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 coefficient of friction between the block and the surface is

• A. $\frac{(P+Qsin\theta )}{(mg+Qcos\theta )}$
• B. $\frac{(Pcos\theta +Q)}{(mg-Qsin\theta )}$
• C. $\frac{(P+Qcos\theta )}{(mg+Qsin\theta )}$
• D. $\frac{(Psin\theta -Q)}{(mg-Qcos\theta )}$

Answer 1

The correct option is A $\frac{(P+Qsin\theta )}{(mg+Qcos\theta )}$

$f=P+Q\sin \theta$, where f is the frictional force
$\mu N=P+Q\sin \theta$
$\mu (mg+Q\cos \theta )=P+Q\sin \theta$

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