Physics · Gravitation

JEE Main 2024 — 6 April, Shift 1 — Question 34

To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_{E}, g=$ acceleration due to gravity on the surface of earth) :

Option A:
$2 \mathrm{mgR}_{\mathrm{E}}$
Option B:
$\mathrm{mgR}_{\mathrm{E}}$
Correct
Option C:
$\frac{1}{2} \operatorname{mgR}_{\mathrm{E}}$
Option D:
$4 \mathrm{mgR}_{\mathrm{E}}$

Answer: B

Step-by-step solution

$\frac{1}{2} \mathrm{mv}_{\mathrm{e}}^{2}=\frac{\mathrm{GMm}}{\mathrm{R}_{\mathrm{E}}}$

$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}_{\mathrm{E}}^{2}}$

$\mathrm{K}=\mathrm{mgR}_{\mathrm{E}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Gravitation
Topic: Motion of Satellites and Escape Speed