The mass of the moon is 1/144 times the mass

JEE MAIN 2024

31.01.24 S2

Question

The mass of the moon is $1 / 144$ times the mass of a planet and its diameter $1 / 16$ times the diameter of a planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be:

Select the correct option:

$\frac{V}{3}$

$\frac{\mathrm{V}}{4}$

$\frac{v}{12}$

$\frac{\mathrm{v}}{6}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} V_{\text {escape }} & =\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\ V_{\text {planet }} & =\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V} \\ \mathrm{V}_{\text {Moon }} & =\sqrt{\frac{2 \mathrm{GM} \times 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\ \mathrm{V}_{\text {Moon }} & =\frac{\mathrm{V}_{\text {Planet }}}{3}=\frac{\mathrm{V}}{3}\end{aligned}$

Question Tags

JEE Main

Physics

Easy

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