Q 11-07-001NEETMedium
A planet has the same average density as Earth but twice its radius. If the escape speed from Earth is $11.2\ \text{km/s}$, the escape speed from the planet is
Answer: (C) $22.4\ \text{km/s}$
Concept. With $M = \dfrac43\pi R^3\rho$, $v_e = \sqrt{\dfrac{2GM}{R}} = R\sqrt{\dfrac{8\pi G\rho}{3}}$, so $v_e \propto R$ at fixed density.
Step 1. Scale. Doubling $R$ doubles $v_e$: $2 \times 11.2 = 22.4$ km/s.
Answer. $22.4\ \text{km/s}$ (Option C).
Solution by Sreeraj P, M.Sc Physics