Gravitation | JEE Main previous year questions with Solutions

Q 1 :

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 [2024]

$6 v$
$12 v$
$\frac{4}{3} v$
$3 v$

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(1)

Q 2 :

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 $4.2 \times 10^{4}$ km) [2024]

$1.05 \times 10^{4}$ km
$1.4 \times 10^{4}$ km
$1.68 \times 10^{5}$ km
$8.4 \times 10^{4}$ km

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(1)

By Kepler's law, $T^{2} = \frac{4 π^{2} R^{3}}{G M} \Rightarrow T^{2} \propto \frac{R^{3}}{M}$

${(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R_{1}}{R_{2}})}^{3} (\frac{M_{2}}{M_{1}})$

${(\frac{24}{6})}^{2} = {(\frac{4.2 \times 10^{4}}{R_{2}})}^{3} \times (\frac{\frac{M_{E}}{4}}{M_{E}})$

$4^{2} \times 4 = {(\frac{4.2 \times 10^{4}}{R_{2}})}^{3} \Rightarrow R_{2} = 1.05 \times 10^{4}$ km

Q 3 :

Correct formula for height of a satellite from Earth's surface is _____. [2024]

${(\frac{T^{2} R^{2} g}{4 π^{2}})}^{1 / 3} - R$
${(\frac{T^{2} R^{2} g}{4 π^{2}})}^{1 / 2} - R$
${(\frac{T^{2} R^{2}}{4 π^{2} g})}^{1 / 3} - R$
${(\frac{T^{2} R^{2} g}{4 π^{2}})}^{- 1 / 3} + R$

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(1)

$\frac{m v^{2}}{(R + h)} = \frac{G M m}{{(R + h)}^{2}} \Rightarrow v = \sqrt{\frac{G M}{R + h}}$

$Now T = \frac{2 π (R + h)}{\sqrt{\frac{G M}{R + h}}}$

$\Rightarrow T = \frac{2 π {(R + h)}^{3 / 2}}{\sqrt{G M}} = \frac{2 π {(R + h)}^{3 / 2}}{R \sqrt{g}}$

$\Rightarrow T^{2} R^{2} g = 4 π^{2} (R + h^{3})$

$\Rightarrow {(\frac{T^{2} R^{2} g}{4 π^{2}})}^{1 / 3} - R = h$

Q 4 :

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$ . The value of x is ________, where M and R are the mass and radius of earth, respectively. (G is the gravitational constant) [2025]

(3)

(i) If earth is assumed to be stationary

Orbital velocity $v_{0} = \sqrt{\frac{G M}{4 R / 3}} = \sqrt{\frac{3 G M}{4 R}}$

Angular momentum of satellite

$L = \frac{M}{2} v_{0} \frac{4 R}{3}$

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

$\Rightarrow x = 3$

Q 5 :

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ___ $\times 10^{10} J$ . (Mass of earth $= 6 \times 10^{24} kg$ , Radius of earth $= 6.4 \times 10^{6} m$ , Gravitational constant $= 6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}$ ) [2025]

(3)

$K = - \frac{U}{2} = \frac{G M m}{2 r}$

$\Rightarrow K = \frac{6.67 \times 10^{- 11} \times 6 \times 10^{24} \times 10^{3}}{2 \times 6670 \times 10^{3}} = 3 \times 10^{10} J$

Q 6 :

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 [2023]

4 hours
6 hours
12 hours
3 hours

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(4)

$T^{2} \propto R^{3}$

$\frac{T_{1}^{2}}{T_{2}^{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}$ $\Rightarrow {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R}{R / 4})}^{3}$

$∴$ $\frac{T_{1}^{2}}{T_{2}^{2}} = 64$

$\Rightarrow T_{2}^{2} = \frac{T_{1}^{2}}{64}$

$\Rightarrow T_{2} = \frac{24}{8} = 3 hr$

Q 7 :

Given below are two statements: [2023]

Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2} .$

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:

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

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(1)

$Energy of satellite in orbit E = \frac{- G M m}{2 R}$

$PE of satellite in orbit U = \frac{- G M m}{R}$

$\Rightarrow U = 2 E$

$KE of satellite in orbit K = E - U$

$K = \frac{G M m}{2 R} = (- E)$

Q 8 :

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 [2023]

$8 L$
$9 L$
$4 L$
$3 L$

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(4)

$L = m v r$

$\Rightarrow v = \sqrt{\frac{G M_{e}}{r}}$

$L = m \sqrt{\frac{G M_{e}}{r} \cdot r}$ $\Rightarrow L \propto r^{1 / 2}$

$Now distance from centre is increased by 8 times.$

$So new distance from center = r + 8 r = 9 r$

$Now angular momentum L' \propto {(9 r)}^{1 / 2}$

$\frac{L}{L'} = \frac{r^{1 / 2}}{{(9 r)}^{1 / 2}} = \frac{1}{3}$ $\Rightarrow L' = 3 L$

Q 9 :

Two satellites of masses $m$ and $3 m$ revolve around the earth in circular orbits of radii $r$ and $3 r$ respectively. The ratio of orbital speeds of the satellites respectively is [2023]

1 : 1
3 : 1
$\sqrt{3}$ : 1
9 : 1

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(3)

$v = \sqrt{\frac{G M}{r}}$

$v \propto \frac{1}{\sqrt{r}}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}} = \sqrt{\frac{3 r}{r}} = \sqrt{3} : 1$

Q 10 :

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) [2023]

$\sqrt{4 R}$
$\sqrt{8 R}$
$\sqrt{32 R}$
$\sqrt{2 R}$

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(3)

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

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

$T = \frac{2 π (2 R)}{v} = \frac{4 π R \sqrt{2}}{\sqrt{R g}} = \sqrt{32 R}$

Q 11 :

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 [2023]

Potential energy
Total energy
Kinetic energy
Speed

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(4)

$P.E. = - \frac{G M_{p} M_{A}}{R}$

$K.E. = + \frac{G M_{p} M_{A}}{2 R}$

$T.E. = - \frac{G M_{p} M_{A}}{2 R}$

$Speed = v = \sqrt{\frac{G M_{p}}{R}}$

$Speed of satellite is independent of mass of satellite.$

Q 12 :

Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 10^{6} J$ of energy. The value of $α$ is______.

$($ Take Radius of Earth $R_{E} = 6 \times 10^{6} m and 𝑔 = 10 m / s^{2})$ [2026]

100
500
1000
150

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(3)

Energy of a satellite in a circular orbit is given as

$E = \frac{- G M_{E} m}{2 r}; r = radius of circular orbit$

$Required energy to be supplied = Δ E = E_{f} - E_{i}$

$Δ E = (\frac{- G M_{E} m}{2 (3 R_{E})}) - (\frac{- G M_{E} m}{2 (1.5 R_{E})})$

$= \frac{G M_{E} m}{6 R_{E}}$

$Now, g = \frac{G M_{E}}{R_{E}^{2}} \Rightarrow \frac{G M_{E}}{R_{E}} = g R_{E}$

$∴$ $Δ E = \frac{1}{6} g m R_{E}$

$= \frac{1}{6} \times 10 \times 100 \times 6 \times 10^{6}$

$= 1000 \times 10^{6}$

$α = 1000$

Q 13 :

Given below are two statements :

Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.

Statement II : The time period of revolution of the satellite is $T = 2 π \sqrt{\frac{R_{e}}{g}}$ (for satellite very close to the earth surface), where $R_{e}$ radius of earth and g acceleration due to gravity.

In the light of the above statements, choose the correct answer from the options given below : [2026]

Statement I is true but Statement II is false
Statement I is false but Statement II is true
Both Statement I and Statement II are true
Both Statement I and Statement II are false

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(3)

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$

$∵$ $M = ρ \cdot \frac{4}{3} π R^{3}$

$∴$ $T = 2 g p \sqrt{\frac{1}{G ρ \frac{4}{3} π}}$

$Statement I is correct.$

$And$ $∴$ $\frac{G M}{R^{2}} = g$

$∴$ $T = 2 π \sqrt{\frac{R}{g}}$

$Statement II is correct$

$Ans. (3)$

Q 14 :

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 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:

(A) is correct but (R) is not correct
Both (A) and (R) are correct and (R) is the correct explanation of (A)
Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(A) is not correct but (R) is correct

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(2)

$ω = \frac{2 π}{T} \Rightarrow ω \propto \frac{1}{T},$ $T_{moon} = 27 days$

$T_{earth} = 365 days 4 hour \Rightarrow ω_{moon} > ω_{earth}$

Q 15 :

Statement-1: Three orbits are marked as 1, 2 and 3. These three orbits have same semi-major axis although their shapes (eccentricities) are different. The three identical satellites are orbiting in these three orbits, respectively. These three satellites have the same binding energy.

[IMAGE 145]

Statement-2: Total energy of a satellite depends on the semi-major axis of orbit according to the expression, $E = - \frac{G M m}{2 a}$ .

Statement-1 is true, Statement-2 is false
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1
Statement-1 is false, Statement-2 is true

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(2)

In all three orbits, length of semi major axis is same

Q 16 :

If a satellite orbits as close to the earth’s surface as possible

Its speed is maximum
Time period of its revolution is minimum
The total energy of the ‘earth plus satellite’ system is minimum
The total energy of the ‘earth plus satellite’ system is maximum

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Select one or more options

(1,2,3)

$For (A): Orbital speed v_{o} = \sqrt{\frac{G M}{r}},$

$For (B): Time period of revolution T^{2} \propto r^{3}$

$For (C/D): Total energy = - \frac{G M m}{2 r}$

Topic Question Set

Q 1 :

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 [2024]

Q 2 :

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 $4.2 \times 10^{4}$ km) [2024]

Q 3 :

Correct formula for height of a satellite from Earth's surface is _____. [2024]

Q 6 :

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 [2023]

Q 8 :

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 [2023]

Q 9 :

Two satellites of masses $m$ and $3 m$ revolve around the earth in circular orbits of radii $r$ and $3 r$ respectively. The ratio of orbital speeds of the satellites respectively is [2023]

Q 10 :

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) [2023]

Q 11 :

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 [2023]

Q 16 :

If a satellite orbits as close to the earth’s surface as possible

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Topic Question Set

Q 1 : 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 [2024]

Q 2 : 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 4.2×104 km) [2024]

Q 3 : Correct formula for height of a satellite from Earth's surface is _____. [2024]

Q 4 : A satellite of mass M2 is revolving around earth in a circular orbit at a height of R3 from earth surface. The angular momentum of the satellite is MGMRx. The value of x is ________, where M and R are the mass and radius of earth, respectively. (G is the gravitational constant) [2025]

Q 6 : 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 [2023]

Q 8 : 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 [2023]

Q 9 : Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r and 3r respectively. The ratio of orbital speeds of the satellites respectively is [2023]

Q 10 : The time period of a satellite, revolving above earth’s surface at a height equal to R will be (Given g=π2 m/s2, R = radius of earth) [2023]

Q 11 : 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 [2023]

Q 12 : Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE . This satellite can be moved to a circular orbit of radius 3RE by supplying α×106 J of energy. The value of α is______. (Take Radius of Earth RE=6×106m and 𝑔=10m/s2) [2026]

Q 16 : If a satellite orbits as close to the earth’s surface as possible

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Q 1 :

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 [2024]

Q 2 :

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 $4.2 \times 10^{4}$ km) [2024]

Q 3 :

Correct formula for height of a satellite from Earth's surface is _____. [2024]

Q 6 :

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 [2023]

Q 8 :

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 [2023]

Q 9 :

Two satellites of masses $m$ and $3 m$ revolve around the earth in circular orbits of radii $r$ and $3 r$ respectively. The ratio of orbital speeds of the satellites respectively is [2023]

Q 10 :

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) [2023]

Q 11 :

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 [2023]

Q 16 :

If a satellite orbits as close to the earth’s surface as possible