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

Physics · Gravitation

JEE Main 2025 — 28 January, Evening Shift — Question 55

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 :

Option A:
11.2
Option B:
5.6
Correct
Option C:
2.8
Option D:
8.4

Answer: B

Step-by-step solution

$\quad V_{\text {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$

$\frac{\left(\mathrm{V}_{\text {escape }}\right)_{\text {Planet }}}{\left(\mathrm{V}_{\text {escape }}\right)_{\text {Earth }}}=\sqrt{\left(\frac{\mathrm{M}_{\mathrm{P}}}{\mathrm{M}_{\mathrm{E}}}\right) \times\left(\frac{\mathrm{R}_{\mathrm{E}}}{\mathrm{R}_{\mathrm{P}}}\right)}=\frac{1}{2}$

$\left(\mathrm{V}_{\text {escape }}\right)_{\text {Planet }}=\frac{1}{2}\left(\mathrm{~V}_{\text {escape }}\right)_{\text {Earth }}=5.6 \mathrm{~km} / \mathrm{s}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Evening Shift
Subject: Physics
Chapter: Gravitation
Topic: Motion of Satellites and Escape Speed