question_answer

A body of mass m rests on horizontal surface, the coefficient of friction between the body and the surface is 4, if the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be:                                                                                                                                                                              [BHU PMT-2004]

A)  \[\mu mg\]                                       

B)  \[\mu \left[ mg+\left( \frac{P}{2} \right) \right]\]

C)  \[\mu \left[ mg-\left( \frac{P}{2} \right) \right]\]            

D) \[\mu \left[ mg-\left( \frac{\sqrt{3}P}{2} \right) \right]\]

Correct Answer: C

Solution :

                 Key Idea: Sketch the free body diagrams. Resoles the force \[P\] is horizontal and vertical components. The free body diagram of the various forces acting on body is shown. \[R\] is the reaction of the surface on mass, \[{{f}_{s}}\] is frictional force. Taking the horizontal and vertical components, we have                                 \[R=mg-P\,\sin \,\,{{30}^{\circ }}=mg-\frac{P}{2}\] Limiting frictional force is                 \[F=\mu R=\mu \left[ mg-\frac{P}{2} \right]\]