Physics · Gravitation

JEE Main 2024 — 27 January, Shift 1 — Question 33

The acceleration due to gravity on the surface of earth is $g$ If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

Option A:
$g / 4$
Option B:
$2 g$
Option C:
$g / 2$
Option D:
$4 g$
Correct

Answer: D

Step-by-step solution

$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \Rightarrow \mathrm{~g} \propto \frac{1}{\mathrm{R}^{2}}$ $\frac{\mathrm{g}_{2}}{\mathrm{~g}_{1}}=\frac{\mathrm{R}_{1}^{2}}{\mathrm{R}_{2}^{2}}$

$\mathrm{g}_{2}=4 \mathrm{~g}_{1}\left(\mathrm{R}_{2}=\frac{\mathrm{R}_{1}}{2}\right)$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 27 January, Shift 1
Subject: Physics
Chapter: Gravitation
Topic: Gravitational Field and Gravity