Question

A board is balanced on a rough horizontal semicircular log. Equilibrium is obtained with the help of addition of a weight to one of the ends of the board when the board makes an angle θ 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

Answer: (A)

$\tan \theta$

Let m be the mass of board and M be the mass placed at one end of board.
For equilibrium, $f\cos \theta =N\sin \theta$
or,$\mu N\cos \theta =N\sin \theta$
$\therefore \mu =\tan \theta$