Q 11-07-010NEETNEET 2021Top questionEasy
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: (A) $4v$
$$v_e = \sqrt{\frac{2GM}{R}} = \sqrt{\frac{2G \cdot \frac{4}{3}\pi R^3\rho}{R}} = R\sqrt{\frac{8\pi G\rho}{3}} \propto R$$
With the same density and $4$ times the radius: $v_e' = 4v$.
Solution by Sreeraj P, M.Sc Physics