Two particles of identical mass are moving in circular orbits under a potential given by $V(r) = K r^{-n}$,where $K$ is a constant. If the radii of their orbits are $r_1$ and $r_2$ and their speeds are $v_1$ and $v_2$,respectively,then:

If $L$ is the angular momentum of a satellite revolving around the Earth in a circular orbit of radius $r$ with speed $v$,then .........

The radius of the orbit of a geostationary satellite is (mean radius of the earth is $R$,angular velocity about its axis is $\omega$,and acceleration due to gravity on the earth's surface is $g$).

$A$ planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^6 \text{ km}$ and $60 \times 10^6 \text{ km}$,respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angles $30^{\circ}$ and $60^{\circ}$ with the major axis of the orbit is:

$A$ geostationary satellite is orbiting the earth at a height of $5R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is:

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$,respectively. If $T_{A}$ and $T_{B}$ are the time periods of star $A$ and star $B$,respectively,then -