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) For equilibrium of the block
[image:5_image230.emf]
$N = mng + Q\cos\theta$
$Q\sin\theta + P = \mu N$
$Q\sin\theta + P = \mu(mg + Q\cos\theta)$
$\mu = \left( \frac{Q\sin{\theta + P}}{mg + Q\cos\theta} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.