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Q.

The escape velocity of a body on a planet ‘A’ is 12 kms^-1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A ', is :

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a

36 ${kms}^{- 1}$

b

12 ${kms}^{- 1}$

c

24 ${kms}^{- 1}$

d

6 ${kms}^{- 1}$

answer is A.

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Detailed Solution

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$\begin{array}{l} V_{esape} = \sqrt{\frac{2 Gm}{R}} \Rightarrow \sqrt{\frac{2 Gρ \times \frac{4}{3} {πR}^{3}}{R}} \\ V_{escape} \propto \sqrt{{ρR}^{2}} \end{array}$
$∴$ if $ρ$ is 4 times and Radius is halved.
$\Rightarrow V_{escape}$ will remain same

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