The change in the gravitational potential energy when a body of mass $m$ is raised to a height $h = nR$ above the surface of the Earth is (where $R$ is the radius of the Earth).

An object of mass $m$ is raised from the surface of the earth to a height equal to the radius of the earth,that is,taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy?

Two hypothetical planets of masses $m_1$ and $m_2$ are at rest when they are at an infinite distance apart. Because of the gravitational force,they move towards each other along the line joining their centres. What is their speed when their separation is $d$? (Speed of $m_1$ is $v_1$ and that of $m_2$ is $v_2$)

If $g$ is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass $m$ raised from the earth's surface to a height equal to the radius $R$ of the earth is

$A$ rocket is fired vertically upwards from the surface of the Earth with a velocity $V$. If $R$ is the radius of the Earth,what is the maximum height attained by the rocket?

Work done in raising a body of mass $m$ from the surface of the earth to a height $\frac{R}{3}$ is ......... (where,$R$ is radius of earth,$M$ is mass of the earth and $G$ is gravitational constant)