A body of mass $m$ is placed on the earth’s surface. It is taken from the earth’s surface to a height $h = 3R$. The change in gravitational potential energy of the body is

A rocket has to be launched from each in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth’s volume is $64$ times the volume of the moon.

To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E, g=$ acceleration due to gravity on the surface of earth) :

Consider two configurations of a system of three particles of masses $m, 2m$ and $3m.$ The work done by external agent in changing the configuration of the system from figure $(i)$ to figure $(ii)$ is

Four particles $A, B, C$ and $D$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $D$ is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $D$ during its movement is ……….