Question

A block of weight 200 N is pulled along a rough horizontal surface at a constant speed by a force of 100 N acting at an angle of ${30}^{\circ }$ above the horizontal. The coefficient of friction between the block and the surface is

• A. 0.43
• B. 0.58
• C. 0.75
• D. 0.85

Answer 1

The correct option is B

0.58

Since the block moves with a constant velocity, no net force acts on it. Therefore, the horizontal component $Fcos\theta$ of force F must balance the frictional force force, i.e., $f_r=Fcos\theta$.

Now, $N+Fsin\theta =mg\Rightarrow N=mg-Fsin\theta$
Also, $f_r=\mu N=\mu (mg-Fsin\theta )\Rightarrow Fcos\theta =\mu (mg-Fsin\theta )\Rightarrow \mu =\frac{Fcos\theta }{mg-Fsin\theta }=\frac{100\times \frac{\sqrt{3}}{2}}{200-100\times \frac{1}{2}}=\frac{1}{\sqrt{3}}=0.58$
Hence, the correct choice is (b).