What is the potential energy of a satellite at a height of $6.4 \times 10^6 \, m$ from the surface of the Earth? ($R_e$ = radius of the Earth)

$A$ particle is kept on the surface of a uniform sphere of mass $1000 \ kg$ and radius $1 \ m$. The work done per unit mass against the gravitational force between them is $\left[G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}\right]$

$A$ 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 $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).

If the gravitational potential energy of two point masses infinitely away is taken to be zero,then the gravitational potential energy of a galaxy is ...............

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

Two concentric shells have masses $M$ and $m$ and their radii are $R$ and $r$ respectively,where $R > r$. If $x$ is the distance from the common centre,what is the gravitational potential at a point for which $r < x < R$?