A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination 45 ° . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder axis will be:-

Physics · Rotational Dynamics

JEE Main 2025 — 24 January, Morning Shift — Question 57

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination $45^{\circ}$ . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder axis will be:-

Option A:
$\frac{1}{\sqrt{2}} g$
Option B:
$\frac{1}{3 \sqrt{2}} g$
Option C:
$\frac{\sqrt{2} g}{3}$
Correct
Option D:
$\sqrt{2} g$

Answer: C

Step-by-step solution

$\mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^{2}}}$

$a=\frac{\frac{g}{\sqrt{2}}}{1+\frac{1}{2}}=\frac{2 \frac{g}{\sqrt{2}}}{3}=\frac{\sqrt{2} g}{3}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 24 January, Morning Shift
Subject: Physics
Chapter: Rotational Dynamics
Topic: Rolling Motion