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The ratio of the acceleration due to gravity on two planets $\mathrm{P}_1$ and $\mathrm{P}_2$ is $\mathrm{K}_1$. The ratio of their respective radii is $\mathrm{K}_2$. The ratio of their respective escape velocities is
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The correct answer is:
$\sqrt{\mathrm{K}_1 \mathrm{~K}_2}$
Since escape velocity from the surface of a planet can be written as $v_e=\sqrt{2 g \mathrm{R}}$
$\text { ratio } \frac{v_{e p_1}}{v_{e p_2}}=\sqrt{\frac{2 g_{p_1} \mathrm{R}_{p_1}}{2 g_{p_2} \mathrm{R}_{p_2}}}=\sqrt{\mathrm{K}_1 \mathrm{~K}_2}$
$\text { ratio } \frac{v_{e p_1}}{v_{e p_2}}=\sqrt{\frac{2 g_{p_1} \mathrm{R}_{p_1}}{2 g_{p_2} \mathrm{R}_{p_2}}}=\sqrt{\mathrm{K}_1 \mathrm{~K}_2}$
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