question_answer

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                     [Haryana CEE 1996]

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) \[\frac{(P\sin \theta -Q)}{(mg-Q\cos \theta )}\]

Correct Answer: A

Solution :

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