The potential energy of a satellite of mass $m$ revolving at a height $R_e$ above the surface of the Earth,where $R_e$ is the radius of the Earth,is:

The particles $A$ and $B$ of mass $m$ each are separated by a distance $r$. Another particle $C$ of mass $M$ is placed at the midpoint of $A$ and $B$. Find the work done in moving $C$ to a point equidistant $r$ from $A$ and $B$ without acceleration. ($G$ is the gravitational constant and only gravitational interaction between $A, B$ and $C$ is considered.)

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)

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

When an object is brought from infinity to a distance $r$ from a mass,its gravitational potential energy ....... . (Fill in the blank)

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 $= R$).