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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(B) 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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(A) 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
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12
10

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

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

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

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

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

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

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

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

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

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

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

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

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]

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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]

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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]