Question

A block of mass $m$ slides down an inclined plane of inclination $\theta$ with uniform speed. The coefficient of friction between the block and the plane is $\mu$. The contact force between the block and the plane is

• A. $mg\sin \theta \sqrt{1+{\mu }^2}$
• B. $\sqrt{{\left(mg\sin \theta \right)}^2+{\left(\mu mg\cos \theta \right)}^2}$
• C. $mg\sin \theta$
• D. $mg$

Answer 1

The correct option is C $mg\sin \theta$

When the book is placed on an inclined plane and its angle of inclination is some angle theta. It is given that the velocity of the book is uniform and it is going down the incline with constant speed.

This shows that the net force on the book must be balanced and hence the component of weight along the incline must be counterbalanced by friction force which is opposite to the motion of the book

Now here we can say

so the kinetic friction must be equal to the component of weight along the inclined plane

Now if we have to find the minimum friction coefficient so that the above condition may hold good then we can use the formula of friction force

here on the inclined plane, we can say

now by the above equation

now by above equation we can equate it with the component of weight

Hence,

option $\left(C\right)$ is correct answer.