Question

Block $M$ slides down a frictionless incline as shown. Find the minimum friction coefficient so that $m$ does not slide with respect to $M$.

Answer 1

Let the slope of the inclination is $\theta$.

Hence component of weight along the slide $=mg\sin \theta$

Normal component of weight , $N=mgcos\theta$

$\Rightarrow$ force of friction $=F=\mu N=\mu mg\cos \theta$

For the block does not slide $F=mg\sin \theta$

$\Rightarrow \mu mg\cos \theta =mg\sin \theta$

$\Rightarrow \mu \cos \theta =\sin \theta$

$\Rightarrow \mu =\tan \theta$

So the block does not slide if the co-efficient of the friction will be $\tan \theta$