If the gravitational potential on the surface of the earth is $V_0$,then the potential at a point at a height equal to half of the radius of the earth is ..........

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).

Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is

If three particles each of mass $M$ are placed at the corners of an equilateral triangle of side $a$,the potential energy of the system and the work done if the side of the triangle is changed from $a$ to $2a$,are

In a certain region of space,the gravitational field is given by $E = -k/r$,where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ is $V_0$,then what is the expression for the gravitational potential $V$?

Obtain an expression for the gravitational potential at a point in the gravitational field of the Earth. Give the relation between gravitational potential and gravitational potential energy.