Gravitation JEE Main 2024 - 2019 PYQs

Chapter Priority: Priority A MathonGo

Q1. An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an
altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is
x
GM e m

21R e
. The value of x is (take R e = 6370 km) : 09 Apr 2024 (M)
(1) 10 (2) 12
(3) 9 (4) 11
4

Q2. A satellite of 10 3
kg mass is revolving in circular orbit of radius 2R. If 10 R

6
J energy is supplied to the satellite,
it would revolve in a new circular orbit of radius
(use g = 10 m/s 2
,R = radius of earth) 09 Apr 2024 (E)
(1) 2.5R (2) 3R
(3) 4R (4) 6R

Q3. Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A
is 3v, the speed of B will be : 08 Apr 2024 (E)
(1) 3v (2) 6v
(3) 4

3
v (4) 12v

Q4. Two planets A and B having masses m and m move around the sun in circular orbits of r and r radii
1 2 1 2

respectively. If angular momentum of A is L and that of B is 3 L, the ratio of time period ( TA

TB
) is:
08 Apr 2024 (M)
3

(1) (2)
3
2 1 m2
r2
( ) ( )
27 m1
r1

(3) 27( (4) (

3 3
m1 r1
) )
m2 r2

Q5. Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How
much it would weigh at R/4 depth under surface of earth ? 06 Apr 2024 (E)
(1) 75 N (2) 300 N
(3) 375 N (4) 225 N

Q6. To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of
earth is R E, g = acceleration due to gravity on the surface of earth): 06 Apr 2024 (M)
(1) 2mgR E (2) 4mgR E

(3) mgR E (4) 1/2mgR E

Q7. A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth
the mass of earth. The radius orbit of planet is :
( Given = Radius of geo-stationary orbit for earth is 4.2 × 10 4
km ) 05 Apr 2024 (E)
(1) 1.4 × 10 4
km (2) 1.05 × 10 4
km

(3) 8.4 × 10 4
km (4) 1.68 × 10 5
km

Q8. In hydrogen like system the ratio of coulombic force and gravitational force between an electron and a proton is
in the order of : 05 Apr 2024 (M)
(1) 10 39
(2) 10 29

(3) 10 19
(4) 10 36

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

Q9. A simple pendulum doing small oscillations at a place R height above earth surface has time period of T 1 = 4 s .
T2 would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the
correct relation [R = radius of earth ] : 05 Apr 2024 (M)
(1) 2 T 1 = T2 (2) 2 T 1 = 3 T2

(3) T 1 = T2 (4) 3 T 1 = 2 T2

Q10. Match List I with List II :

05 Apr 2024 (M)

(1) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (2) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(3) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (4) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Q11. A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a
particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is :
04 Apr 2024 (M)
(1) (2)
2
GmMπ GMmπ
2 2
L 2 L

(3) 0 (4) 2GmMπ

L
2

Q12. A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of :
( R = Radius of earth, g = 10 m s
−2
) 04 Apr 2024 (E)
(1) 100 N (2) 300 N
(3) 225 N (4) 120 N

Q13. Correct formula for height of a satellite from earths surface is: 04 Apr 2024 (E)
(1) ( T
2
R
2

)
1/3

− R
(2) ( T
2
R g
2

)
1/3

− R
2 2
4π g 4π

(3) ( (4) (
2 2
−1/3 2 2
1/2
T R g T R g
2
) + R ) − R
4π 4π

Q14. If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π 2
m s
−2
, then
the length of the second's pendulum at a height h = 2R from the surface of earth will be: 01 Feb 2024 (M)
(1) 2

9
m (2) 1

9
m

(3) 4

9
m (4) 8

9
m

Q15. A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T . If
the force of attraction between planet and star is proportional to R −3/2
then choose the correct option :
01 Feb 2024 (E)

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

(1) T 2
∝ R
5/2
(2) T 2
∝ R
7/2

(3) T 2
∝ R
3/2
(4) T 2
∝ R
3

Q16. Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on
2

one of the masses by the other masses is ( 2√ 2+1

32
)
Gm

L
2
, the length of the sides of the square is
31 Jan 2024 (M)
(1) L

2
(2) 4L
(3) 3L (4) 2L

Q17. The mass of the moon is 1

144
times the mass of a planet and its diameter 1

16
times the diameter of a planet. If
the escape velocity on the planet is v, the escape velocity on the moon will be: 31 Jan 2024 (E)
(1) v

3
(2) v

(3) v

12
(4) v

Q18. The gravitational potential at a point above the surface of earth is −5. 12 × 10 7
J kg
−1
and the acceleration
due to gravity at that point is 6. 4 m s . Assume that the mean radius of earth to be 6400
−2
km . The height of
this point above the earth's surface is: 30 Jan 2024 (M)
(1) 1600 km (2) 540 km

(3) 1200 km (4) 1000 km

Q19. Escape velocity of a body from earth is 11. 2 km s

−1
. If the radius of a planet be one-third the radius of earth
and mass be one-sixth that of earth, the escape velocity from the plate is: 30 Jan 2024 (E)
(1) 11. 2 km s
−1
(2) 8. 4 km s
−1

(3) 4. 2 km s
−1
(4) 7. 9 km s
−1

Q20. At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth
as R)
29 Jan 2024 (M)
(1) √5R − R (2) √ 3R−R

(3) R

2
(4) √ 5R−R

Q21. A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is
reduced to one fourth of the original distance, how many days will it take to complete one revolution?
29 Jan 2024 (E)
(1) 25 (2) 50
(3) 100 (4) 20

Q22. The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its
original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
27 Jan 2024 (M)
(1) g

4
(2) 2g
(3) g

2
(4) 4g

Q23. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

earth in its orbit about the sun.

Reason (R): The moon takes less time to move around the earth than the time taken by the earth to move
around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :
27 Jan 2024 (E)
(1) (A) is correct but (R) is not correct
(2) Both (A) and (R) are correct and (R) is the correct explanation of A.
(3) Both (A) and (R) are correct but (R) is not the correct explanation of A.
(4) (A) is not correct but (R) is correct

Q24. Two identical particles each of mass m go round a circle of radius a under the action of their mutual
gravitational attraction. The angular speed of each particle will be : 15 Apr 2023 (M)
(1) √ Gm
3
(2) √ Gm
3
a 8a

(3) √ Gm
3
(4) √ Gm
3
4a 2a

Q25. A planet having mass 9 Me and radius 4R e , where Me and Re are mass and radius of earth respectively, has
escape velocity in km s
−1
given by: (Given escape velocity on earth V e
= 11. 2 × 10
3
m s
−1
)
13 Apr 2023 (M)
(1) 67. 2 (2) 16. 8
(3) 11. 2 (4) 33. 6

Q26. Given below are two statements:

Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the
planet also increase.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below
13 Apr 2023 (E)
(1) Statement I is incorrect but Statement II is correct
(2) Statement I is correct but statement II is incorrect
(3) Both Statement I and Statement II are incorrect
(4) Both Statement I and Statement II are correct

Q27. Two planets A and B of radii R and 1. 5 R have densities ρ and ρ

2
respectively. The ratio of acceleration due to
gravity at the surface of B to A is: 13 Apr 2023 (E)
(1) 2 : 3 (2) 2 : 1

(3) 3 : 4 (4) 4 : 3

Q28. Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The
quantity which is same for the two satellites will be 12 Apr 2023 (M)
(1) Speed (2) Kinetic energy
(3) Total energy (4) Potential energy

Q29. The ratio of escape velocity of a planet to the escape velocity of earth will be:-
Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

12 Apr 2023 (M)

(1) 4 : 1 (2) 1 : 4

(3) 1 : √2 (4) 2 : 1

Q30. The radii of two planets A and B are R and 4R and their densities are ρ and respectively. The ratio of
ρ

acceleration due to gravity at their surfaces (g A : gB ) will be

11 Apr 2023 (M)
(1) 4 : 3 (2) 1 : 16
(3) 3 : 16 (4) 3 : 4

Q31. A space ship of mass 2 × 10 4

kg is launched into a circular orbit close to the earth surface. The additional
velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if
g = 10 m s
−2
and radius of earth = 6400 km ): 11 Apr 2023 (E)
(1) 11. 2(√2 − 1) km s
−1
(2) 8(√2 − 1) km s
−1

(3) 7. 9(√2 − 1) km s
−1
(4) 7. 4(√2 − 1) km s
−1

Q32. The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given
g = π
2
m s
−2
,R = radius of earth) 10 Apr 2023 (E)
(1) √2R (2) √8R
(3) √32R (4) √4R

Q33. Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d = R

2
from the
surface of earth, if its weight on the surface of earth is 200 N, will be : (Given R = radius of earth)
10 Apr 2023 (M)
(1) 300 N (2) 100 N
(3) 400 N (4) 500 N

Q34. Given below are two statements:

Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
Statement II : The effect of rotation of the earth on the value of g at the equator is minimum and that at the
pole is maximum.
In the light of the above statements, choose the correct answer from the options given below
10 Apr 2023 (E)
(1) Statement I is false but statement II is true (2) Both Statement I and Statement II are true
(3) Both Statement I and Statement II are false (4) Statement I is true but statement II is false

Q35. Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii r & 3r respectively. The
ratio of orbital speeds of the satellites respectively is 10 Apr 2023 (M)
(1) √3 : 1 (2) 3 : 1
(3) 9 : 1 (4) 1 : 1

Q36. If the earth suddenly shrinks to 1

64
th of its original volume with its mass remaining the same, the period of
rotation of earth becomes 24

x
h . The value of x is ________ 10 Apr 2023 (M)

Q37. The acceleration due to gravity at height h above the earth if h ≪ R (Radius of earth) is given by

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

08 Apr 2023 (E)

(1) g (2) g
2
h ′ h
′
= g(1 − ) = g(1 − )
2 2R
2R

(3) g (4) g
2
′ 2h ′ 2h
= g(1 − ) = g(1 − )
R R
2

Q38. Given below are two statements:

Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be
E

2
.
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total
energy E.
In the light of the above statements, choose the most appropriate answer from the options given below.
08 Apr 2023 (M)
(1) Statement I is correct but Statement II is incorrect
(2) Statement I is incorrect but Statement II is correct
(3) Both Statement I and Statement II are correct
(4) Both Statement I and Statement II are incorrect

Q39. The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius
of the earth will be: 08 Apr 2023 (M)
(1) 200 N (2) Zero
(3) 100 N (4) 300 N

Q40. The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth
surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the
new angular momentum will be 08 Apr 2023 (E)
(1) 8 L (2) 9 L
(3) 4 L (4) 3 L

Q41. A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing
W on earth will weigh on that planet:
06 Apr 2023 (M)
(1) 2 (2) 2
1 1

4
W 3
W
2

(3) 2W (4) 2 3
W

Q42. The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height,
from the surface of earth, equal to one-fourth the radius of the earth is: 06 Apr 2023 (E)
(1) 64 N (2) 25 N
(3) 50 N (4) 100 N

Q43. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Earth has atmosphere whereas moon doesn’t have any atmosphere.
Reason R: The escape velocity on moon is very small as compared to that on earth.
In the light of the above statements, choose the correct answer from the options given below:
06 Apr 2023 (M)

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

(1) Both A and R are correct but R is NOT the correct explanation of A
(2) A is false but R is true
(3) Both A and R are correct and R is the correct explanation of A
(4) A is true but R is false

Q44. Choose the incorrect statement from the following: 06 Apr 2023 (E)

(1) The speed of satellite in a given circular orbit remains constant

(2) For a planet revolving around the sun in an elliptical orbit, the total energy of the planet remains constant
(3) The linear speed of a planet revolving around the sun remains constant
(4) When a body falls towards earth, the displacement of earth towards the body is negligible
Q45. Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below
01 Feb 2023 (M)
(1) Both Statement I and Statement II are true (2) Both Statement I and Statement II are false
(3) Statement I is true but Statement II is false (4) Statement I is false but Statement II is true

Q46. For a body projected at an angle with the horizontal from the ground, choose the correct statement
01 Feb 2023 (E)
(1) Gravitational potential energy is maximum at the highest point.
(2) The horizontal component of velocity is zero at highest point.
(3) The vertical component of momentum is maximum at the highest point.
(4) The kinetic energy (K.E.) is zero at the highest point of projectile motion.

Q47. The escape velocities of two planets A and B are in the ratio 1 : 2 . If the ratio of their radii respectively is
1 : 3 , then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will
be: 01 Feb 2023 (E)
(1) 4

3
(2) 3

(3) 2

3
(4) 3

Q48. If earth has a mass nine times and radius twice to the of a planet P . Then ve

3
√xms
−1
will be the minimum
velocity required by a rocket to pull out of gravitational force of P , where ve is escape velocity on earth. The
value of x is 01 Feb 2023 (M)
(1) 2 (2) 3
(3) 18 (4) 1

Q49. At a certain depth d below surface of earth, value of acceleration due to gravity becomes four times that of its
value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400 km ). The depth d is
equal to 31 Jan 2023 (M)
(1) 5260 km (2) 640 km

(3) 2560 km (4) 4800 km

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

Q50. A body weight W , is projected vertically upwards from earth's surface to reach a height above the earth which
is equal to nine times the radius of earth. The weight of the body at that height will be: 31 Jan 2023 (E)
(1) W

91
(2) W

100

(3) W

9
(4) W

Q51. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it
strikes the earth’s surface, ignoring air resistance, will be : 30 Jan 2023 (E)
(1) 2√gR (2) √gR
(3) √ gR (4) √2gR
2

Q52. If the gravitational field in the space is given as (− K

r
2
). Taking the reference point to be at r = 2 cm with
gravitational potential V = 10 J kg
−1
. Find the gravitational potentials at r = 3 cm in SI unit (Given, that
K = 6 J cm kg
−1
) 30 Jan 2023 (M)
(1) 9 (2) 11
(3) 12 (4) 10

Q53. The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is
decreased to one fourth of the previous value, then its new time period will become. 29 Jan 2023 (E)
(1) 4 hours (2) 6 hours
(3) 12 hours (4) 3 hours

Q54. Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational
attraction. The speed of each particle will be : 29 Jan 2023 (M)
(1) √ Gm (2) √ 4Gm

2r r

(3) √ Gm (4) √ Gm

r 4r

Q55. Every planet revolves around the sun in an elliptical orbit :

A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major
axis of elliptical orbit.
Choose the correct answer from the options given below :
25 Jan 2023 (E)
(1) A and D only (2) C and D only
(3) B and C only (4) A and C only

Q56. T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a
height R (equal to earth's radius) above the earth's surface. Then, the value of x will be: 25 Jan 2023 (M)
(1) 4 (2) 2
(3) 1

2
(4) 1

Q57. A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R ), the increasee

in potential energy will be : (g = acceleration due to gravity on the surface of earth) 25 Jan 2023 (E)

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Gravitation JEE Main 2024 - 2019 PYQs
Chapter Priority: Priority A MathonGo

(1) 3mgR e (2) 1

3
mgR e

(3) 2

3
mgR e (4) 1

2
mgR e

Q58. Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the
earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass
of the particle is 100 g . The time period of the motion of the particle will be (approximately) (take
g = 10 ms
−2
, radius of earth = 6400 )
km

25 Jan 2023 (M)

(1) 24 hours (2) 1 hour 24 minutes
(3) 1 hour 40 minutes (4) 12 hours

Q59. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above
the earth's surface is (given, radius of earth R e
= 6400 km ) 24 Jan 2023 (M)
(1) 9. 8 N (2) 4. 9 N
(3) 19. 6 N (4) 8 N

Q60. Given below are two statements:

Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if
h = d.
In the light of above statements, choose the most appropriate answer form the options given below
24 Jan 2023 (E)
(1) Statement I is incorrect but statement II is correct
(2) Both Statement I and Statement II are incorrect
(3) Statement I is correct but statement II is incorrect
(4) Both Statement I and II are correct

Q61. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A pendulum clock when taken to Mount Everest becomes fast.
Reason R: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of
earth.
In the light of the above statements, choose the most appropriate answer from the options given below
24 Jan 2023 (E)
(1) Both A and R are correct and R is the correct explanation of A
(2) Both A and R are correct but R is not the correct explanation of A
(3) A is correct but R is not correct
(4) A is not correct but R is correct

Q62. If the distance of the earth from Sun is 1. 5 × 10 6

, then the distance of an imaginary planet from Sun, if its
km

period of revolution is 2. 83 years is: 24 Jan 2023 (E)

(1) 6 × 10
7
km (2) 6 × 10
6
km

(3) 3 × 10
6
km (4) 3 × 10
7
km

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Q63. If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same
as that of the acceleration due to gravity at a depth αh(h ≪ R e ) ) from the earth surface. The value of α will
be _____. (use R e = 6400 km )
29 Jul 2022 (M)

Q64. An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of
earth. The gain in potential energy of the object will be
[If, g = 10 m s −2
and radius of earth = 6400 km ] 29 Jul 2022 (E)
(1) 48 MJ (2) 24 MJ
(3) 36 MJ (4) 12 MJ

Q65. Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a
space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4 s and
6 s respectively. Then the value of h is -
(consider radius of earth R E = 6400 km and g on earth 10 m s ) −2
28 Jul 2022 (E)
(1) 1200 km (2) 1600 km

(3) 3200 km (4) 4800 km

Q66. If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's
surface will approximately 28 Jul 2022 (M)
(1) decrease by 2% (2) decrease by 4%
(3) increase by 2% (4) increase by 4%

Q67. A body of mass m is projected with velocity λv in vertically upward direction from the surface of the earth
e

into space. It is given that v is escape velocity and λ < 1. If air resistance is considered to the negligible, then
e

the maximum height from the centre of earth, to which the body can go, will be (R : radius of earth)
27 Jul 2022 (E)
(1) R

1+λ
2
(2) R

1−λ
2

(3) R

1−λ
(4) λ R

1−λ
2

Q68. Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii 3r and 4r
respectively around the earth. The ratio of total mechanical energy of A to B is 27 Jul 2022 (M)
(1) 9 : 16 (2) 16 : 9
(3) 1 : 1 (4) 4 : 3

Q69. The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth
will, be
(Radius of earth = 6400 km ) 26 Jul 2022 (M)
(1) 1% (2) 3%
(3) 4% (4) 0. 5%

Q70. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape
velocity. The maximum height attained by the body will be
(Take radius of earth = 6400 km and g = 10 ms
−2
) 26 Jul 2022 (E)

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Gravitation JEE Main 2024 - 2019 PYQs
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(1) 800 km (2) 1600 km

(3) 2133 km (4) 4800 km

Q71. Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m .
The gravitational force on a fourth particle P of the same mass is F , when placed at a distance 13 m from the
particle B on the perpendicular bisector of the line AC . The value of F will be approximately 25 Jul 2022 (M)
(1) 21G (2) 100G
(3) 59G (4) 42G

Q72. The length of a seconds pendulum at a height h = 2R from earth surface will be:
(Given: R = Radius of earth and acceleration due to gravity at the surface of earth g = π 2
m s
−2
)
25 Jul 2022 (E)
(1) 2

9
m (2) 4

9
m

(3) 8

9
m (4) 1

9
m

Q73. An object is taken to a height above the surface of earth at a distance 5

4
R from the centre of the earth. Where
radius of earth, R = 6400 km . The percentage decrease in the weight of the object will be 25 Jul 2022 (E)
(1) 36% (2) 50%
(3) 64% (4) 25%

Q74. The escape velocity of a body on a planet A is 12 km s

−1
. The escape velocity of the body on another planet
B , whose density is four times and radius is half of the planet A, is 29 Jun 2022 (M)
(1) 12 km s
−1
(2) 24 km s
−1

(3) 36 km s
−1
(4) 6 km s
−1

Q75. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is
increased to three times its previous value, then approximate new time period of the satellite will be
29 Jun 2022 (E)
(1) 36 hours (2) 40 hours

(3) 30 hours (4) 25 hours

Q76. Two objects of equal masses placed at certain distance from each other attracts each other with a force of F . If
one-third mass of one object is transferred to the other object, then the new force will be 28 Jun 2022 (E)
(1) 2

9
F (2) 16

9
F

(3) 8

9
F (4) F

Q77. Two planets A and B of equal mass are having their period of revolutions T and T such that T A B A = 2T B .
These planets are revolving in the circular orbits of radii r and r respectively. Which out of the following
A B

would be the correct relationship of their orbits? 28 Jun 2022 (M)

(1) 2r 2
A
= r
3
B
(2) r 3

A
= 2r
3
B
2

(3) r 3

A
= 4r
3
B
(4) T 2
A
− T
2
B
=
π

GM
(r
3
B
− 4r
3

A
)

Q78. Statement I: The law of gravitation holds good for any pair of bodies in the universe.
Statement II: The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.

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27 Jun 2022 (M)

(1) Statement 1 and statement 2 both are true. (2) Statement 1 is true and statement 2 is false.
(3) Statement 1 and statement 2 both are false. (4) Statement 1 is false and statement 2 is true.

Q79. Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass
M is situated at the centre of square. The total gravitational potential energy of the system is

27 Jun 2022 (E)

(1) − Gm

d
[(4 + √ 2)m + 4√ 2M ] (2) − Gm

d
[(4 + √ 2)M + 4√ 2m]

(3) − Gm

d
[3m
2
+ 4√ 2M ] (4) − Gm

d
[6m
2
+ 4√ 2M ]

Q80. The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly
represented by (Given R = radius of earth)
26 Jun 2022 (M)
(1) (2)

(3) (4)

Q81. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always
points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below
26 Jun 2022 (E)
(1) Assertion and reason both are correct and reason is correct explanation of assertion.
(2) Assertion and reason both are correct but reason is not correct explanation of assertion.
(3) Assertion is true but reason is false
(4) Assertion is false but reason is true

Q82. The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration
due to gravity at point P will be : (Given g =acceleration due to gravity at the surface of earth).
25 Jun 2022 (M)
(1) g

2
(2) g

(3) g

3
(4) g

Q83. Two satellites S and S are revolving in circular orbits around a planet with radius R
1 2 I = 3200 km and
R 2 = 800 km respectively. The ratio of speed of satellite S to the speed of satellite S in their respective
1 2

orbits would be 1

x
where x = 25 Jun 2022 (E)

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Q84. The approximate height from the surface of earth at which the weight of the body becomes 1

3
of its weight on
the surface of earth is :
[Radius of earth R = 6400 km and √3 = 1. 732] 24 Jun 2022 (M)
(1) 3840 km (2) 4685 km

(3) 2133 km (4) 4267 km

Q85. The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes
3R will be : 24 Jun 2022 (E)
(1) √3 yr (2) 3√3 yr

(3) 3 yr (4) 9 yr

Q86. Four particles each of mass M, move along a circle of radius R under the action of their
mutual gravitational attraction as shown in figure. The speed of each particle is:

01 Sep 2021 (E)

(1) 1 GM
(2) 1 GM
√ (2√ 2 + 1) 2 √
2 R R(2√ 2+1)

(3) 1
√
GM (4) √ GM

(2√ 2 − 1) R
2 R

Q87. Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of
revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 × 10 3
km. The
angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites
are closest is π

x
rad h
−1
, where x is _______. 01 Sep 2021 (E)

Q88. The masses and radii of the earth and moon are (M 1, R1 ) and (M 2, R2 ) respectively. Their centres are at a
distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle
of these two masses : 31 Aug 2021 (M)
(1) v = √
4G(M 1 +M 2 )
(2) v =
1
√
2G(M 1 +M 2 )

e r e 2 r

(3) v =
1
√
4G(M 1 +M 2 ) (4) v e =
√ 2G(M +M )
1 2

e r
2 r

Q89. If R be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a
E

height r above the earth surface is: (Given: r < R ) E 31 Aug 2021 (E)
2 3 2 3

(1) 1 + r

RE
−
r

R
2
−
r

R
3
(2) 1 + r

RE
+
r

R
2
+
R
r
3
E E E E

(3) 1 − (4) 1 +
2 3 2 3
r r r r r r
− 2
− 3
− 2
+ 3
RE R R RE R R
E E E E

Q90. A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the
gravitational potential at a point, 25 m from the center is V kg m
−1
. The value of V is: 27 Aug 2021 (E)
(1) +2G (2) −20G
(3) −4G (4) −60G

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Q91. A body of mass (2M ) splits into four masses {m, M − m, m, M − m}, which are rearranged
to form a square as shown in the figure. The ratio of M

m
for which, the gravitational potential
energy of the system becomes maximum is x : 1. The value of x is ________.

27 Aug 2021 (M)

Q92. Inside a uniform spherical shell:

(a) The gravitational field is zero. (b) The gravitational potential is zero. (c) The gravitational field is the
same everywhere. (d) The gravitation potential is the same everywhere. (e) All the above.
Choose the most appropriate answer from the options given below:
26 Aug 2021 (M)
(1) (a), (c) and (d) only (2) (a), (b) and (c) only
(3) (b), (c) and (d) only (4) (e) only

Q93. Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual
gravitational attraction. The angular speed of each particle is: 27 Jul 2021 (E)
(1) √ G
3
(2) 1
√
G
3
2R 2 R

(3) 1
√
1 (4) √ 2G
3
2R G R

Q94. The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of
9. 0 × 10
3
km. Find the mass of Mars.
27 Jul 2021 (E)
2

{ Given 4π

G
= 6 × 10
11
N
−1
m
−2 2
kg }

(1) 5. 96 × 10 19
kg (2) 3. 25 × 10 21
kg

(3) 7. 02 × 10 25
kg (4) 6. 00 × 10 23
kg

Q95. Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M

respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass
m is projected from the surface of the planet of mass M directly towards the centre of the
second planet. The minimum speed v required for the satellite to reach the surface of the
second planet is √
a

7
GM

R
, then the value of a is [Given: The two planets are fixed in their
position]
27 Jul 2021 (M)

Q96. Consider a planet in some solar system that has a mass double the mass of earth and density equal to the
average density of the earth. If the weight of an object on earth is W , the weight of the same object on that
planet will be: 25 Jul 2021 (E)
(1) 2W (2) W
(3) 2 (4) √2 W
1

3
W

Q97. A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to
infinity. The time taken by it to reach height h is S.

22 Jul 2021 (M)

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Gravitation JEE Main 2024 - 2019 PYQs
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3 3

(1) √ Re h
2
(2) √ 2R e h
2

[(1 + ) − 1] [(1 + ) − 1]
2 g Re g Re

3 3

(3) 1
√
Re h
2
(4) 1
√
2R c h
2

[(1 + ) − 1] [(1 + ) − 1]
3 2 g Rc 3 g Re

Q98. A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all
other objects in sky and take acceleration due to gravity on the surface of the Earth
and Mars as 10 m s
−2
and 4 m s
−2
, respectively. Identify from the below figures, the
curve that fits best for the weight of the passenger as a function of time.

20 Jul 2021 (M)

(1) (c) (2) (a)
(3) (d) (4) (b)

Q99. Consider a binary star system of star A and star B with masses m and m revolving in a circular orbit of A B

radii r and r
A B, respectively. If T and T are the time period of star A and star B, respectively, then:
A B

20 Jul 2021 (E)

3

(1) TA rA 2
(2) T A = TB
= ( )
TB rB

(3) T A > TB (if m A > mB ) (4) T A > TB (if r A > rB )

Q100. A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a
circular orbit of radius 1. 02 R. The percentage difference in the time periods of the two satellites is:
20 Jul 2021 (E)
(1) 1. 5 (2) 2. 0
(3) 0. 7 (4) 3. 0

Q101. The time period of a satellite in a circular orbit of the radius R is T . The period of another satellite in a
circular orbit of the radius 9R is: 18 Mar 2021 (M)
(1) 9T (2) 27T
(3) 12T (4) 3T

Q102. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is →
L. The

magnitude of the areal velocity of the planet is : 18 Mar 2021 (E)

(1) 4L

M
(2) M
L

(3) 2L

M
(4) 2M
L

Q103. The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the
escape velocity is increased 10 time is _______. 17 Mar 2021 (M)

Q104. A geostationary satellite is orbiting around an arbitrary planet P at a height of 11R above the surface of P , R
being the radius of P . The time period of another satellite in hours at a height of 2R from the surface of P is
________ has the time period of 24 hours. 17 Mar 2021 (E)
(1) 6√2 (2) √2
6

(3) 3 (4) 5

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Q105. If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of
2

energy that needs to be supplied will be where x is _____. (Round off to the Nearest Integer) (M is
x

5
GM

the mass of earth, R is the radius of earth, G is the gravitational constant)

16 Mar 2021 (E)

Q106. Find the gravitational force of attraction between the ring and sphere as shown in the
diagram, where the plane of the ring is perpendicular to the line joining the centres. If
√ 8R is the distance between the centres of a ring (of mass m ) and a sphere (mass M )
where both have equal radius R
26 Feb 2021 (M)
(1) 2√ 2

3
GM m
2
(2) √8

9
GmM

R
R

(3) 1 GM m

R
2
(4) √8

27
GmM
2
3√ 8 R

Q107. In the reported figure of earth, the value of acceleration due to gravity is same at point A and C
but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB

will be x : 5. The value of x is

26 Feb 2021 (E)

Q108. A planet revolving in elliptical orbit has:

A. a constant velocity of revolution. B. has the least velocity when it is nearest to the sun. C. its areal
velocity is directly proportional to its velocity. D. areal velocity is inversely proportional to its velocity. E. to
follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
26 Feb 2021 (M)
(1) A only (2) C only
(3) E only (4) D only

Q109. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.
Reason R: The product of their mass and radius must be same. M1 R1 = M2 R2 In the light of the above
statements, choose the most appropriate answer from the options given below :
25 Feb 2021 (M)
(1) Both A and R are correct and R is the correct explanation of A
(2) Both A and R are correct but R is NOT the correct explanation of A
(3) A is not correct but R is correct
(4) A is correct but R is not correct

Q110. A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre
with a force F1 . Now a spherical cavity of radius (
R

2
) is made in the sphere (as shown
in figure) and the force becomes F . The value of F
2 1 : F2 is:

25 Feb 2021 (M)

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(1) 41 : 50 (2) 50 : 41
(3) 25 : 36 (4) 36 : 25

Q111. The initial velocity v required to project a body vertically upward from the surface of the earth to reach a
i

height of 10R, where R is the radius of the earth, may be described in terms of escape velocity v such that e

vi = √
x

y
× ve . The value of x will be 25 Feb 2021 (E)

Q112. AB200 kg400 kg600 km1600 kmT A T B ABT B − T A = 6400 km,= 6 × 10

24
kg

25 Feb 2021 (M)

(1) 4. 24 × 10 3
s (2) 3. 33 × 10 2
s (3) 1. 33 × 10 3
s (4) 4. 24 × 10 2
s

Q113. Consider two satellites S and S with periods of revolution 1 hr and 8 hr respectively revolving around a
1 2

planet in circular orbits. The ratio of angular velocity of satellite S to the angular velocity of satellite S is:
1 2

24 Feb 2021 (M)

(1) 8 : 1 (2) 2 : 1
(3) 1 : 4 (4) 1 : 8

Q114. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m
under the action of their own mutual gravitational attraction. The speed of each particle will be:
24 Feb 2021 (M)
(1) (2) G
√ G(1 + 2√ 2) √ (1 + 2√ 2)
2

(3) √ G (4) √ (1+2√ 2)G

(2√ 2 − 1)
2
2

Q115. A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same
weighing machine, if it is shifted to the equator?
[Use g = GM

R
2
= 9. 8 m s
−2
and radius of earth, R = 6400 km. ]
24 Feb 2021 (E)
(1) 49. 17 N (2) 48. 83 N
(3) 49. 83 N (4) 49 N

Q116. Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The
period of revolution is 24 Feb 2021 (M)
(1) 2π√ d
3
(2) 2π√ 3Gm
3
3Gm d

(3) 1
√
3Gm
3
(4) 1
√
d
3

2π d 2π 3Gm

Q117. Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the
centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the
smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller
planet, the minimum firing speed needed is : 06 Sep 2020 (E)

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(1) 2√ GM (2) 4√ GM

a a

(3) √ GM
2
(4) 3
√
5 GM

ma 2 a

Q118. The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about
the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles
by using a spring balance. If the weights are found to be same, then h is: (h ≪ R, where R is the radius of the
earth) 05 Sep 2020 (E)
(1) (2)
2 2 2 2
R ω R ω

2g g
2 2 2 2

(3) R ω

4g
(4) R ω

8g

Q119. The value of the acceleration due to gravity is g at a height h = 1

R

2
(R = radius of the earth) from the surface
of the earth. It is again equal to g at a depth d below the surface the earth. The ratio (
1
d

R
) equals:
05 Sep 2020 (M)
(1) 4

9
(2) 5

(3) 1

3
(4) 7

Q120. On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by
2
Ax

2
3/2
in the x-direction. The magnitude of the gravitational potential on the x-axis at a distance x, taking
(x +a )

its value to be zero at infinity is: 04 Sep 2020 (M)

(1) 2
A

2
1/2
(2) 2
A

2
3/2
(x +a ) (x +a )

(3) A(x 2
+ a )
2
1/2
(4) A(x 2
+ a )
2
3/2

Q121. A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can
be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the
planet is: 04 Sep 2020 (E)
(1) √2
1
(2) 2
(3) 1 (4) √2

Q122. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the
earth's radius R . By firing rockets attached to it, its speed is instantaneously increased in the direction of its
e

motion so that it become √ 3

2
times larger. Due to this the farthest distance from the centre of the earth that
the satellite reaches is R. Value of R is : 03 Sep 2020 (M)
(1) 4R e (2) 2. 5R e

(3) 3R e (4) 2R e

Q123. The mass density of a planet of radius R varies with the distance r from its centre as ρ(r) = ρ
2
r
0 (1 − 2
)
R

Then the gravitational field is maximum at: 03 Sep 2020 (E)

(1) r = √ 3
R
(2) r = R
4

(3) r = √3
1
R (4) r = √ 5
R
9

Q124. The mass density of a spherical galaxy varies as K

r
over a large distance r from its center. In that region, a
small star is in a circular orbit of radius R. Then the period of revolution,T depends on R as:

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02 Sep 2020 (M)

(1) T 2
∝ R (2) T 2
∝ R
3

(3) T 2
∝
1

R
3
(4) T ∝ R

Q125. The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of
the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected) 02 Sep 2020 (E)
(1) √5

2
R − R (2) R

(3) √ 5R−R

2
(4) √ 3R−R

Q126. Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape
velocities from the Planets A and B are v and v A B, respectively, then vA

vB
=
n

4
. The value of n is:
09 Jan 2020 (E)
(1) 4 (2) 1
(3) 2 (4) 3

Q127. Consider two solid spheres of radii R 1 ,

= 1 m R2 = 2 m and masses M and M 1 2,

respectively. The gravitational field due to sphere (1) and (2) are shown. The
value of M1

M2
is:

08 Jan 2020 (M)

(1) 2

3
(2) 1

(3) 1

2
(4) 1

Q128. An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of
the earth) from the centre of the earth, it has a speed of 12 km s
−1
. Neglecting the effect of earth's
atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from
the earth is 11.2 km s −1
) ? Give your answer to the nearest integer in km s
−1
__________. 08 Jan 2020 (E)

Q129. A box weighs 196N on a spring balance at the north pole. Its weight recorded on the same balance if it is
shifted to the equator is close to (Take g = 10ms −2
at the north pole and the radius of the earth = 6400km ):
07 Jan 2020 (E)
(1) 195.66N (2) 194.32N
(3) 194.66N (4) 195.32N

Q130. A satellite of massM is launched vertically upwards with an initial speed u from the surface of the earth.
After it reaches height R ( R = radius of the earth), it ejects a rocket of mass M

10
so that subsequently the
satellite moves in a circular orbit. The kinetic energy of the rocket is ( G is the gravitational constant; M is e

the mass of the earth): 07 Jan 2020 (M)

(1) M

20
(u
2
+
113

200
GM e

R
) (2) 5M (u 2
−
119

200
GM e

R
)

(3) (4)
2 2

3M 5GM e M 2GM e
(u + √ ) (u − √ )
8 6R 20 3R

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Q131. The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9 : 4 The mass of the
planet is 1

9
th of that of the Earth. If R is the radius of the Earth, what is the radius of the planet? (Take the
planets to have the same mass density) 12 Apr 2019 (E)
(1) R

4
(2) R

(3) R

3
(4) R

Q132. The value of acceleration due to gravity at Earth's surface is 9.8 m s

−2
. The altitude above its surface at
which the acceleration due to gravity decreases to 4.9 m s
−2
, is close to: (Radius of earth = 6.4 × 10
6
m )
10 Apr 2019 (M)
(1) 1.6 × 10 6
m (2) 2.6 × 10 6
m

(3) 6.4 × 10 6
m (4) 9.0 × 10 6
m

Q133. A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational
field of the planet acts on the spaceship, what will be the number of complete revolutions made by the
spaceship in 24 hours around the planet?
[Given: Mass of planet = 8 × 10
22
kg ,
Radius of planet = 2 × 10 6
m,

Gravitational constant G = 6.67 × 10

−11 2
Nm /kg
2
] 10 Apr 2019 (E)
(1) 17 (2) 9
(3) 13 (4) 11

Q134. A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a
and mass 2M. The gravitational field at distance 3a from the centre will be: 09 Apr 2019 (M)
(1) GM

9a
2
(2) GM

3a
2

(3) 2GM

3a
2
(4) 2GM

9a
2

Q135. A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r) = K

r
2
.

Identify the current relation between the radius R of the particle’s orbit and its period T : 09 Apr 2019 (E)
(1) TR is a constant (2) T
2
/
R
3 is a constant
(3) T
/R is a constant (4) T
/
R
2 is a constant

Q136. Four identical particles of mass M are located at the corners of a square of side ‘ a’ . What should be
their speed if each of them revolves under the influence of other’s gravitational field in a circular
orbit circumscribing the square?
08 Apr 2019 (M)
(1) 1.35√ GM (2) 1.21√
GM

a a

(3) 1.41√ GM (4) 1.16√

GM

a a

Q137. A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy
delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the
same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the
moon are equal and that the earth's volume is 64 times the volume of the moon. 08 Apr 2019 (E)

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(1) E

64
(2) E

(3) E

32
(4) E

16

Q138. Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R and B is in a
circular orbit of radius 2R around the earth. The ratio of their kinetic energies, KA

KB
is: 12 Jan 2019 (E)
(1) 2 (2) 1

(3) 1 (4) √ 1

Q139. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass
'm' at x = 0, if the mass per unit length of the rod is A + Bx , is given by: 2
12 Jan 2019 (M)
(1) Gm[A( a+L
1
−
1

a
) + BL] (2) Gm[A( a+L
1
−
1

a
) − BL]

(3) Gm[A( 1

a
−
1

a+L
) − BL] (4) Gm[A( 1

a
−
1

a+L
) + BL]

Q140. A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same
mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and
the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:
12 Jan 2019 (M)
(1) In an elliptical orbit (2) Such that it escapes to infinity
(3) In a circular orbit of a different radius (4) In the same circular orbit of radius R

Q141. A satellite is revolving in a circular orbit at a height h from the carth surface, such that h << R where R is
the radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase
in the speed required so that the satellite could escape from the gravitational field of earth is 11 Jan 2019 (M)
(1) √2gR (2) √gR
(3) √ gR (4) √gR(√2 − 1)
2

Q142. The mass and the diameter of a planet are three times the respective values for the Earth. The period of
oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the
planet would be: 11 Jan 2019 (E)
(1) √3

2
s (2) √3
2
s

(3) 3

2
s (4) 2√3 s

Q143. Two stars of masses 3 × 10 31

kg each, and at distance 2 × 10 11
m rotate in a plane about their common
centre of mass O. A meteorite passes through O moving perpendicular to the stars's rotation plane. In order to
escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is
(Take Gravitational constant G = 6.67 × 10 −11
N m
2
kg
−2
) 10 Jan 2019 (E)
(1) 2.4 × 10 4
m s
−1
(2) 3.8 × 10 4
m s
−1

(3) 2.8 × 10 5
m s
−1
(4) 1.4 × 10 5
m s
−1

Q144. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of
ejection, the kinetic energy of the object is: 10 Jan 2019 (M)
(1) 3

2
m v
2
(2) m v 2

(3) 1

2
m v
2
(4) 2 m v
2

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Q145. The energy required to take a satellite to a height h above the Earth surface (radius of Earth = 6.4 × 10 3
km

) is E , and the kinetic energy required for the satellite to be in a circular orbit at this height is E . The value
1 2

of h for which E and E are equal, is

1 2 09 Jan 2019 (E)
(1) 1.28 × 10 4
km (2) 6.4 × 10 3
km

(3) 3.2 × 10 3
km (4) 1.6 × 10 3
km

Q146. If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the
center of the Sun, its areal velocity is: 09 Jan 2019 (M)
(1) L

m
(2) 4L

(3) L

2m
(4) 2L

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ANSWER KEYS
1. (4) 2. (4) 3. (2) 4. (2) 5. (4) 6. (3) 7. (2) 8. (1)
9. (4) 10. (2) 11. (4) 12. (1) 13. (2) 14. (2) 15. (1) 16. (2)
17. (1) 18. (1) 19. (4) 20. (4) 21. (1) 22. (4) 23. (2) 24. (3)
25. (2) 26. (2) 27. (3) 28. (1) 29. (4) 30. (4) 31. (2) 32. (3)
33. (2) 34. (4) 35. (1) 36. (16) 37. (3) 38. (4) 39. (1) 40. (4)
41. (2) 42. (1) 43. (3) 44. (3) 45. (3) 46. (1) 47. (4) 48. (1)
49. (4) 50. (2) 51. (2) 52. (2) 53. (4) 54. (4) 55. (1) 56. (2)
57. (3) 58. (2) 59. (4) 60. (3) 61. (4) 62. (3) 63. (2) 64. (1)
65. (3) 66. (4) 67. (2) 68. (2) 69. (1) 70. (1) 71. (2) 72. (4)
73. (1) 74. (1) 75. (1) 76. (3) 77. (3) 78. (1) 79. (1) 80. (1)
81. (4) 82. (4) 83. (2) 84. (2) 85. (2) 86. (1) 87. (3) 88. (1)
89. (1) 90. (3) 91. (2) 92. (1) 93. (2) 94. (4) 95. (4) 96. (3)
97. (4) 98. (1) 99. (2) 100. (4) 101. (2) 102. (4) 103. (64) 104. (3)
105. (3) 106. (4) 107. (4) 108. (3) 109. (4) 110. (2) 111. (10) 112. (3)
113. (1) 114. (4) 115. (2) 116. (1) 117. (4) 118. (1) 119. (2) 120. (1)
121. (1) 122. (3) 123. (4) 124. (1) 125. (3) 126. (1) 127. (2) 128. (16)
129. (4) 130. (2) 131. (2) 132. (2) 133. (4) 134. (2) 135. (3) 136. (4)
137. (4) 138. (3) 139. (4) 140. (1) 141. (4) 142. (4) 143. (3) 144. (2)
145. (3) 146. (3)

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