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 mass and the surface will be

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

Answer 1

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

From the free body diagram,

$N+F\sin {60}^{\text{o}}=mg$,
$\Rightarrow N=mg-F\sin {60}^{\circ }=mg-\frac{\sqrt{3}F}{2}$

We know that for the limiting friction condition $f=\mu N$

$\therefore$ Limiting friction $=\mu N=\mu (mg-\frac{\sqrt{3}F}{2})$

Hence, option B is the correct answer