Q. The escape velocity of a planet having mass $6$ times and radius $2$ times as that of earth is

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A

$\sqrt{3}\, V_{e}$

55%

B

$3\, V_{e}$

18%

C

$\sqrt{2}\, V_{e}$

18%

D

$2\, V_{e}$

9%

Solution:

$\frac{v_{p}}{v_{e}}=\sqrt{\frac{M_{p}}{M_{e}} \times \frac{R_{e}}{R_{p}}}$
$=\sqrt{6 \times \frac{1}{2}}=\sqrt{3}$
$\therefore v_{p}=\sqrt{3} v_{e}$

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