In a gravitational field,at a point where the gravitational potential is zero,

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

Three masses $m, 2m$ and $3m$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$. The work done by an external agent in changing the configuration from figure $1$ to figure $2$ is:

Earth has mass $M_{1}$ and radius $R_{1}$. Moon has mass $M_{2}$ and radius $R_{2}$. The distance between their centres is $r$. $A$ body of mass $M$ is placed on the line joining them at a distance $r/3$ from the centre of the Earth. To project the mass $M$ to escape to infinity,the minimum speed required is:

Two bodies of masses $m$ and $9m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them,where the gravitational field is zero,is ($G$ is the universal gravitational constant).

Find the potential energy of a system of four particles,each of mass $m$,placed at the vertices of a square of side $l$. Also,obtain the gravitational potential at the centre of the square.