Question

The radius in kilometre to which the present radius of earth ($R=6400\text{km}$) to be compressed so that the escape velocity is increased by $10$ times is ______.

Answer 1

Escape velocity is given by :
$v_e=\sqrt{\frac{2GM}{R}}$

$\Rightarrow v_e\sqrt{R}=$ constant

According to the question,

$v_{e1}\sqrt{R_1}=10v_{e2}\sqrt{R_2}$

$\Rightarrow v_e\sqrt{6400}=10v_e\sqrt{R_2}$

$\Rightarrow R_2=64\text{km}$