If the gravitational potential of an object of mass $m$ on the surface of the Earth is $\phi$,what is the gravitational potential of an object of mass $2m$?

The masses $m$ in figures $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

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

$A$ 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 $= 6400 \; km$.

Write the expression for gravitational potential energy and gravitational potential at the surface of the Earth.

$A$ 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: