The ratio of the time periods of a simple pendulum at heights $2 R_E$ and $3 R_E$ from the surface of the Earth is ( $R_E$ is radius of the Earth)

If a body is projected vertically from the surface of the Earth with a speed of $8000 \mathrm{~ms}^{-1}$, then the maximum height reached by the body is

(Radius of the Earth $=6400 \mathrm{~km}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

An object of mass $m$ at a distance of $20 R$ from the centre of a planet of mass $M$ and radius $R$ has an initity velocity $u$. The velocity with which the object hits the surface of the planet is

( $G$-Universal gravitational constant)