The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the Earth is $U$. Express the weight of the body at this point in terms of $U$.

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:

An infinite number of objects,each of mass $1 \ kg$,are placed on the $x$-axis on both sides of $x=0$ at positions $x = \pm 1 \ m, \pm 2 \ m, \pm 4 \ m, \pm 8 \ m, \ldots$ and so on. The magnitude of the resultant gravitational potential (in $SI$ units) at $x=0$ is ($G$ is the universal gravitational constant).

Gravitational potential difference between the surface of a planet and a point situated at a height of $20\,m$ above its surface is $2\,J/kg$. If the gravitational field is uniform,then the work done in taking a $5\,kg$ body to a height of $4\,m$ above the surface will be ........ $J$.

Two bodies of masses $4 \,m$ and $9 \,m$ are separated by a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field becomes zero is:

From a solid sphere of mass $M$ and radius $R$,a spherical portion of radius $R/2$ is removed,as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty$,the potential at the centre of the cavity thus formed is
($G =$ gravitational constant)