61.

A body of mass 2m is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of h, where h = 4R.

• $\frac{2 \mathrm{mgh}}{\mathrm{R}}$

• $\frac{2}{3} \mathrm{mgR}$

• $\frac{8}{5} \mathrm{mgR}$

• $\frac{\mathrm{mgR}}{2}$

A communication satellite of 500 kg revolves around the earth in a circular orbit of radius 4.0 x 10⁷ m in the equatorial plane of the earth from west to east. The magnitude of angular momentum of the satellite is

• ∼ 0.13  × 10¹⁴ kg m² s^-1

• ∼ 1.3  × 10¹⁴ kg m² s^-1

• ∼ 0.58 × 10¹⁴ kg m² s^-1

• ∼ 2.58  × 10¹⁴ kg m² s^-1

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is ( here R is the radius of the earth )

• nn + 1 mgR

• nn - 1 mgR

• nmgR

• mgRn

Assertion:  Two bodies of masses M and m (M > m) are allowed to fall from the same height if the air resistance for each be the same then both the bodies will reach the earth simultaneously. 

Reason:  For same air resistance, acceleration of both the bodies will be same.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion: Kepler's second law can be understood by conservation of angular momentum principle.

Reason:  Kepler's second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as (dA/dt) = ( r²ω / 2 )

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false

Time period of pendulum, on a satellite orbiting the earth, is

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\pi }$}\right.$

• zero

• $\mathrm{\pi }$

• infinity

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R, to another of radius R₂ (R₂ > R₁ ) is

• GmM $\left(\frac{1}{{\mathrm{R}}_1^2} - \frac{1}{{\mathrm{R}}_2^2}\right)$

• GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• 2 GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{1}{2}$ GmM $\left(\frac{1}{{\mathrm{R}}_1}- \frac{1}{{\mathrm{R}}_2}\right)$

A person is standing in an elevator. In which situation he finds himself weightless?

• Elevator is going up with constant speed.

• Elevator is moving down with constant speed.

• Elevator is accelerating up with g.

• Elevator is accelerating down with g.

A satellite is in an orbit around the earth. If its kinetic energy is doubled, then

• it will maintain its path

• it will fall on the earth

• it will rotate with a great speed

• it will escape out of earth's gravitational field

What will be the effect on the weight of a body placed on the surface of earth, if earth suddenly ' stops rotating?

• No effect

• Weight will increase

• Weight will decrease

• Weight will become zero