$A$ body of mass $m$ starts falling from a point $2R$ above the Earth's surface. What is its kinetic energy when it has fallen to a point $R$ above the Earth's surface? [$R$ = Radius of Earth,$M$ = Mass of Earth,$G$ = Gravitational Constant]

Write the change in gravitational potential energy of a body lifted at height $h$ from the surface of Earth.

What is the minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ to an altitude of $2R$?

$A$ body is projected vertically upwards from the Earth's surface of radius $R$ with a velocity equal to $\frac{1}{3}$ of the escape velocity. The maximum height reached by the body is

$A$ mass '$m$' on the surface of the Earth is shifted to a height equal to the radius of the Earth. If '$R$' is the radius and '$M$' is the mass of the Earth,then the work done in this process is:

Two planets have masses $M$ and $16\, M$ and their radii are $a$ and $2\, a$ respectively. The separation between the centres of the planets is $10\, a.$ $A$ body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of the smaller planet,the minimum firing speed needed is