$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

If the escape velocity of a body from the surface of the earth is $11.2 \,km \,s^{-1}$, then the orbital velocity of a satellite in an orbit which is at a height equal to the radius of the earth is

The distance between two stars of masses $3 M_S$ and $6 M_S$ is $9 R$. Here $R$ is the mean distance between the centers of the Earth and the Sun,and $M_S$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $n T$,where $T$ is the period of Earth's revolution around the Sun. The value of $n$ is. . . . .

Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is

What is the effect on the time period of a satellite orbiting around the Earth if its height decreases?

Two satellites of masses $m$ and $3\,m$ revolve around the earth in circular orbits of radii $r$ and $3r$ respectively. The ratio of orbital speeds of the satellites respectively is: