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The escape velocity from the Earth's Surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:

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2 v

3 v

4 v

answer is A.

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Detailed Solution

$\begin{array}{l} V_{e} = \sqrt{\frac{2 GM}{R}} = \sqrt{\frac{2 G \frac{4}{3} {πR}^{3} ρ}{R}} \Rightarrow V_{e} \propto R \\ ∴ \frac{V^{'}}{V} = \frac{4 R}{R} \Rightarrow V^{'} = 4 V \end{array}$

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