The mass of planet is six times that of 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 :

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$v$

$\sqrt{3} v$

$\sqrt{5} v$

$\sqrt{2} v$

answer is A.

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Detailed Solution

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

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