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  4. The escape velocity for the earth is 11.2 km / sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is:

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Q. The escape velocity for the earth is $11.2 \,km / sec$. The mass of another planet $100$ times mass of earth and its radius is $4$ times radius of the earth. The escape velocity for the planet is:

JIPMERJIPMER 2003Gravitation

Solution:

$v_{\text {escape }}=\sqrt{\frac{2 G M}{R}} \propto \sqrt{\frac{M}{R}}$,
Hence, $\frac{v_{p}}{v_{e}}=\sqrt{\frac{M_{p}}{R_{p}} \times \frac{R_{e}}{M_{e}}}$
or $\frac{v_{p}}{v_{e}}=\sqrt{100 \times \frac{1}{4}}=5$
$v_{p}=5 \times 11.2=56 \,km / sec$