$A$ planet of mass $M$ has a satellite of mass $m$,revolving around the planet in a circular orbit of radius $r$ and time period $T$. The mass $(M)$ of the planet is

If the angular velocity of a planet about its axis is halved,the distance of the stationary satellite of this planet from the centre of the planet becomes $2^{n}$ times the initial distance. Then the value of '$n$' is

The distance of a geostationary satellite from the surface of the Earth (radius $R_e = 6400 \ km$) in terms of $R_e$ is ....... (in $R_e$)

$A$ satellite revolving around the earth at a certain height experiences acceleration due to gravity equal to $\frac{16}{49} g_0$,where $g_0$ is the acceleration due to gravity on the earth's surface. If $R$ is the radius of earth,then the square of time period of the satellite's revolution is equal to $K\left[\frac{\pi^2 R^3}{G M}\right]$. The value of $K$ is

The orbital speed of a satellite revolving around a planet in a circular orbit is $v_0$. If its speed is increased by $10 \%$,then ..........

Two satellites $P$ and $Q$ go round a planet in circular orbits having radii $3R$ and $R$ respectively. If the speed of satellite $P$ is $2V$,what will be the speed of satellite $Q$?