Question

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is $ v, $ then the escape velocity from the planet is

• A. $ \sqrt{3}\,v $
• B. $ \sqrt{2}\,v $
• C. $ \sqrt{5}\,v $
• D. $ \sqrt{12}\,v $

Answer 1

Answer: (A)

Escape velocity from the earth
$ {{v}_{e}}=\sqrt{\frac{2GM}{R}} $
For a given planet
$ {{v}_{p}}=\sqrt{\frac{2G(6M)}{2R}}=\sqrt{3}{{v}_{e}}=\sqrt{3}v $