Question

A force of $30\text{N}$ is sufficient just to pull a block of mass $4\text{kg}$, horizontally over a flat rough surface. The angle of friction is

• A. ${45}^{\circ }$
• B. ${53}^{\circ }$
• C. ${37}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is C ${37}^{\circ }$

$FBD$

For equilibrium
$R=4g=40N$
$f_s=30N$
Given that body is just about to slide in this situation, so
$\because (f{)}_{max}={\mu }_{s}R=30$
$\Rightarrow {\mu }_s=\frac{30}{40}=0.75$

From definition; Angle of friction $\theta =ta{n}^{-1}\left({\mu }_s\right)=ta{n}^{-1}\left(0.75\right)={37}^{\circ }$