Question

Block of mass $10kg$ is moving on an inclined plane with constant velocity $10m/s$. The coefficient of kinetic friction between the incline plane and block is:

• A. $0.57$
• B. $0.75$
• C. $0.5$
• D. None of these

Answer 1

The correct option is B $0.75$

$\sum Fy=0$

$\Rightarrow N-mg\cos \theta =0$

$\Rightarrow N=mg\cos \theta ----\left(1\right)$

$Fx=0$ (as constant velocity $\Rightarrow$ No acceleration)

$\Rightarrow mg\sin \theta -{\mu }_{k}N=0$

$\Rightarrow mg\sin \theta -{\mu }_{k}mg\cos \theta =0$ |From (1)

$\Rightarrow \cos \theta (\tan \theta -{\mu }_k)=0$

$\Rightarrow {\mu }_k=\tan \theta =\tan {37}^o=\frac{3}{4}=0.75$