Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is $11.2 \mathrm{~km} / \mathrm{s}$, the escape velocity in $\mathrm{km} / \mathrm{s}$ from the planet will be :

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{V}_{	ext {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \ & \frac{\left(\mathrm{V}_{	ext {escape }}ight)_{	ext {Planet }}}{\left(\mathrm{V}_{	ext {escape }}ight)_{	ext {Earth }}}=\sqrt{\left(\frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{M}_{\mathrm{E}}}ight) 	imes\left(\frac{\mathrm{R}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{P}}}ight)}=\frac{1}{2} \ & \left(\mathrm{~V}_{	ext {escape }}ight)_{	ext {Planet }}=\frac{1}{2}\left(\mathrm{~V}_{	ext {escape }}ight)_{	ext {Earth }}=5.6 \mathrm{~km} / \mathrm{s}\end{aligned}$

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is $11.2…

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