Question

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. $\frac{P\sin \theta -Q}{mg-Q\cos \theta }$

Answer 1

Answer: (A)

For equilibrium of the block
$N=mng+Q\cos \theta$
$Q\sin \theta +P=\mu N$
$Q\sin \theta +P=\mu (mg+Q\cos \theta )$

$\therefore \mu =\left(\frac{Q\sin \theta +P}{mg+Q\cos \theta }\right)$