Dixit Physics

GRAVITATION NEET
NEET-UG - Physics
Time Allowed: 3 hours Maximum Marks: 240

1. The maximum vertical distance through which a full dressed astronaut can jump on the earth is 0.5 m. Estimate [4]
the maximum vertical distance through which he can jump on the moon, which has a mean density 2

3
rd that of
the earth and radius one quarter that of the earth.

a) 6m b) 7.5 m

c) 1.5m d) 3m
2. Different points in the earth are at slightly different distances from the sun and hence experience different forces [4]
due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion
is as if a net force acts on the c.m. (centre of mass) causing translation and net torque at the c.m. causing rotation
around an axis through the c.m. For the earth-sun system (approximating the earth as a uniform density sphere)

a) the torque is zero b) the torque causes the earth to spin

c) the rigid body result is not applicable since d) the torque causes the earth to move around
the earth is not even approximately a rigid the sun
body
3. The asteroid Toro has a radius of about 5.0 km. Assuming that the density of Toro is the same as that of the earth [4]
(5.5 g/cm3) find its total mass and find the acceleration due to gravity at its surface. Mass of the earth = 6.0 ×
1024 kg; radius of the earth = 6.4 × 106 m; G = 6.67 × 10−11 N m2 kg-2.

a) 2.7 × 1015 kg, 0.0077 m/s2 b) 3.1 × 1015 kg, 0.0077 m/s2

c) 2.5 × 1015 kg, 0.0077 m/s2 d) 2.9 × 1015 kg, 0.0077 m/s2

4. The period of a planet around sun is 27 times that of earth. The ratio of radius of planet's orbit to the radius of [4]
earth's orbit is:

a) 27 b) 4

c) 9 d) 64
5. If the radius of earth shrinks by one percent and its mass remaining the same, then acceleration due to gravity on [4]
the earth's surface will:

a) decrease b) either decrease or remain constant

c) remain constant d) increase

6. The values of the acceleration of free fall g on the surface of two planets are the same provided the planets have [4]
the same:

a) radius b) mass

2
(radius)

c) mass

radius
d) mass
[4]

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 7. A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this

planet will experience acceleration due to gravity, equal to:

GMp GMp m
a) 2
b) 2
D D
p p

4GMp 4GMp m
c) 2
d) 2
D D
p p

8. The percentage change in the acceleration of the Earth towards the Sun from a total eclipse of the Sun to the [4]
point where the moon is on a side of Earth directly opposite to the Sun is:
2 2
a) ( r1
)
Ms
× 100 b) Ms
(
r2
) × 100
r2 Mm Mm r1

2 Ms r2
c) 2( r1
)
Mm
× 100 d) r1
× 100
Min
r2 Ms

[4]
9.

Two hypothetical planets of masses m1 and m2 are at rest when they are an infinite distance apart. Because of
the gravitational force they move towards each other along the line joining their centres. What is their speed
when their separation is d?
(Speed of m1 is v1 and that of m2 is v2)
−−−−−−− −−−−−−− −−−−−−−
a) v 1 = m1 √
2G
v2 = m2 √
2G
b) v1 = m2 √
2G

d(m1 +m2 ) d(m1 +m2 ) d(m1 +m2 )

−−−−−−−
2G
v2 = m1 √
d(m1 +m2 )

−
−− −
−−
c) v1 = v2 d) v1 = m2 √
2G
v2 = m2 √
2G

m1 m2

10. Weightlessness experienced while orbiting the earth, in spaceships, is the result of: [4]

a) centre of gravity b) zero gravity

c) inertia d) acceleration
11. A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the [4]
satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is:
2 2

a) mg R
0
b) 2mg R
0

2(R + h) R + h

2 2

c) − mg R
0
d) −
2mg R
0

2(R + h) R + h

12. The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of [4]
earth. Then:

a) d = 1

2
km b) d = 1 km

c) d = 2 km d) d = 3

2
km
13. A satellite is in a circular orbit round the earth at an altitude R above the earth's surface, where R is the radius of [4]
the earth. If g is the acceleration due to gravity on the surface of the earth, the speed of the satellite is:
−
−− −−−
−
a) √ Rg
b) √2Rg
2

−
−− −
−−
c) √Rg d) √
Rg

14. If a body weighing 40 kg is taken inside the earth to a depth to 1

4
th radius of the earth, the weight of the body at [4]

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 that point is:

a) 40 kg-wt b) zero

c) 10 kg-wt d) 30 kg-wt
15. The linear velocity of the particle on the N-pole of the earth will be: [4]

a) Infinite b) 125 ms-1

c) Zero d) 486 km h-1

16. The Earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, [4]
then on the surface of the Earth, the acceleration due to gravity:

a) will be same everywhere in magnitude b) will be directed towards the centre but not
directed towards the centre the same everywhere

c) will have the same value everywhere but not d) cannot be zero at any point
directed towards the centre
am
17. If value of acceleration due to gravity at the surface of a sphere is am, then its value will be 3
at a distance... [4]
from the centre.
–
a) 2√3r b) r

–
c) r
d) √3r
√3

18. A spring balance is graduated on sea level. If a body is weighed with this balance at consecutively increasing [4]
heights from Earth’s surface, the weight indicated by the balance:

a) will go on decreasing continuously b) will go on increasing continuously

c) will first increase and then decrease d) will remain same

19. The gravitational potential at a distance r from the centre of the earth (r > R) is given by (consider, mass of the [4]
earth = Me, radius of the earth = R)

GMe −GMe
a) R
b) R

+GMe −GMe
c) r
d) r

20. Three particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational potential [4]
energy possessed by this system is
2 2

a) − 2Gm

L
b) +3Gm

2 2

c) −3Gm
d) −Gm

L L

21. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to [4]
transfer it from a circular orbit of radius R1 to another of radius R2(R2 > R1) is:

a) 2GmM ( 1
−
1
) b) GmM(
1
−
1
)
R1 R2 R1 R2

c) 1
GmM (
1
−
1
) d) 1 1
2 R1 R2 GmM( − )
2 2
R R
1 2

22. The change in the gravitational potential energy when a body of mass m is raised to a height nR above the [4]
surface of the earth is (here R is the radius of the earth)
mgR
a) nmgR b) n

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 c) ( n
) mgR d) (
n
) mgR
n − 1 n + 1

23. If V is the gravitational potential due to sphere of uniform density on it’s surface, then it’s value at the center of [4]
sphere will be:

a) 4

3
V b) V

c) 3 V
d) V

2
2

24. If g = acceleration due to gravity and V be gravitational potential at a distance r from the centre of the earth [4]
(where r > R), then what is the relation between g and V?
2

a) g = − b) g = −
d V dV

2 dr
dr

c) g = − V

2
d) g = V

r
r

25. Two concentric shells have masses M and m and their radii are R and r respectively, where R > r. What is the [4]
gravitational potential at their common centre, what is the gravitational intensity at a point for which x < r?

a) b)
Gm Gm

2 2
r x

c) GM

2
d) Zero
R

26. What is the ratio of potential energy to the kinetic energy of the moon orbiting around the earth? [4]

a) 1:2 b) 1:4

c) 4:1 d) 2:1
27. In a gravitational field, at a point where the gravitational potential is zero: [4]

a) the gravitational field is necessarily zero b) any value between Zero to One

c) any value between one and infinite d) the gravitational field is not necessarily zero
28. Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side a. The only forces [4]
acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while
maintaining their original separation 4a. The initial velocity that should be given to each particle and time period
of circular motion are respectively:
−−−− −−−− −−− −−−−
a) √ b)
3
3GM a GM 1 3GM
, 2π√ √ , √
a 3GM a 2π a
3

−−− −−−− −−− −−−−

c) √ d)
3 3
GM a GM a
, 2π√ √ , 2π√
a 3GM 3a 3GM

29. Two concentric shells of masses M1 and M2 are having radii r1 and r2. Which of the following is the correct [4]
expression for the gravitational field on a mass m?

GM2
a) F = b) F =
G(M1 +M2 )

2
, for r1 < r < r2 2
, for r < r1
r r

GM1
c) F = d) F =
G(M1 +M2 )

2
, for r < r2 2
, for r1 < r < r2
r r

30. In what manner, does the escape velocity of a particle depend upon its mass? [4]

a) m b)

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 m2

c) m-1 d) m0

31. For a satellite to be in a circular orbit 780 km above the surface of the earth, what is the period of the orbit (in [4]
hours)?

a) 1.98 hr b) 1.65 hr

c) 1.78 hr d) 1.88 hr
32. Which of the following quantities does not depend upon the orbital radius of the satellite? [4]
2

a) T

R
b) T

3
R

2 2

c) T

2
d) T

R R

33. Escape velocity from a planet is ve. If its mass is increased to 8 times and its radius is increased to 2 times, then [4]
the new escape velocity would be:
–
a) 2ve b) 2√2ve

–
c) ve d) √2ve

34. The orbital velocity of a satellite orbiting near the surface of the earth is given by [4]
−−− GMe
−
−−
a) v = √gR , where g =
e 2
b) v = √ gh
where g =
GMe

2
R Re R
e
e

−−− GMe −− GMe

c) v = √gRe , where g = 2
d) v = √gh where g = 2
R R
e e

35. A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s−1. If 20 percent of its initial energy [4]

is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of Mars before
returning to it? Mass of mars = 6.4 × 1023 kg; radius of mars = 3395 km; G = 6.67 × 10−11 N m2 kg-2.

a) 435 km b) 525 km

c) 495 km d) 465 km

36. A spaceship is fired from the Earth’s surface with an initial speed of 2.00 × 104 m/s. What will its speed be [4]

when it is very far from the Earth? (Neglect friction.)

a) 1.46 × 104 m/s b) 1.26 × 104 m/s

c) 1.66 × 104 m/s d) 1.06 × 104 m/s

37. Mass of moon is 1

81
time that of earth and its radius is 1

4
the earth's radius. If escape velocity at surface of earth [4]
is 11.2 km/s, then its value at surface of moon is:

a) 0.5 km/s b) 0.14 km/s

c) 2.5 km/s d) 5 km/s

38. The ratio of escape velocity at earth (ve) to the escape velocity at a planet (up) whose radius and mean density [4]
are twice as that of earth is:
–
a) 1 : 2√2 b) 1 : 4
–
c) 1 : √2 d) 1 : 2
39. The radius in kilometres to which the present radius of the earth (R = 6400 km) to be compressed so that the [4]

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 escape velocity is increased 10 times, is:

a) 640 b) 6.4

c) 64 d) 4800
40. The escape speed from the earth is about 11 km/s. The escape speed from a planet, having twice the radius and [4]
the same mean density as the earth, is:

a) 15.5 km/s b) 5.5 km/s

c) 22 km/s d) 11 km/s

41. How much energy will be necessary for making a body of 500 kg escape from the earth? (g = 9.8 m/s2, radius of [4]

the earth = 6.4 × 106 m).

a) About 3.1 × 1010 J b) About 9.8 × 106 J

c) About 6.4 × 108 J d) About 27.4 × 1012 J

42. A planet having mass 9 Me and radius 4 Re, where Me and Re are mass and radius of earth respectively, has [4]

escape velocity in km/s given by: (Given escape velocity on earth Ve= 11.2 × 103m/s)

a) 67.2 b) 16.8

c) 33.6 d) 11.2
43. A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 [4]
and mass of the earth is M, the angular momentum about the centre of the earth is:
−−−−−− −−−−−−
a) m√GM R 0 b) M √GM R0

−−− −−−
c) M √ GM
d) m√
GM

R0 R0

44. A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased [4]
by 1 %, the speed of the satellite will:

a) increase by 1% b) increase by 0.5%

c) decrease by 1% d) decrease by 0.5%

45. The escape velocity from the Earth's surface is V. The escape velocity from the surface of another planet having [4]
a radius, four times that of Earth and same mass density is:

a) 2 V b) 4 V

c) V d) 3 V
46. The radii of a planet and its satellite are 2r and r and their densities are ρ and 2ρ respectively. Their centres are [4]
separated by a distance d. The minimum speed with which a body should be projected from the mid point of the
line joining their centres so that the body escapes to infinity is (G-universal gravitational constant)
−−−−−− −−−−−−
a) 3
10Gπr ρ b) 3
10Gπr ρ
2 (√ ) 4 (√ )
d 3d

−−−−−− −−−−−−
c) d)
3
3 40Gπr p
10Gπr p
1 √
(√ ) 3d
4 3d

47. Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii r & 3r respectively. The [4]
ratio of orbital speeds of the satellites respectively is:

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 –
a) √3 : 1 b) 1 : 1

c) 9 : 1 d) 3 : 1
48. Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because, [4]

a) of viscous forces causing the speed of the b) the solar cells and batteries in satellites run
satellite and hence height to gradually out.
decrease.

c) of collisions with other satellites. d) the laws of gravitation predict a trajectory

spiralling inwards.
49. A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the [4]
radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the
surface of the earth is

a) R ( b)
gR R
− 1) 2gR
2
2V ( −1)
2
v

c) d) R (
R 2gR

gR
− 1)
2
( −1) V
2
2v

50. The total energy of a satellite is E. What is its P.E.? [4]

a) -E b) E

c) -2 E d) 2 E
51. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how [4]
many times greater than that of B from the sun?

a) 3 b) 4

c) 2 d) 5
52. The time period of a satellite is related to the density of earth (ρ ) as: [4]
1

a) ρ b) ρ 2

−1 −3

c) ρ 2
d) ρ 2

53. A small body is projected from the earth's surface vertically up with the escape velocity of the earth. Out of the [4]
following curves, the one that represents the variation of KE with altitude h is:

a) b)

c) d)

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54. A satellite is orbiting around the earth with total energy E. What will happen if the satellite’s kinetic energy is [4]
made 2 E?

a) Radius of the orbit is halved b) Period of revolution is doubled

c) Satellite escapes away d) Radius of the orbit is doubled

55. The figure shows a planet in an elliptical orbit around the sun S. Where is the kinetic energy of the planet [4]
maximum?

a) P4 b) P2

c) P3 d) P1

56. Figure shows a planet in an elliptical orbit around the sun S. Where is the kinetic energy of the planet [4]
maximum?

a) P3 b) P1

c) P2 d) P4

57. Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii 3 r and 4 r [4]
respectively around the earth. The ratio of total mechanical energy of A to B is:

a) 9 : 16 b) 1 : 1

c) 4 : 3 d) 16 : 9
58. A space-ship moves from the earth to the moon and back. The greatest energy required for the space-ship is to [4]
overcome the difficulty in:

a) take-off from the earth’s field b) entering the earth’s gravitational field

c) entering the moon’s lunar surface d) take-off from lunar surface

59. Two satellites are moving in the same circular orbit around the earth. They must have the same: [4]

a) angular momentum b) kinetic energy

c) speed d) mass
60. Choose the correct statement from the following. Weightlessness of an astronaut moving in a satellite is a [4]

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situation of:

a) no gravity b) zero

c) zero mass d) free fall

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