$A$ 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:

$A$ planet is revolving around the sun in a circular orbit with a radius $r$. The time period is $T$. If the force between the planet and the star is proportional to $r^{-3/2}$,then the square of the time period is proportional to

Two satellites are revolving around the Earth with orbital velocities $v_1$ and $v_2$ at radii $r_1$ and $r_2$ respectively,where $r_1 > r_2$. Then:

The distance of a geostationary satellite from the centre of the earth (Radius $R = 6400 \ km$) is nearest to (in $R$)

Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4R$ and $R$,respectively. If the speed of satellite $A$ is $3v$,then the speed of satellite $B$ is:

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication.
$(a)$ Calculate the height of such a satellite.
$(b)$ Find out the minimum number of satellites that are needed to cover the entire Earth,so that at least one satellite is visible from any point on the equator.
Given: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.