Question

A board is balanced on a rough horizontal semicircular log. Equilibrium is obtained with the help of addition of a weight on the board, when the board makes an angle $\theta$ with the horizontal. Coefficient of friction between the log and the board is:

• A. $\tan \theta$
• B. $\cos \theta$
• C. $\cot \theta$
• D. $\sin \theta$

Answer 1

The correct option is A $\tan \theta$

For equilibrium condition
$(M+m)g\sin \theta =\mu (M+m)g\cos \theta$
$\tan \theta =\mu$
Here $\mu \to$ coefficient of friction between board & log.