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 ...............

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

Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

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)

$A$ shell of mass $M$ and radius $R$ has a point mass $m$ placed at a distance $r$ from its centre. The gravitational potential energy $U(r)$ vs $r$ graph will be:

In a certain region of space,the gravitational field is given by $E = -\frac{K}{r}$,where $r$ is the distance from a fixed point and $K$ is a constant. Taking the reference point to be at $r = r_0$ with potential $V = V_0$,the potential at a distance $r$ is: