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)

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 $