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 $S.I.$ unit of gravitational potential is

Give the formula of gravitational potential at distance $r$ $(r > R_E)$ from the centre of the Earth.

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth 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:

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the center of the circle?