Question

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

Answer 1

$v=\sqrt{gR}=\sqrt{\frac{GM}R}=\sqrt{\frac{G\rho V}R}=\sqrt{\frac{G\rho \frac 43 \pi R^3}R}=R\sqrt{\frac 43\pi \rho G,}$

$v\sim R,$

$v_2=4v_1.$