$A$ body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

$A$ geostationary satellite is at a height $h$ above the surface of the Earth. If the Earth's radius is $R$,which of the following statements is correct?

The mass density of a spherical body is given by $\rho(r) = \frac{k}{r}$ for $r \leq R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration,$a$,of a test particle as a function of $r$ 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

Two particles,each of mass $m$,are moving in a circle of radius $R$ under the influence of their mutual gravitational attraction. What is their speed?

The orbital velocity of a body near the surface of a planet $A$ is equal to the escape velocity of a body from the planet $B$. If the masses of planets $A$ and $B$ are the same,the ratio of their radii is