In both the figures all other factors are same, except that in figure (i) `AB` is rough and `BC` is smooth while in figure (ii) `AB` is smooth and `BC` is rough. In figure (i), if a sphere is released from rest it starts rolling. Now consider the figure (ii), if same sphere is A released from top of the inclined plane, what will be the kinetic energy of the sphere on reaching the bottom:

Options

A. is same in both the cases
B. is greater in case (i)
C. is greater in case (ii)
D. information insufficient

Answer

D

Explanation

Let `J` be the linear impulse impacted to the ball. Applying impulse `=` change momentum
we have `J=mv_(0)`……….i
`J.h=Iomega_(0)=2/5mr^(2)omega_(0)`……….ii
From eqn i and i we get `omega_(0)=5/2(v_(0)h)/r^(2)`