The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter is $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be :
Solution
<p>$$\begin{aligned}
& \mathrm{V}_{\text {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\
& \mathrm{V}_{\text {planet }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V} \\
& \mathrm{V}_{\text {Moon }}=\sqrt{\frac{2 \mathrm{GM} \times 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\
& \mathrm{V}_{\text {Moon }}=\frac{\mathrm{V}_{\text {Planet }}}{3}=\frac{\mathrm{V}}{3}
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Gravitation · Topic: Escape Velocity
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