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)

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(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]

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

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(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

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(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

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(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

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(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]

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

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(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

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(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

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(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

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(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]

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

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(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]

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

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(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]

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

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(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
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10

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(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]

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

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(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
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(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]

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

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(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

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(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]

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

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(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]

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

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(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

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(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

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(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

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(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]

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

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(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]

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

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(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]

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

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(3)

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

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

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

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

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]

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	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]

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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]

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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]