Physics - Gravitation Question with Solution | TestHub

For escape velocity the formula is, $v_e=\sqrt{\frac{2GM}{R}}=\frac{\sqrt{2G\left(\frac{4}{3}\pi R^3\right)\rho }}{R}=\sqrt{\frac{8}{3}G\pi R^2\rho }$ Where, $\rho$ is density of the planet and $\mathrm{R}$ is its radius. $\begin{array}{rl}& \therefore v_e=R\sqrt{\frac{8}{3}G\pi \rho }\\ & \therefore v_e\propto R\end{array}$ So, the escape velocity on the planet would be $22.4\mathrm{km}/\mathrm{s}$.