Question

Two planets $A$ and $B$ have the same material density. If the radius of $A$ is twice that of $B$ , then the ratio of escape velocity $\frac{v_{A}}{v_{B}}$ is

• A. $2$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$2$

Answer 2

Escape velocity is given by $v_{e} = \sqrt{\frac{2GM}{R}} =\sqrt{\frac{2G}{R} \times \frac{4}{3} \pi R^{3} \rho}$ $\Rightarrow v_{e} =R\sqrt{\frac{8}{3} \pi G\rho}$ $\therefore \frac{v_{A}}{v_{B}} = \frac{R_{A}}{R_{B}} = 2$