Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its centre. In that region,a small star is in a circular orbit of radius $R$. Then the period of revolution,$T$ depends on $R$ as

Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively,measured from the centre of mass of the system. The magnitude of the gravitational force that $m_1$ exerts on $m_2$ is

Two satellites $A$ and $B$ move around the Earth in the same orbit. The mass of $A$ is twice the mass of $B$. The quantity which is the same for the two satellites will be:

$A$ small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force between the planet and the star were proportional to $R^{-5/2}$,then $T$ would be proportional to: