If the potential at the surface of the Earth is assigned a zero value,then the potential at the center of the Earth will be (Mass $= M$,Radius $= R$).

If the gravitational field intensity at a point is given by $E = K/x^3$,what is the gravitational potential at that point?

Compare the gravitational potential at the center $O$ for the given arcs,each having mass $M$ and radius $R$.

Find the potential energy of a system of four particles,each of mass $m$,placed at the vertices of a square of side $l$. Also,obtain the gravitational potential at the centre of the square.

$A$ geostationary satellite orbits the Earth at a height of nearly $36,000 \; km$ from the surface of the Earth. What is the potential due to Earth's gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the Earth $= 6.0 \times 10^{24} \; kg$,radius $= 6400 \; km$.

The gravitational field in a region is given by $E = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. If a particle of mass $2 \text{ kg}$ is moved from the origin to the point $(12 \text{ m}, 15 \text{ m})$ in this region,the change in gravitational potential energy is (in $\text{ J}$)