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  4. The ratio of escape velocity at earth ve to the escape velocity at a planet vp whose radius and mean density are twice as that of earth is :

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Q. The ratio of escape velocity at earth $v_e$ to the escape velocity at a planet $v_p$ whose radius and mean density are twice as that of earth is :

NEETNEET 2016Gravitation

Solution:

$Ve = \sqrt{\frac{2GM}{R}} = \sqrt{\frac{2G}{R}.\left(\frac{4}{3} \pi R^{3}\rho\right)} \propto R\sqrt{\rho} $
$\therefore $ Ratio = $1 : 2 \sqrt{2}$