Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is

$A$ body of mass $m$ is kept at a small height $h$ above the ground. If the radius of the earth is $R$ and its mass is $M$,the potential energy of the body and earth system (with $h = \infty$ being the reference position) is

$A$ 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 $\left[G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}\right]$

The bodies of masses $100 \,kg$ and $8100 \,kg$ are held at a distance of $1 \,m$. The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in $J/kg$ is $\left(G = 6.67 \times 10^{-11} \,Nm^2/kg^2\right)$

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

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 $= R$).