A carpet of mass M made of inextensible material is rolled along its length in the form of a cyliner of radius R and is kept on a rough floor.The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it.Calculate the horizontal velocity of the axis of the cylindrical part of the carpet when its radius reduces to R/2.

 

How do you do the question? Please solve. Thanks.

in this case work done by the friction is equal to the change in transl. and rotational kinetic energy..