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
$\frac{{(P + Q\sin \theta )}}{{(mg + Q\cos \theta )}}$
$\frac{{(P\cos \theta + Q)}}{{(mg - Q\sin \theta )}}$
$\frac{{(P + Q\cos \theta )}}{{(mg + Q\sin \theta )}}$
$\frac{{(P\sin \theta - Q)}}{{(mg - Q\cos \theta )}}$
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
By drawing the free body diagram of the block for critical condition
$F = \mu \,R$ $⇒$ $P + Q\sin \theta $
$ = \mu \,(mg + Q\cos \theta )$
$\therefore \mu = \frac{{P + Q\sin \theta }}{{mg + Q\cos \theta }}$
$F = \mu \,R$ $⇒$ $P + Q\sin \theta $
$ = \mu \,(mg + Q\cos \theta )$
$\therefore \mu = \frac{{P + Q\sin \theta }}{{mg + Q\cos \theta }}$
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