A body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$ , and the other mass, in a circular orbit of radius $\frac{3R}{2}$. The difference between the final and initial total energies is

The gravitational potential energy of a body of mass $‘m’$ at the earth’s surface $ – mg{R_e}$. Its gravitational potential energy at a height ${R_e}$ from the earth’s surface will be (Here ${R_e}$ is the radius of the earth)

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 ……….

Asatellite of mass $5\,M$ orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes into two pieces, one of mass $M$ and the other of mass $4M.$ After the explosion the mass $M$ ends up travelling in the same circular orbit, but in opposite direction. After explosion the mass $4M$ is in

If radius of an orbiting satellite is decreased, then its kinetic energy