Q 11-07-052JEE MainJEE Main 2025 (28 Jan, Shift 2)Easy
Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is $11.2\ \text{km/s}$, the escape velocity in km/s from the planet will be
Answer: (C) $5.6$
$v_e = \sqrt{\dfrac{2GM}{R}} \propto \sqrt{\dfrac{M}{R}}$.
$$\frac{v_p}{v_e} = \sqrt{\frac{M/8}{R/2}\cdot\frac{R}{M}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \Rightarrow v_p = 5.6\ \text{km/s}$$
Solution by Sreeraj P, M.Sc Physics