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

Given that the mass of the Earth is $M$ and its radius is $R$. $A$ body is dropped from a height equal to the radius of the Earth above the surface of the Earth. When it reaches the ground,its velocity will be:

The escape velocity from a planet is $V_e$. $A$ tunnel is dug along the diameter of the planet and a small body is dropped into it. The speed of the body at the centre of the planet will be

Assuming that the gravitational potential energy of an object at infinity is zero,the change in potential energy (final - initial) of an object of mass $m$,when moved to a height $h$ from the surface of the Earth (of radius $R$),is given by:

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

From the pole of the earth,a body of mass $m$ is imparted a velocity $v_0$ directed vertically up. If $M$ is the mass of the earth,$R$ its radius and $g$ is the free-fall acceleration on its surface,then the height $h$ to which the body will ascend is (neglect air resistance).