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

The Correct Option is A

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