Question

The minimum coefficient of static friction between a plane and a cylinder, for the cylinder not slipping on the inclined plane is given by $\mu =\left(\frac{tan\theta }{I}\right)$, the value of I will be ___

Answer 1

$mgsin\theta -f=mafR=\tau =I\alpha =\frac{mRa}{2}a=\frac{2}{3}gsin\theta f_s=\mu mgcos\theta \Rightarrow \frac{mgsin\theta }{3}=\mu mgcos\theta \mu =\frac{tan\theta }{3},I=3$