$A$ hollow spherical shell is compressed to half its radius. The gravitational potential at the centre

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

What is the magnitude of potential energy at infinity distance?

Two bodies of mass $m$ and $9 m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero,will be ($G=$ gravitational constant):

An infinite number of bodies,each of mass $2 \, kg$,are situated on the $x-$axis at distances $1 \, m, 2 \, m, 4 \, m, 8 \, m, \dots$ respectively,from the origin. The resulting gravitational potential due to this system at the origin will be:

The mass of the earth is $6.00 \times 10^{24} \ kg$ and that of the moon is $7.40 \times 10^{22} \ kg$. The gravitational constant is $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$. The potential energy of the system is $-7.79 \times 10^{28} \ J$. The mean distance between the earth and the moon is: