Question

A mass $m$ rests on a horizontal surface. The coefficient of friction between the mass and the surface is $\mu$. If the mass is pulled by a force $F$ as shown in figure, the limiting friction between the mass and the surface will be

• A. $\mu mg$
• B. $\mu [mg-\left(\frac{\sqrt{3}}{2}F\right)]$
• C. $\mu [mg-\left(\frac{F}{2}\right)]$
• D. $\mu [mg+\left(\frac{F}{2}\right)]$

Answer 1

The correct option is B $\mu [mg-\left(\frac{\sqrt{3}}{2}F\right)]$

By free body diagram,
Resolving the forces in horizontal and vertical direction,
the limiting friction will be equal to the horizontal force for equilibrium.
$f=\frac{F}{2}=\mu N$
Also, $N=mg-\frac{\sqrt{3}}{2}F$
$\Rightarrow f=\mu (mg-\frac{\sqrt{3}}{2}F)$

Hence option B is the correct answer