$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a.$ The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre,will be

Four identical particles of equal masses $m = 1 \, kg$ are made to move along the circumference of a circle of radius $R = 1 \, m$ under the action of their own mutual gravitational attraction. The speed of each particle will be

If a satellite orbits as close to the earth's surface as possible,

Four particles,each of mass $M$ and equidistant from each other,move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

$A$ study of binary stars is most helpful in

$A$ 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