A) \[mg\,\,\sin \,\theta \]
B) \[\mu mg\,\,\cos \,\theta \]
C) \[\mu mg\,\,\cos \,\theta +mg\,\,\sin \,\theta \]
D) \[\mu mg\,\,\cos \,\theta -mg\,\,\sin \,\theta \]
Correct Answer: D
Solution :
The free body diagram showing the various forces acting on the block are as follows: The frictional force \[({{F}_{k}})\] acts opposite to direction of motion of block, given by \[{{F}_{k}}=\mu R\] where R is reaction of the plane on block. \[R=mg\,\,\cos \theta \] \[\therefore \] \[{{F}_{k}}=\mu mg\,\,\cos \theta \] Also, downward force is \[F'=mg\,\,\sin \theta \] The resultant of F' and F provides the necessary acceleration to the block. \[\therefore \] Resultant force upwards \[=\mu mg\,\cos \theta -mg\sin \theta \]You need to login to perform this action.
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