Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be :

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Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be :

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8.4

2.8

11.2

5.6

answer is B.

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Detailed Solution

$\begin{array}{l} V_{escape} = \sqrt{\frac{2 GM}{R}} \\ \frac{{(V_{escape})}_{Planet}}{{(V_{escape})}_{Earth}} = \sqrt{(\frac{M_{P}}{M_{E}}) \times (\frac{R_{E}}{R_{P}})} = \frac{1}{2} \\ {(V_{escape})}_{Planet} = \frac{1}{2} {(V_{escape})}_{Earth} = 5.6 km / s \end{array}$