A string of mass M as a circular loop rotates abot its axis on a frictionless horizontal plane at a uniform rate so that the tangential plane at a uniform rate so that the tangential speed of any particle of the string is `v`. If a small transverse disturbance is produced at a point of the loop, then speed (relative to the string) of disturbance on the string is

Options

A. `vsqrt((M)/(2))`
B. `sqrt(2)v`
C. `v`
D. `(v)/(sqrt(2))`

Answer

C

Explanation

Mass of string of length `R d theta`, `m.=(M)/(2piR)R d theta=(Md theta)/(2pi)`
`2Tsin.(d theta)/(2)=(mv^(2))/(R )` As `d theta` is small
`2T (d theta)/(2)=(Md theta)/(2pi)(v^(2))/(R )impliesT=(Mv^(2))/(2piR)`
`V_("wave")=sqrt((T)/(mu))=sqrt((Mv^(2)//2piR)/(M//2piR))=v`