# JEE Main > Gravitation

Explore popular questions from Gravitation for JEE Main. This collection covers Gravitation previous year JEE Main questions hand picked by popular teachers.

Physics
Chemistry
Maths

Q 1.

Correct4

Incorrect-1

The kinetic energy needed to project a body of mass {tex} m {/tex} from
the earth surface (radius {tex} R {/tex} ) to infinity is

A

{tex} m g R / 2 {/tex}

B

2{tex} m g R {/tex}

{tex} m g R {/tex}

D

{tex} m g R / 4 {/tex}

##### Explanation  Q 2.

Correct4

Incorrect-1

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

A

continue to move in its orbit with same velocity

move tangentially to the original orbit in the same velocity

C

become stationary in its orbit

D

move towards the earth

##### Explanation Q 3.

Correct4

Incorrect-1

Energy required to move a body of mass {tex} m {/tex} from an orbit of
radius 2{tex} R {/tex} to 3{tex} R {/tex} is

A

{tex} G M m / 12 R ^ { 2 } {/tex}

B

{tex} G M m / 3 R ^ { 2 } {/tex}

C

{tex} G M m / 8 R {/tex}

{tex} G M m / 6 R {/tex}

##### Explanation   Q 4.

Correct4

Incorrect-1

The escape velocity of a body depends upon mass as

{tex} m ^ { 0 } {/tex}

B

{tex} m ^ { 1 } {/tex}

C

{tex} m ^ { 2 } {/tex}

D

{tex} m ^ { 3 } {/tex}

##### Explanation  Q 5.

Correct4

Incorrect-1

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

A

10 hours

B

80 hours

40 hours

D

20 hours

##### Explanation Q 6.

Correct4

Incorrect-1

Two spherical bodies of mass {tex} M {/tex} and {tex}5\ M {/tex} & radii {tex} R {/tex} & {tex} 2 R {/tex} respectively are released in free space with initial separation between their centres equal to {tex}12 R {/tex} . If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

A

{tex}2.5 R {/tex}

B

{tex}4.5\ R {/tex}

{tex}7.5 \ R {/tex}

D

{tex}1.5\ R {/tex}

##### Explanation     Q 7.

Correct4

Incorrect-1

The escape velocity for a body projected vertically upwards from the surface of earth is 11{tex} \mathrm { km } / \mathrm { s } {/tex} . If the body is projected at an angle of {tex} 45 ^ { \circ } {/tex} with the vertical, the escape velocity will be

A

11{tex} \sqrt { 2 } \mathrm { km } / \mathrm { s } {/tex}

B

22{tex} \mathrm { km } / \mathrm { s } {/tex}

11{tex} \mathrm { km } / \mathrm { s } {/tex}

D

{tex} \frac { 11 } { \sqrt { 2 } } \mathrm { km } / \mathrm { s } {/tex}

##### Explanation  Q 8.

Correct4

Incorrect-1

A satellite of mass {tex} m {/tex} revolves around the earth of radius {tex} R {/tex} at a height {tex} x {/tex} from its surface. If {tex} g {/tex} is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

A

{tex} \frac { g R ^ { 2 } } { R + x } {/tex}

B

{tex} \frac { g R } { R - x } {/tex}

C

{tex} g x {/tex}

{tex} \left( \frac { g R ^ { 2 } } { R + x } \right) ^ { 1 / 2 } {/tex}

##### Explanation  Q 9.

Correct4

Incorrect-1

The time period of an earth satellite in circular orbit is independent of

A

both the mass and radius of the orbit

B

the mass of the satellite

D

neither the mass of the satellite nor the radius of its orbit.

##### Explanation  Q 10.

Correct4

Incorrect-1

If {tex} ^ { ' } g ^ { \prime } {/tex} is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass {tex}'m' {/tex} raised from the surface of the earth to a height equal to the radius 'R' of the earth is

A

{tex} \frac { 1 } { 4 } m g R {/tex}

{tex} \frac { 1 } { 2 } m g R {/tex}

C

2{tex} m g R {/tex}

D

{tex} m g R {/tex}

##### Explanation Q 11.

Correct4

Incorrect-1

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius 'R' around the sun will be proportional to

A

{tex} R ^ { n } {/tex}

B

{tex} R ^ { \left( \frac { n - 1 } { 2 } \right) } {/tex}

{tex} R ^ { \left( \frac { n + 1 } { 2 } \right) } {/tex}

D

{tex} R ^ { \left( \frac { n - 2 } { 2 } \right) } {/tex}

##### Explanation Q 12.

Correct4

Incorrect-1

The change in the value of {tex} 'g' {/tex} at a height {tex} 'h' {/tex} above the surface of the earth is the same as at a depth {tex} ^ { \prime } d ^ { \prime } {/tex} below the surface of earth. When both {tex}'d' {/tex} and {tex} ^ { \prime } h ^ { \prime } {/tex} are much smaller than the radius of earth, then which one of the following is correct?

A

{tex} d = \frac { 3 h } { 2 } {/tex}

B

{tex} d = \frac { h } { 2 } {/tex}

C

{tex} d = h {/tex}

{tex} d = 2 h {/tex}

##### Explanation  Q 13.

Correct4

Incorrect-1

A particle of mass 10{tex} \mathrm { g } {/tex} is kept on the surface of a uniform sphere of mass 100{tex} \mathrm { kg } {/tex} and radius {tex} 10 \mathrm { cm } . {/tex} Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take {tex} G {/tex}{tex} \left.= 6.67 \times 10 ^ { - 11 } \mathrm { Nm } ^ { 2 } / \mathrm { kg } ^ { 2 } \right) {/tex}

A

{tex} 3.33 \times 10 ^ { - 10 } \mathrm { J } {/tex}

B

{tex} 13.34 \times 10 ^ { - 10 } \mathrm { J } {/tex}

{tex} 6.67 \times 10 ^ { - 10 } \mathrm { J } {/tex}

D

{tex} 6.67 \times 10 ^ { - 9 } \mathrm { J } {/tex}

##### Explanation Q 14.

Correct4

Incorrect-1

Average density of the earth

A

is a complex function of {tex} g {/tex}

B

does not depend on {tex} g {/tex}

C

is inversely proportional to {tex} g {/tex}

is directly proportional to {tex} g {/tex}

##### Explanation Q 15.

Correct4

Incorrect-1

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11{tex} \mathrm { km } \mathrm { s } ^ { - 1 } {/tex} , the escape velocity from the surface of the planet would be

A

1.1{tex} \mathrm { km } \mathrm { s } ^ { - 1 } {/tex}

B

11{tex} \mathrm { km } \mathrm { s } ^ { - 1 } {/tex}

110{tex} \mathrm { km } \mathrm { s } ^ { - 1 } {/tex}

D

0.11{tex} \mathrm { kms } ^ { - 1 } {/tex}

##### Explanation  Q 16.

Correct4

Incorrect-1

This question contains Statement- 1 and Statement- {tex} 2 . {/tex} Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1:
For a mass {tex} M {/tex} kept at the centre of a cube of side {tex}'a', {/tex} the flux of gravitational field passing through its sides {tex} 4 \pi G M . {/tex}
Statement-2:
If the direction of a field due to a point source is radial and its dependence on the distance {tex} 'r' {/tex} from the source is given as {tex} \frac { 1 } { r ^ { 2 } } , {/tex} its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

A

Statement - 1 is false, Statement- 2 is true

Statement -1 is true, Statement- 2 is true; Statement -2 is a correct explanation for Statement- 1

C

Statement -1 is true, Statement- 2 is true; Statement -2 is not a correct explanation for Statement- 1

D

Statement -1 is true, Statement- 2 is false

##### Explanation  Q 17.

Correct4

Incorrect-1

The height at which the acceleration due to gravity becomes {tex} \frac { g } { 9 } {/tex} (where {tex} g = {/tex} the acceleration due to gravity on the surface of the earth) in terms of {tex} R {/tex} , the radius of the earth, is :

A

{tex} \frac { R } { \sqrt { 2 } } {/tex}

B

{tex} R / 2 {/tex}

C

{tex} \sqrt { 2 } R {/tex}

{tex}2{ R } {/tex}

##### Explanation  Q 18.

Correct4

Incorrect-1

Two bodies of masses {tex} m {/tex} and 4{tex} m {/tex} are placed at a distance {tex} r . {/tex} The gravitational potential at a point on the line joining them where the gravitational field is zero is:

A

{tex} - \frac { 4 G m } { r } {/tex}

B

{tex} - \frac { 6 G m } { r } {/tex}

{tex} - \frac { 9 G m } { r } {/tex}

D

{tex} \mathrm {zero}{/tex}

##### Explanation    Q 19.

Correct4

Incorrect-1

The mass of a spaceship is {tex}1000 \mathrm { kg } {/tex} . It is to be launched from the earth's surface out into free space. The value of {tex} g {/tex} and {tex} R {/tex} (radius of earth) are 10{tex} \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} and {tex}6400 \mathrm { km } {/tex} respectively. The required energy for this work will be :

A

{tex} 6.4 \times 10 ^ { \mathrm { 11 } } {/tex} Joules

B

{tex} 6.4 \times 10 ^ { 8 } {/tex} Joules

C

{tex} 6.4 \times 10 ^ { 9 } {/tex} Joules

{tex} 6.4 \times 10 ^ { 10 } {/tex} Joules

##### Explanation  Q 20.

Correct4

Incorrect-1

What is the minimum energy required to launch a satellite of mass {tex} \mathrm { m } {/tex} from the surface of a planet of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } {/tex} in a circular orbit at an altitude of {tex}2 \mathrm { R }{/tex} ?

{tex} \frac { 5 \mathrm { GmM } } { 6 \mathrm { R } } {/tex}

B

{tex} \frac { 2 \mathrm { GmM } } { 3 \mathrm { R } } {/tex}

C

{tex} \frac { \mathrm { GmM } } { 2 \mathrm { R } } {/tex}

D

{tex} \frac { \mathrm { GmM } } { \mathrm { R } } {/tex}

##### Explanation  Q 21.

Correct4

Incorrect-1

Four particles, each of mass {tex} \mathrm { M } {/tex} and equidistant from each other, move along a circle of radius {tex} \mathrm { R } {/tex} under the action of their mutual gravitational attraction. The speed of each particle is:

A

{tex} \sqrt { \frac { \mathrm { GM } } { \mathrm { R } } } {/tex}

B

{tex} \sqrt { 2 \sqrt { 2 } \frac { \mathrm { GM } } { \mathrm { R } } } {/tex}

C

{tex} \sqrt { \frac { \mathrm { GM } } { \mathrm { R } } ( 1 + 2 \sqrt { 2 } ) } {/tex}

{tex} \frac { 1 } { 2 } \sqrt { \frac { \mathrm { GM } } { \mathrm { R } } ( 1 + 2 \sqrt { 2 } ) } {/tex}

##### Explanation   Q 22.

Correct4

Incorrect-1

From a solid sphere of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } , {/tex} a spherical portion of radius {tex} \mathrm { R } / 2 {/tex} is removed, as shown in the figure. Taking gravitational potential {tex} \mathrm { V } = 0 {/tex} at {tex} r = \infty , {/tex} the potential at the centre of the cavity thus formed is : {tex} ( G = \text { gravitational constant) } {/tex} A

{tex} \frac { - 2 \mathrm { GM } } { 3 \mathrm { R } } {/tex}

B

{tex} \frac { - 2 \mathrm { GM } } { \mathrm { R } } {/tex}

C

{tex} \frac { - \mathrm { GM } } { 2 \mathrm { R } } {/tex}

{tex} \frac { - \mathrm { GM } } { \mathrm { R } } {/tex}

##### Explanation     Q 23.

Correct4

Incorrect-1

A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R; h< R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)

A

{tex} \sqrt { \mathrm { gR } / 2 } {/tex}

{tex} \sqrt { \mathrm { gR } } ( \sqrt { 2 } - 1 ) {/tex}

C

{tex} \sqrt { 2 \mathrm { gR } } {/tex}

D

{tex} \sqrt { \mathrm { gR } } {/tex}

##### Explanation Q 24.

Correct4

Incorrect-1

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

A

continue to move in its orbit with same velocity

move tangentially to the original orbit in the same velocity

C

become stationary in its orbit

D

move towards the earth.

##### Explanation  Q 25.

Correct4

Incorrect-1

Energy required to move a body of mass {tex} m {/tex} from an orbit of radius {tex} 2 R {/tex} to {tex} 3 R {/tex} is

A

{tex} G M m / 12 R ^ { 2 } {/tex}

B

{tex} G M m / 3 R ^ { 2 } {/tex}

C

{tex} G M m / 8 R {/tex}

{tex} G M m / 6 R {/tex}

##### Explanation  