Question

The coefficient of friction for an inclined plane inclined at angle $\alpha$ with horizontal in order that a solid cylinder will roll down without slipping is

• A. $\frac{2}{3}\tan \alpha$
• B. $\frac{2}{7}\tan \alpha$
• C. $\tan \alpha$
• D. $\frac{5}{7}\tan \alpha$

Answer 1

Answer: (C)

$\tan \alpha$

Acceleration of point A must be zero due to pure rolling.

Thus $mgsin\alpha -f=0$ for point A

$mgsin\alpha -\mu mgcos\alpha =0$

$⟹\mu =tan\alpha$