A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force\[P\]and another force Q is 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) \[\frac{(P\sin \theta -Q)}{(mg-Q\cos \theta )}\]
Correct Answer: A
Solution :
The free body diagram of the block for critical condition is shown below. |
\[F=\mu R\Rightarrow P+Q\,\sin \theta =\mu \,(mg+Q\,\cos \theta )\] |
\[\therefore \] \[\mu =\frac{P+Q\,\sin \theta }{mg+Q\,\cos \theta }\] |
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