A thin carpet of mass `2m` is rolled over a hollow cylinder of mass `m`. The cylinder wall is thin and radius of the cylinder is R. The carpet rolled over it has outer radius 2R (see figure). This roll is placed on a rough horizontal surface and given gentle push so that the carpet begins to roll and unwind. Friction is large enough to prevent any slipping of the carpet on the floor. Also assume that the carpet does not slip on the surface of the cylinder. The entire carpet is laid out on the floor and the hollow cylinder rolls out with speed V. Find V.

Answer

`V = sqrt(5gR)`