Question

A cylinder of mass $m$ and radius $R$ rolls down an incline plane of inclination $\theta$. The linear acceleration of the axis of the cylinder is given as $a=\frac{x}{3}gsin\theta$. Find $x$.

Answer 1

Acceleration of a body rolling down the inclined plane, $a=\frac{gsin\theta }{1+\frac{I}{m{R}^2}}$

For cylinder, $I=\frac{1}{2}m{R}^2$

$⟹a=\frac{2}{3}gsin\theta$