The magnitudes of the gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then-

$A$ satellite of mass $5M$ 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 the opposite direction. After the explosion,the mass $4M$ is in:

Two point masses of mass $4m$ and $m$ respectively,separated by a distance $d$,are revolving under their mutual force of attraction. The ratio of their kinetic energies is:

During the motion of a planet from perihelion to aphelion,the work done by the gravitational force of the sun on it is ...........

$A$ spiral galaxy can be approximated as an infinitesimally thin disc of uniform surface mass density located at $z=0$. Two stars $A$ and $B$ start from rest from heights $2z_{0}$ and $z_{0}$ (where $z_{0} \ll$ radial extent of the disc),respectively,and fall towards the disc,cross over to the other side,and execute periodic oscillations. The ratio of the time periods of $A$ and $B$ is

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)