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  4. The escape velocity for the earth is V e. The escape velocity for a planet whose radius (1/4) th radius of earth and mass half that of earth is

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Q. The escape velocity for the earth is $V _{e}$. The escape velocity for a planet whose radius $\frac{1}{4}$ th radius of earth and mass half that of earth is

Gravitation

Solution:

$V_{e}=\sqrt{\frac{2 G M_{e}}{R_{e}}}$
$M_{p}=\frac{M_{e}}{2}, R_{p}=\frac{R_{e}}{4}$
$V'_{e}=\sqrt{\frac{2 G M_{e} \times 4}{2 R_{e}}}=\sqrt{2} V_{e}$