Question

A satellite orbiting earth in a circular orbit of radius $4R_e$ is suddenly stopped and then released. This satellite then fall onto surface of earth at speed of $\sqrt{\frac{nGM}{R_e}}$ then n is [where $R_e$ is radius of earth] (Answer upto two digits after the decimal point.)

Answer 1

By conservation of energy,

$\frac{-GMm}{4R_e}=\frac{-GMm}{R_e}+\frac{1}{2}m{v}^2$
$\frac{v^2}{2}=\frac{3}{4}\frac{GM}{R_e}\Rightarrow v=\sqrt{\frac{3}{2}\frac{GM}{R_e}}$