Physics · Gravitation

JEE Main 2024 — 31 January, Shift 2 — Question 44

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:

Option A:
$\frac{v}{3}$
Correct
Option B:
$\frac{\mathrm{V}}{4}$
Option C:
$\frac{\mathrm{v}}{12}$
Option D:
$\frac{v}{6}$

Answer: A

Step-by-step solution

$\mathrm{V}_{\text {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$

$\mathrm{V}_{\text {planet }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V}$

$\mathrm{V}_{\text {Moon }}=\sqrt{\frac{2 \mathrm{GM} \times 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$

$\mathrm{V}_{\text {Moon }}=\frac{\mathrm{V}_{\text {Planet }}}{3}=\frac{\mathrm{V}}{3}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 31 January, Shift 2
Subject: Physics
Chapter: Gravitation
Topic: Motion of Satellites and Escape Speed