2. Two identical cylinders R and S are released simultaneously from rest at the top of two inclined planes having the same length and slope. Cylinder R rolls without slipping while cylinder S moves down a perfectly smooth plane. The two cylinders reach the bottom of their respective planes.

Step-by-step explanation:

Both cylinders have same radius R and released from the same height.

If R rolls without slipping i.e. Pure rolling and S rolls on the smooth Plane.

Velocity possessed by both cylinder at bottom will be different because one is in pure rolling while other is not.

acceleration for pure rolling is given by

where a=acceleration

=inclination of Plane

I=moment of inertia

for cylinder without rolling acceleration is given by

Thus we can see that acceleration of S is more therefore  S takes less time to reach bottom.            

step-by-step explanation: