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 $V$?

$A$ hollow spherical shell is compressed to half its radius. The gravitational potential at the centre

Two heavy spheres each of mass $100 \; kg$ and radius $0.10 \; m$ are placed $1.0 \; m$ apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so,is the equilibrium stable or unstable?

The diagram showing the variation of gravitational potential of Earth with distance from the centre of Earth is

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?

$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is: