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

Physics
Chemistry
Mathematics
Q 1.

Correct4

Incorrect-1

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

A

decrease

B

remain unchanged

increase

D

be zero

##### Explanation

Q 2.

Correct4

Incorrect-1

If {tex} g {/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

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

B

{tex} 2 m g R {/tex}

C

{tex} m g R {/tex}

D

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

##### Explanation

Q 3.

Correct4

Incorrect-1

If the distance between the earth and the sun were half its present value, the number of days in a year would have been

A

64.5

129

C

182.5

D

730

##### Explanation

Q 4.

Correct4

Incorrect-1

A geo-stationary satellite orbits around the earth in a circular orbit of radius {tex} 36,000 \mathrm { km } {/tex}. Then, the time period of a spy satellite orbiting a few hundred {tex} \mathrm { km } {/tex} above the earth's surface {tex} \left( R _ { \text {earth } } = 6,400 \mathrm { km } \right) {/tex} will approximately be

A

{tex} 1 / 2 \mathrm { hr } {/tex}

B

{tex} 1 \mathrm { hr } {/tex}

{tex} 2 \mathrm { hr } {/tex}

D

{tex} 4 \mathrm { hr } {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector {tex} \vec { a } {/tex} is correctly shown in :

A

B

D

##### Explanation

Q 6.

Correct4

Incorrect-1

A binary star system consists of two stars {tex} A {/tex} and {tex} B {/tex} which have time period {tex} T _ { A } {/tex} and {tex} T _ { B } , {/tex} radius {tex} R _ { A } {/tex} and {tex} R _ { B } {/tex} and mass {tex} M _ { A } {/tex} and {tex} M _ { B } {/tex}. Then

A

if {tex} T _ { A } > T _ { B } {/tex} then {tex} R _ { A } > R _ { B } {/tex}

B

if {tex} T _ { A } > T _ { B } {/tex} then {tex} M _ { A } > M _ { B } {/tex}

C

{tex} \left( \frac { T _ { A } } { T _ { B } } \right) ^ { 2 } = \left( \frac { R _ { A } } { R _ { B } } \right) ^ { 3 } {/tex}

{tex} T _ { A } = T _ { B } {/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

A spherically symmetric gravitational system of particles has a mass density {tex} \rho = \left\{ \begin{array} { l l } { \rho _ { 0 } } & { \text { for } \mathrm { r } \leq \mathrm { R } } \\ { 0 } & { \text { for } \mathrm { r } > \mathrm { R } } \end{array} \right. {/tex}
where {tex} \rho _ { 0 } {/tex} is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distance {tex} r ( 0 < r < \infty ) {/tex} from the centre of the system is represented by

A

B

D

##### Explanation

Q 8.

Correct4

Incorrect-1

A thin uniform annular disc (see figure) of mass {tex} M {/tex} has outer radius {tex} 4 R {/tex} and inner radius {tex} 3 R . {/tex} The work required to take a unit mass from point P on its axis to infinity is

{tex} \frac { 2 G M } { 7 R } ( 4 \sqrt { 2 } - 5 ) {/tex}

B

{tex} - \frac { 2 G M } { 7 R } ( 4 \sqrt { 2 } - 5 ) {/tex}

C

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

D

{tex} \frac { 2 G M } { 5 R } ( \sqrt { 2 } - 1 ) {/tex}

##### Explanation

Q 9.

Correct4

Incorrect-1

A satellite is moving with a constant speed {tex} 'V' {/tex} in a circular orbit about the earth. An object of mass {tex} 'm' {/tex} is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

A

{tex} \frac { 1 } { 2 } m V ^ { 2 } {/tex}

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

C

{tex} \frac { 3 } { 2 } m V ^ { 2 } {/tex}

D

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

##### Explanation

Q 10.

Correct4

Incorrect-1

A planet of radius {tex} R = \frac { 1 } { 10 } \times {/tex}( radius of Earth) has the same mass density as Earth. Scientists dig a well of depth {tex} \frac { R } { 5 } {/tex} on it and lower a wire of the same length and a linear mass density {tex} 10 ^ { - 3 }\ \mathrm { kg }\ \mathrm { m } ^ { - 1 } {/tex} into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth {tex} = 6 \times 10 ^ { 6 }\ \mathrm { m } {/tex} and the acceleration due to gravity on Earth is {tex} 10\ \mathrm { ms } ^ { - 2 } {/tex} )

A

{tex} 96 \mathrm { N } {/tex}

{tex} 108 \mathrm { N } {/tex}

C

{tex} 120 \mathrm { N } {/tex}

D

{tex} 150 \mathrm { N } {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is {tex} 3 \times 10 ^ { 5 } {/tex} times heavier than the Earth and is at a distance {tex} 2.5 \times 10 ^ { 4 } {/tex} times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is {tex}\mathrm {v_e}\ =\ 11.2\ \mathrm {km\ s^{-1}}{/tex}. The minimum initial velocity ({tex}\mathrm {v_s}{/tex}) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)

A

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

{tex} \mathrm { v } _ { \mathrm { s } } = 42\ \mathrm { km }\ \mathrm { s } ^ { - 1 } {/tex}

C

{tex} \mathrm { v } _ { \mathrm { s } } = 62\ \mathrm { km }\ \mathrm { s } ^ { - 1 } {/tex}

D

{tex} \mathrm { v } _ { \mathrm { s } } = 72\ \mathrm { km }\ \mathrm { s } ^ { - 1 } {/tex}

##### Explanation

Q 12.

Correct4

Incorrect-1

Consider a spherical gaseous cloud of mass density {tex} \rho ( r ) {/tex} in a free space where {tex} r {/tex} is the radical distance from its center. The gaseous cloud is made of particles of equal mass {tex} \mathrm { m } {/tex} moving in circular orbits about the common centre with the same kinetic energy {tex} \mathrm { K } {/tex}. The force acting on the particles is their mutual gravitational force. If {tex} \rho ( r ) {/tex} is constant in time. The particle number density {tex} n ( r ) = \rho ( r ) / \mathrm { m } {/tex} is
[ G is universal gravitational constant]

A

{tex} \frac { 3 K } { \pi r ^ { 2 } m ^ { 2 } G } {/tex}

{tex} \frac { K } { 2 \pi r ^ { 2 } m ^ { 2 } G } {/tex}

C

{tex} \frac { K } { \pi r ^ { 2 } m ^ { 2 } G } {/tex}

D

{tex} \frac { K } { 6 \pi r ^ { 2 } m ^ { 2 } G } {/tex}