Answer to Question #80639 in Classical Mechanics for Kavita samant

Question

A body holds one end of a rope of length l and the other end is fixed to a thin pole of radius r (r<<l) keeping the rope taut the body goes around the pole causing the rope to get wound around the pole. Each round takes 10 second. What is the speed (in units of s^-1) with which the body approaches the pole?

Answer 1

Each round the length of the rope decreases by
2πr.
Each round takes 10 second.
Thus, the speed with which the body approaches the pole is
2πr/10 s^(-1)=πr/5 s^(-1)