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 released from top of the inclined plane, what will be the kinetic energy of the sphere on reaching the bottom:
As we know that for pure rolling motion friction is necessary. So according to Fig (i) the sphere will roll from A to B then it will slip from B to C. In Fig(ii) the sphere slips from A to B and then it will roll from B to C.
And we know then while rolling work done by friction force is zero hence kinetic energy after reaching bottom will be equal to mgh.
Option (A) is correct choice.
6th Floor, NCC Building, Durgamma Cheruvu Road, Vittal Rao Nagar, HITEC City, Hyderabad, Telangana 500081.
