The acceleration due to gravity at a height of $(\sqrt{2}-1) \mathrm{R}$ from the surface of the Earth is

(Acceleration due to gravity on the surface of the Earth $=10 \mathrm{~ms}^{-2}$ and $R$ is radius of the Earth)

The escape velocity of a body from a planet of mass $M$ and radius $R$ is $14 \mathrm{~km} \mathrm{~s}^{-1}$. The escape velocity of the body from another planet having same mass and diameter 8 R (in $\mathrm{km} \mathrm{s}^{-1}$ ) is

The potential energy of a satellite of mass ' $m$ ' revolving around the Earth at a height of $R_e$ from the surface of the Earth is

( $R_e=$ Radius of Earth, $\mathrm{g}=$ acceleration due to gravity)

The time period of a simple pendulum on the surface of the Earth is $T$. If the pendulum is taken to a height equal to half of the radius of the Earth, then its time period is