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

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}$. The value of $x$ is (take $R_{\mathrm{e}}=6370 \mathrm{~km}$ ):

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy 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 ……….

If the gravitational acceleration at surface of Earth is $g,$  then increase in potential energy in lifting an object of mass $m$  to a height equal to half of radius of earth from surface will be