Gravitation | JEE Main previous year questions with Solutions

Q 1 :

Match List-I with List-II [2024]

List - I List - II

A Kinetic energy of planet (I) $- G M m / a$

B Gravitation Potential energy of sun planet system (II) $G M m / 2 a$

C Total mechanical energy of planet (III) $G M m / r$

D Escape energy at the surface of planet for unit mass object (IV) $- G M m / 2 a$

(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

1

2

3

4

(2)

Potential energy = $- \frac{G M m}{a}$

Total energy = $- \frac{G M m}{2 a}$

kinetic energy = $\frac{G M m}{r}$

Escape energy = $\frac{G M m}{r}$

Q 2 :

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: [2024]

$m g R_{E}$
$1 / 2 m g R_{E}$
$4 m g R_{E}$
$2 m g R_{E}$

1

2

3

4

(1)

Escape speed $v_{e} = \sqrt{\frac{2 G M}{R_{E}}}$

Escape kinetic energy $K_{e} = \frac{1}{2} m v_{e}^{2}$

$K_{e} = \frac{1}{2} m {(\sqrt{\frac{2 G M}{R_{E}}})}^{2} = \frac{G M m}{R_{E}}$

Also, $G M = g R_{E}^{2} \Rightarrow K_{e} = \frac{(g R_{E}^{2}) m}{R_{E}} = m g R_{E}$

Q 3 :

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 $x \frac{G M_{e} m}{21 R_{e}} .$ The value of $x$ is (take $R_{e}$ = 6370 km): [2024]

11
9
12
10

1

2

3

4

(1)

$h = 318.5 \approx (\frac{R_{e}}{20})$

$T \cdot E_{i} = \frac{- G M_{e} m}{R_{e}}$

$T \cdot E_{f} = \frac{- G M_{e} m}{2 (R_{e} + h)} = \frac{- G M_{e} m}{2 (R_{e} + \frac{R_{e}}{20})}$

Change in total mechanical energy = $T E_{f} - T E_{i}$

$= \frac{G M_{e} m}{R_{e}} [1 - \frac{10}{21}] = \frac{11 G M_{e} m}{21 R_{e}} n$

Q 4 :

The gravitational potential at a point above the surface of earth is $- 5.12 \times 10^{7}$ J/kg and the acceleration due to gravity at that point is 6.4 $m / s^{2} .$

Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is: [2024]

1600 km
540 km
1200 km
1000 km

1

2

3

4

(1)

$V_{g} = \frac{- G M}{(R + h)} = - 5.12 \times 10^{7} J / k g$

$g = \frac{G M}{{(R + h)}^{2}} = 6.4 m / s^{2}$

$\frac{V_{g}}{g} = - (R + h)$

$\Rightarrow \frac{- 5.12 \times 10^{7}}{6.4} = - (R + h)$

6400 km + h = 8000 km

h = 1600 km

Q 5 :

Escape velocity of a body from earth is 11.2 km/s. 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 planet is [2024]

11.2 km/s
8.4 km/s
4.2 km/s
7.9 km/s

1

2

3

4

(4)

$R_{P} = \frac{R_{E}}{3},$ $M_{P} = \frac{M_{E}}{6}$

$V_{e} = \sqrt{\frac{2 G M}{R}}$ for earth

$V_{e}^{'} = \sqrt{\frac{2 G (M / 6)}{(R / 3)}} = \sqrt{\frac{G M}{R}}$ for planet

$\sqrt{2} V_{e}^{'} = V_{e}$

$V_{e}^{'} = \frac{V_{e}}{\sqrt{2}} = \frac{11.2}{\sqrt{2}} = (11.2) \times 0.7$ km/sec

$V_{e}^{'} = 7.84 k m / s e c \approx 7.9 k m / s e c$

Q 6 :

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 [2024]

$V / 3$
$V / 4$
$V / 12$
$V / 6$

1

2

3

4

(1)

$V_{e s c a p e} = \sqrt{\frac{2 G M}{R}}$

$V_{p l a n e t} = \sqrt{\frac{2 G M}{R}} = V$

$V_{M o o n} = \sqrt{\frac{2 G M \times 16}{144 R}} = \frac{1}{3} \sqrt{\frac{2 G M}{R}}$

$V_{M o o n} = \frac{V_{P l a n e t}}{3} = \frac{V}{3}$

Q 7 :

A satellite of $10^{3}$ kg mass is revolving in a circular orbit of radius 2R. If $\frac{10^{4} R}{6} J$ 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) [2024]

2.5 R
3 R
4 R
6 R

1

2

3

4

(4)

$Total energy = \frac{- G M m}{2 (2 R)}$

$If energy = \frac{10^{4} R}{6} is added then,$

$\frac{- G M m}{4 R} + \frac{10^{4} R}{6} = \frac{- G M m}{2 r}, where r is new radius of revolving$

$- \frac{m g R}{4} + \frac{10^{4} R}{6} = - \frac{m g R^{2}}{2 r}, As g = \frac{G M}{R^{2}}$

$- \frac{10^{3} \times 10 \times R}{4} + \frac{10^{4} R}{6} = - \frac{10^{3} \times 10 \times R^{2}}{2 r}$

$\Rightarrow - \frac{1}{4} + \frac{1}{6} = - \frac{R}{2 r} \Rightarrow r = 6 R$

Q 8 :

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : [2025]

11.2
5.6
2.8
8.4

1

2

3

4

(2)

$v_{escape} = \sqrt{\frac{2 G M}{R}}; M_{earth} = 8 M_{planet}; R_{earth} = 2 R_{planet}$

$\frac{v_{planet}}{v_{earth}} = \sqrt{\frac{M_{planet}}{M_{earth}} \times \frac{R_{earth}}{R_{planet}}}$

$v_{planet} = (11.2 km / s) \sqrt{\frac{1}{8} \times 2} = 5.6 km / s$

Q 9 :

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2} m g R$ , where R is the radius of earth.

Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.

in the light of the above statements, choose the correct answer from the options given below [2025]

A is false but R is true
Both A and R are true and R is the correct explanation of A
A is true but R is false
Both A and R are true but R is NOT the correct explanation of A

1

2

3

4

(1)

At $\infty$ , PE is zero, U = 0

$\frac{1}{2} m v^{2} - \frac{G M m}{R} = 0$

$KE = \frac{G M}{R^{2}} \cdot m R = m g R$

Q 10 :

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant) [2025]

$\sqrt{\frac{G M}{2 R}}$
$\sqrt{\frac{G M}{R}}$
$\sqrt{\frac{3 G M}{R}}$
$\sqrt{\frac{2 G M}{R}}$

1

2

3

4

(1)

$K E_{i} + P E_{i} = K E_{g} + P E_{g}$

$\frac{1}{2} m v^{2} - \frac{G M m}{4 R} = 0 + 0$

$v^{2} = \frac{G M}{R} \frac{1}{2} \Rightarrow v = \sqrt{\frac{G M}{2 R}}$

Q 11 :

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 [2023]

$\sqrt{\frac{G M}{2 r}}$
$\sqrt{\frac{4 G M}{r}}$
$\sqrt{\frac{G M}{r}}$
$\sqrt{\frac{G M}{4 r}}$

1

2

3

4

(4)

$\frac{G m^{2}}{4 r^{2}} = \frac{m v^{2}}{r} \Rightarrow v = \sqrt{\frac{G m}{4 r}}$

Q 12 :

A body of mass m is taken from Earth’s surface to the height h equal to twice the radius of Earth $(R_{e})$ , the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth) [2023]

$\frac{1}{2} m g R_{e}$
$3 m g R_{e}$
$\frac{2}{3} m g R_{e}$
$\frac{1}{3} m g R_{e}$

1

2

3

4

(3)

$U = \frac{- G M_{e} m}{r} and U_{i} = \frac{- G M_{e} m}{R_{e}}$

$U_{f} = \frac{- G M_{e} m}{(R_{e} + h)} = \frac{- G M_{e} m}{R_{e} + 2 R_{e}} = \frac{- G M_{e} m}{3 R_{e}}$

$Increase in internal energy Δ U = U_{f} - U_{i}$

$= \frac{2}{3} \frac{G M_{e} m}{R_{e}}$

$= \frac{2}{3} \frac{G M_{e}}{R_{e}^{2}} m R_{e} = \frac{2}{3} m g R_{e}$

Q 13 :

If the gravitational field in space is given as $(- \frac{K}{r^{2}})$ Taking the reference point to be at $r = 2$ cm with gravitational potential $V = 10 J/kg,$ find the gravitational potential at $r$ = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

9
11
12
10

1

2

3

4

(2)

$- \frac{d V}{d r} = - \frac{k}{r^{2}} \Rightarrow \int_{10}^{V} d V = \int_{2}^{3} \frac{k}{r^{2}} d r$

$V - 10 = k [\frac{1}{2} - \frac{1}{3}]$

$V - 10 = \frac{k}{6} \Rightarrow V = 11 volts$

Q 14 :

An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

$2 \sqrt{g R}$
$\sqrt{g R}$
$\sqrt{\frac{g R}{2}}$
$\sqrt{2 g R}$

1

2

3

4

(2)

$Loss in PE = Gain in KE$

$(- \frac{G M m}{2 R}) - (- \frac{G M m}{R}) = \frac{1}{2} m v^{2}$

$\Rightarrow v^{2} = \frac{G M}{R} = g R$

$\Rightarrow v = \sqrt{g R}$

Q 15 :

If Earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_{e}}{3} \sqrt{x} {ms}^{- 1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_{e}$ is escape velocity on Earth. The value of $x$ is [2023]

2
3
18
1

1

2

3

4

(1)

$v_{(escape)planet} = \sqrt{\frac{2 G M_{p}}{R_{p}}}$

$= \sqrt{\frac{2 G (\frac{M_{e}}{9})}{(\frac{R_{e}}{2})}} = \frac{v_{e} \sqrt{2}}{3}$

$∴$ $x = 2$

Q 16 :

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 [2023]

$\frac{4}{3}$
$\frac{3}{2}$
$\frac{2}{3}$
$\frac{3}{4}$

1

2

3

4

(4)

Q 17 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. [2023]

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:

A is true but R is false
Both A and R are correct but R is NOT the correct explanation of A
Both A and R are correct and R is the correct explanation of A
A is false but R is true

1

2

3

4

(3)

At Moon, due to low escape velocity, the rms velocity of molecules is greater than escape velocity. Hence molecules escape and there is no atmosphere at Moon.

Q 18 :

If $V$ is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

$\frac{3 V}{2}$
$V$
$\frac{4}{3} V$
$\frac{V}{2}$

1

2

3

4

(1)

$V = \frac{G M}{2 R^{3}} (3 R^{2} - r^{2}) at r = R \Rightarrow V = (\frac{G M}{R})$

$At r = 0, V_{0} = \frac{3 G M}{2 R} = (\frac{3 V}{2})$

Q 19 :

A spaceship of mass $2 \times 10^{4} kg$ is launched into a circular orbit close to the Earth’s surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if $g = 10 {m/s}^{2}$ and radius of Earth = 6400 km) [2023]

$11.2 (\sqrt{2} - 1) km/s$
$7.9 (\sqrt{2} - 1) km/s$
$8 (\sqrt{2} - 1) km/s$
$7.4 (\sqrt{2} - 1) km/s$

1

2

3

4

(3)

$v_{orbit} = \sqrt{\frac{G M}{R}} = \sqrt{g R}$

$v_{escape} = \sqrt{\frac{2 G M}{R}} = \sqrt{2 g R}$

$Δ v = (\sqrt{2} - 1) \sqrt{g R} = 8 (\sqrt{2} - 1) km/s$

Q 20 :

The ratio of escape velocity of a planet to the escape velocity of Earth will be:

Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

4 : 1
2 : 1
1 : $\sqrt{2}$
1 : 4

1

2

3

4

(2)

$v_{escape} = \sqrt{\frac{2 G M}{R}}$

$∴$ $v_{escape} for planet = \sqrt{\frac{2 G (16 M_{E})}{4 R_{E}}} = 2 \sqrt{\frac{2 G M_{E}}{R_{E}}}$

$= 2 (v_{escape} for Earth)$

Q 21 :

A planet having mass $9 M_{e}$ and radius $4 R_{e}$ , where $M_{e}$ and $R_{e}$ are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth $V_{e} = 11.2 \times 10^{3} m/s$ ) [2023]

67.2
16.8
33.6
11.2

1

2

3

4

(2)

$V_{P} = \sqrt{\frac{2 G M_{P}}{R_{P}}}, V_{E} = \sqrt{\frac{2 G M_{E}}{R_{E}}}$

$\frac{V_{P}}{V_{E}} = \frac{\sqrt{\frac{2 G M_{P}}{R_{P}}}}{\sqrt{\frac{2 G M_{E}}{R_{E}}}} = \sqrt{\frac{R_{E}}{R_{P}} \times \frac{M_{P}}{M_{E}}}$

$V_{P} = \sqrt{\frac{1}{4} \times 9} \times V_{E} = \frac{3}{2} V_{E}$

$V_{P} = \frac{3}{2} \times 11.2 km/sec = 16.8 km/sec$

Q 22 :

Given below are two statements: [2023]

Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.

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:

Both Statement I and Statement II are incorrect
Statement I is correct but Statement II is incorrect
Statement I is incorrect but Statement II is correct
Both Statement I and Statement II are correct

1

2

3

4

(2)

$V_{e} = \sqrt{\frac{2 G M}{R}} \Rightarrow V_{e} \propto \sqrt{\frac{M}{R}}$

$As \frac{M}{R} increases \Rightarrow V_{e} increases$

$Statement (1) is correct$

$Also, V_{e} \propto \frac{1}{\sqrt{R}}$

$As V_{e} depends upon R$

$\Rightarrow Statement (2) is incorrect$

Q 23 :

A body is released from a height equal to the radius (R) of the Earth. The velocity of the body when it strikes the surface of the Earth will be (Given g = acceleration due to gravity on the Earth.) [2023]

$\sqrt{g R}$
$\sqrt{4 g R}$
$\sqrt{2 g R}$
$\sqrt{\frac{g R}{2}}$

1

2

3

4

(1)

$By conservation of mechanical energy$

$U_{i} + K_{i} = U_{f} + K_{f}$

$- \frac{G M m}{2 R} + 0 = - \frac{G M m}{R} + \frac{1}{2} m v^{2}$

$\frac{G M m}{2 R} = \frac{1}{2} m v^{2}$

$v = \sqrt{\frac{G M}{R}} = \sqrt{g R}$

Q 24 :

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with side 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process is __________ J.

(Gravitational constant $G = 6.7 \times 10^{- 11} {N m}^{2} / {kg}^{2}$ ) [2026]

$2.85 \times 10^{- 7}$
$1.74 \times 10^{- 7}$
$9.86 \times 10^{- 6}$
$4.77 \times 10^{- 7}$

1

2

3

4

(2)

$Work done by external agent:$

$W_{ext} = Δ U$

$U_{i} = - \frac{G m_{1} m_{2}}{r_{i}} - \frac{G m_{2} m_{3}}{r_{i}} - \frac{G m_{1} m_{3}}{r_{i}} : r_{i} = 20 m$

$U_{f} = - \frac{G m_{1} m_{2}}{r_{f}} - \frac{G m_{2} m_{3}}{r_{f}} - \frac{G m_{1} m_{3}}{r_{f}} : r_{f} = 25 m$

$U_{i} = \frac{- 6.67 \times 10^{- 11}}{20} [200 \times 300 + 300 \times 400 + 200 \times 400]$

$= \frac{- 6.67 \times 10^{- 11}}{20} \times 26 \times 10^{4} = - 86.71 \times 10^{- 8} J$

$U_{f} = \frac{- 6.67 \times 10^{- 11}}{25} [200 \times 300 + 300 \times 400 + 200 \times 400]$

$= \frac{- 6.67 \times 10^{- 11}}{25} \times 26 \times 10^{4} = - 693.68 \times 10^{- 9}$

$= - 69.36 \times 10^{- 8} J$

$Δ U = U_{f} - U_{i} = 1.74 \times 10^{- 7} J$

Q 25 :

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]

$200 \sqrt{5}$
$1000$
$100 \sqrt{10}$
$1000 \sqrt{2}$

1

2

3

4

(3)

$V_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{\frac{2 G \times ρ \times \frac{4 π R^{3}}{3}}{R}} \Rightarrow V_{e} \propto \sqrt{ρ} \times R$

$\frac{{(V_{e})}_{B}}{{(V_{e})}_{A}} = \sqrt{\frac{ρ_{B}}{ρ_{A}}} \times \frac{R_{B}}{R_{A}} = \sqrt{\frac{0.1 ρ_{A}}{ρ_{A}}} \times (\frac{0.1 R_{A}}{R_{A}})$

$\frac{{(V_{e})}_{B}}{{(V_{e})}_{A}} = \frac{1}{10} \times \frac{1}{\sqrt{10}}$

${(V_{e})}_{B} = \frac{10 \times 1000}{10 \sqrt{10}} = 100 \sqrt{10} m/sec$

Q 26 :

Two identical spherically symmetric planets, each of mass M, are somehow held at rest with respect to each other. Each planet has radius R, and the distance between the centers of the planets is 4R. If a rocket is launched from the surface of one planet with speed v, what is the minimum speed v so that the rocket can reach the other planet?

$\sqrt{\frac{2 G M}{R}}$
$\sqrt{\frac{G M}{R}}$
$\sqrt{\frac{3 G M}{4 R}}$
$\sqrt{\frac{2 G M}{3 R}}$

1

2

3

4

(4)

The gravitational force vanishes at the midway point between the planets, so the rocket only needs to have enough energy to get there. The initial and final gravitational potential energies are $U_{i} = - \frac{G M m}{R} - \frac{G M m}{3 R} = - \frac{4 G M m}{3 R}$ and $U_{f} = - \frac{2 G M m}{2 R} = - \frac{G M m}{R}$

Topic Question Set

Q 2 :

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: [2024]

Q 4 :

The gravitational potential at a point above the surface of earth is $- 5.12 \times 10^{7}$ J/kg and the acceleration due to gravity at that point is 6.4 $m / s^{2} .$

Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is: [2024]

Q 5 :

Escape velocity of a body from earth is 11.2 km/s. 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 planet is [2024]

Q 6 :

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 [2024]

Q 7 :

A satellite of $10^{3}$ kg mass is revolving in a circular orbit of radius 2R. If $\frac{10^{4} R}{6} J$ 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) [2024]

Q 8 :

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : [2025]

Q 10 :

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant) [2025]

Q 11 :

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 [2023]

Q 12 :

A body of mass m is taken from Earth’s surface to the height h equal to twice the radius of Earth $(R_{e})$ , the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth) [2023]

Q 13 :

If the gravitational field in space is given as $(- \frac{K}{r^{2}})$ Taking the reference point to be at $r = 2$ cm with gravitational potential $V = 10 J/kg,$ find the gravitational potential at $r$ = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

Q 14 :

An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

Q 15 :

If Earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_{e}}{3} \sqrt{x} {ms}^{- 1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_{e}$ is escape velocity on Earth. The value of $x$ is [2023]

Q 16 :

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 [2023]

(4)

Q 18 :

If $V$ is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

Q 19 :

A spaceship of mass $2 \times 10^{4} kg$ is launched into a circular orbit close to the Earth’s surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if $g = 10 {m/s}^{2}$ and radius of Earth = 6400 km) [2023]

Q 20 :

The ratio of escape velocity of a planet to the escape velocity of Earth will be:

Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

Q 21 :

A planet having mass $9 M_{e}$ and radius $4 R_{e}$ , where $M_{e}$ and $R_{e}$ are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth $V_{e} = 11.2 \times 10^{3} m/s$ ) [2023]

Q 23 :

A body is released from a height equal to the radius (R) of the Earth. The velocity of the body when it strikes the surface of the Earth will be (Given g = acceleration due to gravity on the Earth.) [2023]

Q 25 :

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]

Want Us to Email you About Special Offers & Updates?

	List - I		List - II
A	Kinetic energy of planet	(I)	$- G M m / a$
B	Gravitation Potential energy of sun planet system	(II)	$G M m / 2 a$
C	Total mechanical energy of planet	(III)	$G M m / r$
D	Escape energy at the surface of planet for unit mass object	(IV)	$- G M m / 2 a$

Topic Question Set

Q 1 : Match List-I with List-II [2024] List - I List - II A Kinetic energy of planet (I) -GMm/a B Gravitation Potential energy of sun planet system (II) GMm/2a C Total mechanical energy of planet (III) GMm/r D Escape energy at the surface of planet for unit mass object (IV) -GMm/2a

Q 2 : To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE) g = acceleration due to gravity on the surface of earth: [2024]

Q 3 : 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 xGMem21Re. The value of x is (take Re= 6370 km): [2024]

Q 4 : The gravitational potential at a point above the surface of earth is -5.12×107 J/kg and the acceleration due to gravity at that point is 6.4 m/s2. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is: [2024]

Q 5 : Escape velocity of a body from earth is 11.2 km/s. 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 planet is [2024]

Q 6 : 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 [2024]

Q 7 : A satellite of 103 kg mass is revolving in a circular orbit of radius 2R. If 104R6J energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use g = 10 m/s2, R = radius of Earth) [2024]

Q 8 : Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : [2025]

Q 10 : An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant) [2025]

Q 11 : 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 [2023]

Q 12 : A body of mass m is taken from Earth’s surface to the height h equal to twice the radius of Earth (Re), the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth) [2023]

Q 13 : If the gravitational field in space is given as (-Kr2) Taking the reference point to be at r=2 cm with gravitational potential V=10 J/kg, find the gravitational potential at r = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

Q 14 : An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

Q 15 : If Earth has a mass nine times and radius twice to that of a planet P. Then ve3x ms-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 [2023]

Q 16 : 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 [2023]

(4)

Q 18 : If V is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

Q 19 : A spaceship of mass 2×104 kg is launched into a circular orbit close to the Earth’s surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if g=10 m/s2 and radius of Earth = 6400 km) [2023]

Q 20 : The ratio of escape velocity of a planet to the escape velocity of Earth will be: Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

Q 21 : A planet having mass 9Me and radius 4Re, where Me and Re are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth Ve=11.2×103 m/s) [2023]

Q 23 : A body is released from a height equal to the radius (R) of the Earth. The velocity of the body when it strikes the surface of the Earth will be (Given g = acceleration due to gravity on the Earth.) [2023]

Q 25 : The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]

Want Us to Email you About Special Offers & Updates?

Q 2 :

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: [2024]

Q 4 :

The gravitational potential at a point above the surface of earth is $- 5.12 \times 10^{7}$ J/kg and the acceleration due to gravity at that point is 6.4 $m / s^{2} .$

Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is: [2024]

Q 5 :

Escape velocity of a body from earth is 11.2 km/s. 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 planet is [2024]

Q 6 :

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 [2024]

Q 7 :

A satellite of $10^{3}$ kg mass is revolving in a circular orbit of radius 2R. If $\frac{10^{4} R}{6} J$ 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) [2024]

Q 8 :

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : [2025]

Q 10 :

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume M = mass of earth, G = Universal gravitational constant) [2025]

Q 11 :

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 [2023]

Q 12 :

A body of mass m is taken from Earth’s surface to the height h equal to twice the radius of Earth $(R_{e})$ , the increase in potential energy will be: (g = acceleration due to gravity on the surface of Earth) [2023]

Q 13 :

If the gravitational field in space is given as $(- \frac{K}{r^{2}})$ Taking the reference point to be at $r = 2$ cm with gravitational potential $V = 10 J/kg,$ find the gravitational potential at $r$ = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

Q 14 :

An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

Q 15 :

If Earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_{e}}{3} \sqrt{x} {ms}^{- 1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_{e}$ is escape velocity on Earth. The value of $x$ is [2023]

Q 16 :

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 [2023]

Q 18 :

If $V$ is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

Q 19 :

A spaceship of mass $2 \times 10^{4} kg$ is launched into a circular orbit close to the Earth’s surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if $g = 10 {m/s}^{2}$ and radius of Earth = 6400 km) [2023]

Q 20 :

The ratio of escape velocity of a planet to the escape velocity of Earth will be:

Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

Q 21 :

A planet having mass $9 M_{e}$ and radius $4 R_{e}$ , where $M_{e}$ and $R_{e}$ are mass and radius of Earth respectively, has escape velocity in km/s given by: (Given escape velocity on Earth $V_{e} = 11.2 \times 10^{3} m/s$ ) [2023]

Q 23 :

A body is released from a height equal to the radius (R) of the Earth. The velocity of the body when it strikes the surface of the Earth will be (Given g = acceleration due to gravity on the Earth.) [2023]

Q 25 :

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]