A ring of mass M and radius R lies flat on a horizontal table. A light thread is wound around it and its free end is pulled with a constant velocity `v`. (a) Two small segment A and B (see fig.) in the ring are rough and have a coefficient of friction `mu` with the table. Rest of the ring is smooth. Find the speed with which the ring moves. (b) Find the speed of the ring if coefficient of friction is `mu` everywhere, for all points on the ring.

A ring of mass M and radius R lies flat on a horizontal table. A light

1.	A ring of mass M and radius R lies flat on a horizontal table. A light thread is wound around it and its free end is pulled with a constant velocity `v`. (a) Two small segment A and B (see fig.) in the ring are rough and have a coefficient of friction `mu` with the table. Rest of the ring is smooth. Find the speed with which the ring moves. (b) Find the speed of the ring if coefficient of friction is `mu` everywhere, for all points on the ring.
Answer» Correct Answer - (a) `(v)/(2)` (b) `(v)/(2)`

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