Question

A solid cylinder rolls without slipping on an inclined plane inclined at an angle $\theta$. Find the linear acceleration of the cylinder. Mass of the cylinder is $M$.

• A. $a=\frac{1}{3}g\sin \theta$
• B. $a=\frac{2}{3}g\sin \theta$
• C. $a=\frac{1}{3}g\cos \theta$
• D. $a=\frac{2}{3}g\cos \theta$

Answer 1

The correct option is B $a=\frac{2}{3}g\sin \theta$

Force along the incline plane

$mgsin\theta -f=ma$ ....(1)

Writing torque about center

$fr=I\alpha$ ...(2) where $I=\frac{m{r}^2}{2}$ ...(3)

for pure rolling $a=\alpha r$ ...(4)

on solving the above equations we get $a=\frac{2gsin\theta }{3}$