Q. A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
A) $\frac{(P + Q\sin\theta)}{(mg + Q\cos\theta)}$
B) $\frac{(P\cos\theta + Q)}{(mg - Q\sin\theta)}$
C) $\frac{(P + Q\cos\theta)}{(mg + Q\sin\theta)}$
D) $\frac{(P\sin\theta - Q)}{(mg - Q\cos\theta)}$
Explanation
(a) By drawing the free body diagram of the block for critical condition
$F = \mu\ R \Rightarrow P + Q\sin\theta$
$= \mu\ (mg + Q\cos\theta)$
$\therefore\mu = \frac{P + Q\sin\theta}{mg + Q\cos\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.