Q 11-06-068JEE MainJEE Main 2025 (24 Jan, Shift 1)Easy
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's axis will be
Answer: (C) $\dfrac{\sqrt2}{3}g$
For rolling without slipping, $a = \dfrac{g\sin\theta}{1 + k^2/r^2}$. For a solid cylinder $k^2/r^2 = \tfrac{1}{2}$:
$$a = \frac{2}{3}g\sin45^\circ = \frac{2}{3}\cdot\frac{g}{\sqrt2} = \frac{\sqrt2}{3}g$$
Solution by Sreeraj P, M.Sc Physics