The gravitational potential energy of a body of mass $m$ at the earth's surface is $-mgR_e$. Its gravitational potential energy at a height $R_e$ from the earth's surface will be (Here $R_e$ is the radius of the earth).

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

Four particles each of mass $m$ are placed at the vertices of a square of side $l.$ The potential energy of the system is

What is the binding energy of a body of mass $m$ lying on the surface of the Earth at a distance $r$ from the center of the Earth?

Three masses $m, 2m$ and $3m$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$. The work done by an external agent in changing the configuration from figure $1$ to figure $2$ is:

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