Question

If the potential energy of a $3kg$ body at the surface of a planet is $-54J$, then its escape velocity (in $m/s$ ) will be

Answer 1

Answer: 6

Gravitational potential energy $=\frac{-GMm}{R}$
$-54=\frac{-GM\times 3}{R}$
Hence, $\frac{GM}{R}=18$
But $v_{\text{esc }}=\sqrt{\frac{2GM}{R}}=\sqrt{36}=6m/s$