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

A satellite orbits the earth at a height of $400\; km$ above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $=200 \;kg ;$ mass of the earth $=6.0 \times 10^{24} \;kg ;$ radius of the earth $=6.4 \times 10^{6}\;m$ ; $G =6.67 \times 10^{-11}\; N m ^{2} kg ^{-2}$

Two masses $m_1\, \& m_2$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of $d$ is :

Give the binding energy of body lying on the earth at distance $r$ from the centre of earth $\left(+\frac{ GM _{ E } m}{r}=\frac{ GM _{e} m}{ R _{ E }+h}\right)$

A satellite of mass $\mathrm{m}$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $\mathrm{R}$ ($R =$ radius of the earth), it ejects a rocket of mass $\frac{\mathrm{m}}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is

($G$ is the gravitational constant: $\mathrm{M}$ is the mass of the earth)