On account of the disruption in education due to the corona pandemic, we're are providing a 7-day Free trial of our platform to teachers. Know More →

JEE Advanced

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

Select Subject

Mathematics

Physics

Chemistry

Gravitation

Correct Marks 4

Incorrectly Marks -1

Q 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


Correct Marks 4

Incorrectly Marks -1

Q 2. 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


Correct Marks 4

Incorrectly Marks -1

Q 3. 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

Correct Marks 4

Incorrectly Marks -1

Q 4. 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

Correct Marks 4

Incorrectly Marks -1

Q 5. 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


Correct Marks 4

Incorrectly Marks -1

Q 6. 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



Correct Marks 4

Incorrectly Marks -1

Q 7. 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

Correct Marks 4

Incorrectly Marks -1

Q 8. 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


Correct Marks 4

Incorrectly Marks -1

Q 9. 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

Correct Marks 4

Incorrectly Marks -1

Q 10. 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}

Explanation