# JEE Main

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

## Mathematics

Gravitation

Correct Marks 4

Incorrectly Marks -1

Q 1. The Fig. shows a planet in elliptical orbit around the sun {tex} S {/tex}. Where is the kinetic energy of the planet maximum? A

{tex} P_1 {/tex}

B

{tex} P _ { 2 } {/tex}

C

{tex} P _ { 3 } {/tex}

{tex} P_4 {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 2. The ratio of the radii of the planets {tex} P _ { 1 } {/tex} and {tex} P _ { 2 } {/tex} is {tex} k _ { 1 } {/tex} . The ratio of the acceleration due to the gravity on them is {tex} k _ { 2 } . {/tex} The ratio of the escape velocities from them will be

A

{tex} k _ { 1 } k _ { 2 } {/tex}

{tex} \sqrt { k _ { 1 } k _ { 2 } } {/tex}

C

{tex} \sqrt { \left( k _ { 1 } / k _ { 2 } \right) } {/tex}

D

{tex} \sqrt { \left( k _ { 2 } / k _ { 1 } \right) } {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 3. Which of the following graphs represent correctly the variation of intensity of gravitational field {tex} l {/tex} with the distance {tex} r {/tex} from the centre of a spherical shell of mass {tex} M {/tex} and radius {tex} a ? {/tex}

A B C  ##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 4. The period of a satellite in a circular orbit of radius {tex} R {/tex} is {tex} T {/tex} . The period of another satellite in a circular orbit of radius {tex}4R {/tex} is

A

{tex}4\ T {/tex}

B

{tex} T / 4 {/tex}

{tex}8\ T {/tex}

D

{tex} T / 8 {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 5. An artificial satellite moving in a circular orbit around the earth has a total energy{tex} (KE + \mathrm { PE } ){/tex} is {tex} E _ { 0 } {/tex}. Its potential energy is

A

{tex} - E _ { 0 } {/tex}

B

{tex}1.5E _ { 0 } {/tex}

{tex}2 E _ { 0 } {/tex}

D

{tex} E _ { 0 } {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 6. A simple pendulum has a time period {tex}T_1{/tex} when on the earth's surface, and {tex}T_2{/tex} when taken to a height R above the earth's surface, where R is radius of earth. The value of {tex}T_2/T_1{/tex} is

A

{tex}1{/tex}

B

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

C

{tex}4{/tex}

{tex}2{/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 7. A body of mass {tex} m {/tex} rises to a height {tex} h = R / 5 {/tex} from the earth's surface where {tex} R {/tex} is radius of the earth. If {tex} g {/tex} is acceleration due to gravity at the earth surface, the increase in potential energy is

A

{tex} m g R {/tex}

B

{tex} ( 4 / 5 ) m g R {/tex}

{tex} ( 1 / 6 ) m g R {/tex}

D

{tex} ( 6 / 7 ) m g R {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 8. Imagine a light planet revolving around a very massive star in a circular orbit of radius {tex} R {/tex} with a period of revolution {tex} T . {/tex} If the gravitational force of attraction between the planet and the star is proportional to {tex} R ^ { - 5 / 2 } {/tex} , {tex} T ^ { 2 } {/tex} is proportional to

A

{tex} R ^ { 3 } {/tex}

{tex} R ^ { 7 / 2 } {/tex}

C

{tex} R ^ { 3 / 2 } {/tex}

D

{tex} R ^ { 3.75 } {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 9. The orbital velocity of an artificial satellite in a circular orbit just above earth's surface is {tex} v _ { 0 } {/tex} . For a satellite orbiting in a circular orbit at an altitude of half of earth's radius is

A

{tex} \sqrt { \frac { 3 } { 2 } } v _ { 0 } {/tex}

{tex} \sqrt { \frac { 2 } { 3 } } v _ { 0 } {/tex}

C

{tex} \frac { 3 } { 2 } v _ { 0 } {/tex}

D

{tex} \frac { 2 } { 3 } v _ { 0 } {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 10. A particle is placed in a field characterized by a value of gravitational potential given by {tex} V = - k x y , {/tex} where {tex} k {/tex} is a constant. If {tex} \vec { E } _ { g } {/tex} is the gravitational field then,

A

{tex} \vec { E } _ { g } = k ( x \hat { i } + y \hat { j } ) {/tex} and is conservative in nature.

{tex} \vec { E } _ { g } = k ( y \hat { i } + x \hat { j } ) {/tex} and is conservative in nature.

C

{tex} \vec { E } _ { g } = k ( x \hat { i } + y \hat { j } ) {/tex} and is non-conservative in nature

D

{tex} \vec { E } _ { g } = k ( y \hat { i } + x \hat { j } ) {/tex} and is non-conservative in nature.

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 11. If three uniform spheres, each having mass {tex} M {/tex} and radius {tex} R , {/tex} are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

A

{tex} \frac { G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

B

{tex} \frac { 2 G M ^ { 2 } } { R ^ { 2 } } {/tex}

C

{tex} \frac { 2 G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

{tex} \frac { \sqrt { 3 } G M ^ { 2 } } { 4 R ^ { 2 } } {/tex}

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 12. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity.

A

Will be directed towards the centre but not the same everywhere.

B

Will have the same value everywhere but not directed towards the centre.

C

Will be same everywhere in magnitude directed towards the centre.

Cannot be zero at any point.

##### Explanation  Correct Marks 4

Incorrectly Marks -1

Q 13. Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the CM (centre of mass) causing translation and a net torque at the CM causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere).

The torque is zero.

B

The torque cause the earth to spin.

C

The rigid body result is not applicable since the earth is not even approximately a rigid body.

D

The torque causes the earth to move around the sun.

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 14. Both the earth and the moon are subject to the gravita- tional force of the sun. As observed from the sun, the orbit of the moon

A

will be elliptical.

will not be strictly elliptical because the total gravitational force on it is not central.

C

is not elliptical but will necessarily be a closed curve.

D

deviates considerably from being elliptical due to influence of planets other than the earth.

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 15. Choose the wrong option.

A

Inertial mass is a measure of difficulty of accel- erating a body by an external force whereas the gravitational mass is relevant in determining the gravitational force on it by an external mass.

B

That the gravitational mass and inertial mass are equal is an experimental result.

C

That the acceleration due to gravity on the carth is the same for all bodies is due to the equality of gravitational mass and inertial mass.

Gravitational mass of a particle like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot.

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 16. The kinetic energy needed to project a body of mass {tex} m {/tex} from the earth's surface (radius {tex} R {/tex} ) to infinity is

A

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

B

2{tex} m g R {/tex}

{tex} m g R {/tex}

D

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

##### Explanation Correct Marks 4

Incorrectly Marks -1

Q 17. Two spherical bodies of mass {tex} M {/tex} and {tex}5 M {/tex} and radii {tex} R {/tex} and {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  Correct Marks 4

Incorrectly Marks -1

Q 18. The escape velocity for a body projected vertically upwards from the surface of earth is {tex}11\ \mathrm { km } \mathrm { s^{-1} } {/tex} . If the body is projected at an angle of {tex} 45 ^ { \circ } {/tex} with the vertical, the escape velocity will be

A

{tex}11 \sqrt { 2 } \mathrm { km } \mathrm { s^{-1} } {/tex}

B

{tex}22\ \mathrm { km } \mathrm { s^{-1} } {/tex}

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

D

{tex} \frac { 11 } { \sqrt { 2 } } \mathrm { m } \mathrm { s^{-1} } {/tex}

##### Explanation 