When a body of known mass is placed on a inclined plane, the entire weight acts in vertical downward direction. We can resolve that weight into components. One component of weight acts downward along the inclined plane and the other component of weight acts normal to the inclined plane. This second component generates the normal reaction.
If the surface is smooth, there is no frictional force force acts in the system and if the surface is rough, we shall consider the frictional force against the relative motion while we are studying the motion of the body.
We can write the time taken by the body to slide down the inclined plane assuming that it is starting from the state of rest. We can use equation of motion for this derivation.
If there is a relation between the time taken by the body in reaching the bottom of smooth and rough inclined plane, using that relation, we can find coefficient of friction as shown below in the video presented.
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