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

$A$ thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$. The work required to take a unit mass from point $P$ on its axis to infinity is

$A$ body of mass $m$ is taken from the Earth's surface to a height $h$ equal to twice the radius of the Earth $(R_e)$. The increase in potential energy will be: (where $g$ is the acceleration due to gravity on the surface of the Earth)

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 an equation for the potential energy of a satellite. Why is the potential energy of a satellite negative?

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)