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) $22.4\ \text{km/s}$
Write mass in terms of density: $M = \tfrac43\pi R^3 \rho$.
$$v_e = \sqrt{\frac{2GM}{R}} = \sqrt{\tfrac83 \pi G \rho}\; R \;\Rightarrow\; v_e \propto R \ \text{(same } \rho)$$
Doubling $R$ doubles $v_e$: $2 \times 11.2 = 22.4\ \text{km/s}$.
Solution by Sreeraj P, M.Sc Physics