In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth, the work done is

Given that 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

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is

Maximum height reached by an object projected perpendicular to the surface of the earth with a speed equal to $50\%$ of the escape velocity from earth surface is - ( $R =$ Radius of Earth)

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is

A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on  the surface of the shell is