Two planets $P_{1}$ and $P_{2}$ with equal mass have radii $R_{1}$ and $R_{2}$, respectively, where

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Two planets $P_{1}$ and $P_{2}$ with equal mass have radii $R_{1}$ and $R_{2}$, respectively, where $R_{2} = \frac{R_{1}}{2}$. The escape speeds of $P_{1}$ and $P_{2}$ are $v_{1}$ and $v_{2}$, respectively. Then $\frac{v_{2}}{v_{1}}$ is:

Accepted Answer

Sol. [Key Concept: Gravitation — g and escape velocity on planets] $V_{e} = \sqrt{2gR} = \sqrt{\frac{2GM}{R}}$$$\begin{matrix} & V_{e} \propto \frac{1}{\sqrt{R}}\ \lbrack\because M = 	ext{~}	ext{constant}	ext{~}brack \ & \frac{V_{e2}}{V_{e1}} = \sqrt{\frac{R_{1}}{R_{2}}} = \sqrt{2} \end{matrix}$$

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