The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ is

The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If $R$ is the radius of earth, then radius of the planet would be

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relation is correct? [h $h_1 \ll R, h_3 \gg h_2=R, R=$ radius of the earth ]

A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant angular velocity ' $\omega$ '. The angular momentum of satellite is ( $\mathrm{G}=$ Universal constant of gravitation)