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 :

Correct answer: C. 5.6 aligned & V_ escape = 2 GM R & (V_ escape )_ Planet (V_ escape )_ Earth = ( M_ P M_ E ) ×( R_ E R_ P ) =(1)/(2) & ( V_ escape )_ Planet =(1)/(2)( V_ escape )_ Earth =5.6 km / s aligned

JEE Main 202528 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 28 January
Shift: Evening Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2025 · 28 January · Evening Shift · Physics · Gravitation

Earth has mass 8 times and radius 2 times that of a planet. If the...

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 :

Options

A $2.8$
B $11.2$
C $5.6$
D $8.4$

Correct answer

C. $5.6$

Step-by-step solution

\begin{aligned} & \mathrm{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}\end{aligned}

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