A loop of rope is whirled at a high angular velocity`omega`, so that it becomes a taut circle of radius`R`. A kink develops in the whirling rope.
(a) Show that the speed of the kink in the rope is `v = omegaR`.
(b) Under what conditions does the kink remains stationary relative to an observer on the ground?

Answer

A, B, C, D

Explanation

(a) `T cos d theta` components are cancelled. `T sin d theta` components provided the necessary centriprtal force to `P theta`.

`:. 2T sin d theta = m_(PQ)R omega^(2)`
For small angles `sin d theta ~~ d theta`
`:. 2T d theta = [mu(2R)d theta]R omega^(2)`
Solving thr equation, we get
`sqrt((T)/(mu)) =v =R omega`