution of the planet will be are moving with speeds v1 and v2 in orbits of
proportional to : radii r1 and r2 respectively. If r1 > r2 then
(1) r13/2 (2) r23/2 which of the following statements in true :-
(3) (r1 − r2 )3/2 (4) (r1 + r2 )3/2 (1) v1 = v2 (2) v1 > v2
(3) v1 < v2 (4) v1/r1 = v2/r2

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 NEET : Physics
80. Orbital radius of a satellite S of earth is four 88. A communication satellite of earth which
times that of a communication satellite C. takes 24 hrs. to complete one circular orbit
Period of revolution of S is :- eventually has to be replaced by another
(1) 4 days (2) 8 days satellite of double mass. If the new satellites
(3) 16 days (4) 32 days
also has an orbital time period of 24 hrs, then
81. If a satellite is revolving very close to the
what is the ratio of the radius of the new orbit
surface of earth, then its orbital velocity does
not depend upon:- to the original orbit ?
(1) Mass of satellite (2) Mass of earth (1) 1 : 1 (2) 2 : 1 (3) 2 :1 (4) 1 : 2
(3) Radius of earth (4) Orbital radius 89. Escape velocity for a projectile at earth's
82. Two identical satellites are at the heights R surface is Ve. A body is projected form earth's
and 7R from the earth's surface. Then which surface with velocity 2 Ve. The velocity of the
of the following statement is incorrect :–
body when it is at infinite distance from the
(R = Radius of the earth)
centre of the earth is :-
(1) Ratio of total energy of both is 5
(2) Ratio of kinetic energy of both is 4 (1) Ve (2) 2Ve
(3) Ratio of potential energy of both 4 (3) 2 Ve (4) 3 Ve
(4) Ratio of total energy of both is 4 90. For a satellite moving in an orbit around the
83. The minimum projection velocity of a body earth, the ratio of kinetic energy to potential
from the earth's surface so that it becomes the
energy is :-
satellite of the earth (Re = 6.4 × 106 m).
(1) 2 (2) 1/2
(1) 11 × 103 m/s (2) 8 × 103 m/s
(3) 6.4 × 103 m/s (4) 4 × 103 m/s 1
(3) (4) 2
84. Geostationary satellite :- 2
(1) is situated at a great height above the 91. The orbital velocity of an artificial satellite in
surface of earth a circular orbit just above the earth’s surface
(2) moves in equatorial plane is v0. The orbital velocity of satellite orbiting
(3) have time period of 24 hours at an altitude of half of the radius is :-
(4) have time period of 24 hours and moves
3 2
in equatorial plane (1) v 0 (2) v 0
85. The maximum and minimum distances of a 2 3
comet from the sun are 8 × 1012 m and 2 3
(3) v0 (4) v0
1.6 × 1012 m respecting. If its velocity when it 3 2
is nearest to the sun is 60 m/s then what will 92. The earth revolves around the sun in one
be its velocity in m/s when it is farthest ? year. If distance between them becomes
(1) 12 (2) 60 (3) 112 (4) 6 double, the new time period of revolution will
86. A satellite of mass m goes round the earth
be :-
along a circular path of radius r. Let mE be the
mass of the earth and RE its radius then the (1) 4 2 years (2) 2 2 years
linear speed of the satellite depends on. (3) 4 years (4) 8 years
(1) m, mE and r (2) m, RE and r 93. A satellite of mass m revolves in a circular
(3) mE only (4) mE and r orbit of radius R a round a planet of mass M.
87. Near the earth's surface time period of a Its total energy E is :-
satellite is 1.4 hrs. Find its time period if it is
GMm GMm
at the distance '4R' from the centre of earth :- (1) − (2) +
2R 3R
 1 
(1) 32 hrs. (2)   hrs. GMm GMm
8 2 (3) − (4) +
R R
(3) 8 2 hrs. (4) 16 hrs.

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Gravitation
94. A satellite is orbiting earth at a distance r. 95. The mean distance of mars from sun is 1.5
Variations of its kinetic energy, potential times that of earth from sun. What is
energy and total energy, is shown in the approximately the number of years required
figure. Of the three curves shown in figure, by mars to make one revolution about sun ?
identify the type of mechanical energy they (1) 2.35 years (2) 1.85 years
represent. (3) 3.65 years (4) 2.75 years
Energy
1

0
r
2
3

(1) 1 Potential, 2 Kinetic, 3 Total

(2) 1 Total, 2 Kinetic, 3 Potential
(3) 1 Kinetic, 2 Total, 3 Potential
(4) 1 Potential, 2 Total, 3 Kinetic

EXERCISE-I (Conceptual Questions) ANSWER KEY

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Answer 3 1 4 4 1 3 2 2 4 4 1 3 2 4 4
Question 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Answer 2 3 3 4 3 3 2 4 3 2 1 1 1 2 1
Question 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Answer 1 2 2 3 1 4 3 1 3 1 2 1 2 4 1
Question 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Answer 4 4 4 4 1 4 1 1 2 2 1 1 2 3 3
Question 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Answer 2 1 3 2 1 3 1 3 4 3 1 1 4 3 2
Question 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
Answer 3 2 3 3 2 1 1 2 4 1 4 3 1 4 2
Question 91 92 93 94 95
Answer 3 2 1 3 2

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 NEET : Physics

Exercise - II (Previous Year Questions) AIPMT/NEET

AIPMT 2007 5. The dependence of acceleration due to
1. Two satellites of earth, S1 and S2, are gravity 'g' on the distance 'r' from the
moving in the same orbit. The mass of S1 centre of the earth, assumed to be a
is four times the mass of S2. Which one of sphere of radius R of uniform density, is
the following statements is true? as shown in figure below :-
(1) The kinetic energies of the two satellites g g
are equal
(2) The time period of S1 is four times that (a) (b)
of S2 r
R r
(3) The potential energies of earth and R
satellite in the two cases are equal g
(4) S1 and S2 are moving with the same speed g

AIPMT 2009 (c) (d)

2. The figure shows elliptical orbit of a r r
R
R
planet m about the sun S. The shaded area
SCD is twice the shaded area SAB. If t1 is The correct figure is :-
the time for the planet to move from C to (1) (a) (2) (b) (3) (c) (4) (d)
D and t2 is the time to move from A to B 6. The additional kinetic energy to be
then :- provided to a satellite of mass m
v revolving around a planet of mass M, to
m
transfer it from a circular orbit of radius
C
B R1 to another of radius R2(R2 > R1) is :-
S  1 1 
A D (1) GmM  − 
 R1 R2 
(1) t1 = t2 (2) t1 < t2  1 1 
(2) 2GmM  − 
(3) t1 = 4t2 (4) t1 = 2t2  R1 R2 
AIPMT 2010 1  1 1 
(3) GmM  − 
3. The radii of circular orbits of two satellites 2  R1 R2 
A and B of the earth are 4R and R,
 1 1 
respectively. If the speed of satellite A is (4) GmM  − 2
2
3V, then the speed of satellite B will be :-  R1 R2 
(1) 3V/2 (2) 3V/4 (3) 6V (4) 12V
4. A particle of mass M is situated at the AIPMT 2011
centre of a spherical shell of same mass 7. A planet moving along an elliptical orbit is
and radius a. The gravitational potential closest to the sun at a distance r1 and
a farthest away at a distance of r2. If v1 and
at a point situated at distance from the
2 v2 are the linear velocities at these points
centre, will be :- v
4GM 3GM respectively, then the ratio 1 is :-
(1) − (2) − v2
a a
(1) (r1/r2)2 (2) r2/r1
2GM GM
(3) − (4) − (3) (r2/r1)2 (4) r1/r2
a a
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Gravitation
AIPMT Pre. 2012 12. If ve is escape velocity and v0 is orbital
8. A spherical planet has a mass Mp and velocity of a satellite for orbit close to the
diameter Dp. A particle of mass m falling earth's surface, then these are related by :
freely near the surface of this planet will (1) v e = 2v0 (2) v e = 2v0
experience an acceleration due to gravity,
(3) v0 = 2v e (4) v0 = ve
equal to :-
(1) GMp/DP2 (2) 4GMpm/Dp2
AIPMT 2014
(3) 4GMp/Dp2 (4) GMpm/ Dp2
13. A black hole is an object whose
9. A geostationary satellite is orbiting the
gravitational field is so strong that even
earth at a height of 5R above that surface
light cannot escape from it. To what
of the earth, R being the radius of the
approximate radius would earth (mass =
earth. The time period of another satellite
5.98 × 1024 kg) have to be compressed to
in hours at a height of 2R from the surface
be a black hole ?
of the earth is :-
(1) 10–9 m (2) 10–6 m
(1) 6 2 (2) 6 2 (3) 5 (4) 10 (3) 10–2 m (4) 100 m
10. The height at which the weight of a body 14. Dependence of intensity of gravitational
becomes 1/16th of its weight on the field (E) of earth with distance (r) from
surface of earth (radius R), is :- centre of earth is correctly represented
(1) 3R (2) 4R by :-
(3) 5R (4) 15R E E
R
AIPMT Mains 2012 (1) O r (2) O R r
11. Which one of the following plots
represents the variation of gravitational E E
field on a particle with distance r due to a O
R
thin spherical shell of radius R? (r is (3) r (4) O R r
measured from the centre of the spherical
shell)
E AIPMT 2015
15. Kepler's third law states that square of
(1) period of revolution (T) of a planet
O R r
around the sun, is proportional to third
E
power of average distance r between sun
and planet i.e. T2 = Kr3 here K is constant.
(2) If the masses of sun and planet are M and
O r m respectively then as per Newton's law
R
of gravitation force of attraction between
E
GMm
them is F = , here G is gravitational
(3) r2
O R r
constant. The relation between G and K is
E described as :
(1) GMK = 42 (2) K = G
(4)

O r (3) K = (4) GK = 42
R G

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 NEET : Physics
Re-AIPMT 2015 NEET-II 2016
16. A satellite S is moving in an elliptical orbit 20. Starting from the centre of the earth
around the earth. The mass of the satellite having radius R, the variation of g
is very small compared to the mass of the (acceleration due to gravity) is shown by :-
earth. Then,
g g
(1) the acceleration of S is always directed
towards the centre of the earth. (1) (2)
(2) the angular momentum of S about the O R r O R r
centre of the earth changes in
g g
direction, but its magnitude remains
constant. (3) (4)
(3) the total mechanical energy of S varies O R r O R r
periodically with time. 21. A satellite of mass m is orbiting the earth
(4) the linear momentum of S remains (of radius R) at a height h from its surface.
constant in magnitude. The total energy of the satellite in terms
17. A remote - sensing satellite of earth revolves of g0, the value of acceleration due to
in a circular orbit at a height of 0.25 × 106 m gravity at the earth's surface, is:-
above the surface of earth. If earth's radius is 2mg0R 2 2mg 0R 2
6.38 × 106 m and g = 9.8 m/s2, then the (1) (2) −
R+h R+h
orbital speed of the satellite is :
mg 0R 2 mg 0R 2
(1) 6.67 km/s (3) (4) −
2(R + h) 2(R + h)
(2) 7.76 km/s
(3) 8.56 km/s
NEET(UG) 2017
(4) 9.13 km/s
22. The acceleration due to gravity at a height 1
NEET-I 2016 km above the earth is the same as at a depth d
18. At what height from the surface of earth below the surface of earth. Then :-
the gravitation potential and the value of 3
(1) d = 1 km (2) d = km
2
g are –5.4×107 J/kg and 6.0 m/s2
1
respectively ? (3) d = 2 km (4) d = km
2
Take the radius of earth as 6400 km :
(1) 2600 km (2) 1600 km 23. Two astronauts are floating in gravitational
(3) 1400 km (4) 2000 km free space after having lost contact with
19. The ratio of escape velocity at earth (ve) their spaceship. The two will :-
(1) Move towards each other.
to the escape velocity at a planet (vp)
whose radius and mean density are twice (2) Move away from each other.
as that of earth is :- (3) Will become stationary
(1) 1 : 2 (2) 1 : 2 2 (4) Keep floating at the same distance
between them.
(3) 1 : 4 (4) 1 : 2

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Gravitation
NEET(UG) 2018 29. Assuming that the gravitational potential
24. If the mass of the Sun were ten times smaller energy of an object at infinity is zero, the
and the universal gravitational constant change in potential energy (final – initial)
were ten time larger in magnitude, which of of an object of mass m, when taken to a
the following is not correct ? height h from the surface of earth (of
(1) Raindrops will fall faster radius R), is given by,
(2) Walking on the ground would become GMm GMmh
more difficult (1) − (2)
R+h R (R + h)
(3) Time period of a simple pendulum on
GMm
the Earth would decrease (3) mgh (4)
R+h
(4) 'g' on the Earth will not change
25. The kinetic energies of a planet in an
NEET (UG) 2020
elliptical orbit about the Sun, at positions A,
B and C are KA, KB and KC respectively. AC is 30. A body weighs 72 N on the surface of the
the major axis and SB is perpendicular to earth. What is the gravitational force on it,
AC at the position of the Sun S as shown in at a height equal to half the radius of the
the figure. Then earth?
B (1) 24 N (2) 48 N
(3) 32 N (4) 30 N
A C
S
NEET (UG) 2020 (Covid-19)
(1) KA < KB < KC (2) KA > KB > KC
31. What is the depth at which the value of
(3) KB < KA < KC (4) KB > KA > KC
acceleration due to gravity becomes 1/n
times the value that at the surface of
NEET(UG) 2019
earth? (radius of earth = R)
26. A body weighs 200 N on the surface of the
earth. How much will it weigh half way (1) R/n2 (2) R(n – 1)/n
down to the centre of the earth ? (3) Rn/(n – 1) (4) R/n
(1) 150 N (2) 200 N
(3) 250 N (4) 100 N NEET (UG) 2021
27. The work done to raise a mass m from the 32. The escape velocity from the Earth's
surface of the earth to a height h, which is surface is . The escape velocity from the
equal to the radius of the earth, is : surface of another planet having a radius,
(1) mgR (2) 2 mgR four times that of Earth and same mass
1 3 density is:
(3) mgR (4) mgR
2 2 (1)  (2) 2  (3) 3  (4) 4 
33. A particle of mass 'm' is projected with a
NEET(UG) 2019 (Odisha) velocity  = kVe (k < 1) from the surface of
28. The time period of a geostationary satellite
the earth. (Ve = escape velocity) The
is 24 h, which is at a height 6RE (RE is
maximum height above the surface
radius of earth) from surface of earth. The
reached by the particle is :
time period of another satellite whose 2 2
height is 2.5 RE from surface will be,  k   k 
(1) R   (2) R  
(1) 6 2 h (2) 12 2 h 1−k  1+k 
24 12 R2k Rk 2
(3) h (4) h (3) (4)
2.5 2.5 1+k 1 − k2
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 NEET : Physics
NEET (UG) 2022 Choose the correct answer from the
34. A body of mass 60g experiences a options given below :
gravitational force of 3.0 N, when placed at (1) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
a particular point. The magnitude of the (2) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
gravitational field intensity at that point is: (3) (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)
(1) 50 N/kg (2) 20 N/kg (4) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(3) 180 N/kg (4) 0.05 N/kg
35. Match List - I with List - II : RE-NEET (UG) 2022
36. In a gravitational field, the gravitational
List - I List – II K
(a) Gravitational (i) [L2T–2] potential is given by, V = − (J/kg). The
x
constant (G) gravitational field intensity at point
(b) Gravitational (ii) [M–1L3T–2] (2, 0, 3) m is:
potential K K
energy (1) + (2) −
2 2
(c) Gravitational (iii) [LT–2] K K
Potential (3) − (4) +
4 4
(d) Gravitational (iv) [ML2T–2]
intensity

EXERCISE-II (Previous Year Questions) ANSWER KEY

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Answer 4 4 3 2 4 3 2 3 1 1 4 2 3 1 1
Question 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Answer 1 2 1 2 4 4 3 4 4 2 4 3 1 2 3
Question 31 32 33 34 35 36
Answer 2 4 4 1 1 3

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Gravitation

Exercise - III (Analytical Questions) Master Your Understanding

1. Given below are two statements: One is (1) be approximately
labelled as Assertion (A) and the other is (2) not be true because the force between
labelled as Reason (R). earth & mercury is not inverse square
Assertion (A) : An artificial satellite is law
moving in a circular orbit of the earth. If (3) not be true because the major
the gravitational pull suddenly disappears, gravitational force on mercury is due
then it moves with the same speed to sun
tangential to the original orbit. (4) not be true because mercury is
Reason (R) : The orbital speed of a influenced by forces other than
satellite decreases with the increase in gravitational
radius of the orbit. 4. Choose the correct statement(s) from the
In the light of the above statements, following:-
choose the most appropriate answer (A) The magnitude of the gravitational
from the options given below: force between two bodies of mass 1 kg
(1) Both (A) and (R) are true and (R) is each and separated by a distance of
the correct explanation of (A). 1 m is 9.8 N.
(2) Both (A) and (R) are true and (R) is
(B) Higher the value of escape velocity for
NOT the correct explanation of (A).
a planet, higher is the abundance of
(3) (A) is true but (R) is false.
lighter gases in its atmosphere.
(4) (A) is false but (R) is true.
(C) Force of friction arises due to
2. Given below are two statements: One is
gravitational attraction.
labelled as Assertion (A) and the other is
(D) The gravitational force of attraction
labelled as Reason (R).
between two bodies of ordinary mass
Assertion (A) : Total energy is conserved
in moving a satellite to higher orbit. is not noticeable because the value of
Reason (R) : For a satellite change in the gravitational constant is extremely
potential energy and kinetic energy is small.
same in magnitude and opposite in (1) A, B (2) B, C, D (3) D (4) B, D
nature. 5. A satellite is moving round the earth in a
In the light of the above statements, circular orbit. The following statements
choose the most appropriate answer are given :-
from the options given below: (i) It is moving with a constant velocity.
(1) Both (A) and (R) are true and (R) is (ii) It has no acceleration.
the correct explanation of (A). (iii) It’s angular momentum w.r.t. centre
(2) Both (A) and (R) are true and (R) is of the earth remains conserved.
NOT the correct explanation of (A). (iv) Its distance from center must be
(3) (A) is true but (R) is false.
equal to times of earth's radius.
(4) Both (A) and (R) are false.
The correct option is :-
3. As observed from earth, the sun appears
(1) i & ii are true
to move in approximate circular orbit. For
(2) i, iii & iv are true
the motion of another planets like
(3) only iii is true
mercury as observed from the earth. This
(4) i & iv are true
would :-
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 NEET : Physics
6. Consider the following statement for a 8. Two concentric spherical shells of non-
satellite S moving in an elliptical orbit zero masses are as shown in the figure :-
around the earth (mass of satellite is B
negligibly small compared to earth) A D
I: The acc. of S is always towards earth.
C
II: The total mechanical energy of S
varies periodically with time.
III: The linear momentum of 'S' remain Column - I Column - II
constant in magnitude. (A) Potential at (P) Greater than
The correct sequence of true (T) and false A B
(F) for the above statement is :- (B) Gravitational (Q) Less than B
(1) TTF (2) TFT (3) TFF (4) FFF field at A
7. A satellite is in a circular equatorial orbit (C) As one (R) Potential
moves from remains
of radius 7000 km around the earth. If it is
C to D constant
transferred to a circular orbit of double of
(D) As one (S) Gravitational
radius :- moves from field
Column - I Column - II D to A decreases
(A) Angular (P) Increases (T) Data
momentum insufficient
(B) Area of earth (Q) Decreases (1) (A) → P; (B) → Q; (C) → R; (D) → S
covered by (2) (A) → Q; (B) → T; (C) → R; (D) → S
satellite (3) (A) → P; (B) → Q; (C) → S; (D) → R
signal (4) (A) → Q; (B) → P; (C) → S; (D) → R
(C) Potential (R) Becomes
energy double
(D) Kinetic (S) Becomes
energy half
(1) (A)→ Q; (B) → P; (C) → P, R; (D) → Q, S
(2) (A)→ P; (B) → P; (C) → P; (D) → Q, S
(3) (A)→ Q; (B) → Q; (C) → P, S; (D) → P, R
(4) (A)→ P; (B) → Q; (C) → P; (D) → P, R

EXERCISE-III (Analytical Questions) ANSWER KEY

Question 1 2 3 4 5 6 7 8
Answer 2 4 1 4 3 1 2 2

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