A circular loop of rope of length L rotates with uniform angular velocity `omega` about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with resppect to rope ) produce due to slight radiul displacement is given by

Explanation

`2 T sin d theta = dm r . omega^(2)`
` 2 T sin d theta = m//l 2 R d theta omega ^(2) R `
If `d theta ` is small
`T = m //l R^(2)omega^(2) rArr m//l = mu`
`T = mu (v^(2))`
`v = sqrt((T)/(mu)) = omega R `
`omega R = sqrt((T)/(mu)) " "2 pi R = L `
`v = omega R " " r = ((L)/(2 pi))`
`[ v = ((omega L)/(2pi))]`