Question

A uniform solid cylinder of mass m and radius R is released from the top of a fixed rough inclined plane of inclination $\theta$. The coefficient of friction between the cylinder and the inclined plane is $\mu =\left(1/4\right)\tan \theta$. Find the time taken by the cylinder to reach the bottom.

Answer 1

$mgsin\theta -\mu mgcos\theta$

$a=gsin\theta -\mu gcos\theta$

$a=gsin\theta -\frac{tan\theta }{4}gcos\theta$

$a=gsin\theta -\frac{sin\theta }{cos\theta \times 4}gcos\theta$

$a=gsin\theta -\frac{gsin\theta }{4}$

$\frac{3gsin\theta }{4}$