A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is v. if a small transvers disturbance is produced at a point of the loop,with what speed (relative to the string) will this disturbance travel on the string?

A circular loop of string rotates about its axis on a frictionless hor

1.	A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is v. if a small transvers disturbance is produced at a point of the loop,with what speed (relative to the string) will this disturbance travel on the string?
Answer» Solution :Suppose F is the TENSION in the string due to its ROTATION. CHOOSE a small element of the string of length l. if `mu` is the mass per unit length of the string, then mass of the element, using newton's second law for the element, we have `2F sin theta//2=mv^(2)//R` For small `theta, sin theta//2=theta//2` 2F(theta/2)=(mv^(2))/(R)` `Ftheta=(muRtheta)V^(2)/R` `F=MUV^(2)` The speed of the disturbance `=sqrt(F)/(mu)=sqrt(muv^(2))/(mu)=v`