Question

A body of weight 20 N is on a horizontal surface, minimum force applied to pull it when applied force makes an angle ${60}^0$ with horizontal (angle of friction a = ${30}^0$) is:

• A. 20 N
• B. 20 $\sqrt{3}$ N
• C. $\frac{20}{\sqrt{3}}$ N
• D. zero

Answer 1

The correct option is C $\frac{20}{\sqrt{3}}$ N

For minimum force, we will use limiting friction i.e.

$\Rightarrow \tan \varphi ={\mu }_s$

and ATQ, $\varphi =30$

$\Rightarrow \tan 30={\mu }_s$

$\Rightarrow {\mu }_s=\frac{1}{\sqrt{3}}$

Minimum force can be calculated as $={\mu }_{s}mg$

ATQ, $mg=20N,\mu =\frac{1}{\sqrt{3}}$

$\Rightarrow F_{min}=\frac{20}{\sqrt{3}}N$