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

Answer: (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
$F=\mu R=\mu \left[mg-\frac{P}{2}\right]$