question_answer

A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is \[\mu .\] If the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be [BHU 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 :

                Normal reaction \[R=mg-P\sin {{30}^{o}}\]\[=mg-\frac{P}{2}\]                 \ Limiting friction between body and surface is given by, \[F=\mu R=\mu \left( mg-\frac{P}{2} \right)\].