Question

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:

• 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] $

Answer 1

The Correct Option is C

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] $