A circular loop of string is rotating about its axis on a frictionless horizontal plane at a uniform rate, ensuring that the tangential speed of any particle of the string is v . When a small transverse disturbance is generated at a point on the loop, at what speed (relative to the string) does this disturbance propagate along the string?

Step-by-step solution

Consider a small element of the string subtending an angle d at the center of the circular loop. Let the radius of the loop be R and the mass per unit length of the string be . The mass of this small element is dm = R d . The element is rotating in a circle of radius R with a constant tangential speed v . The centripetal force required for this circular motion is provided by the inward component of the tension T at the two ends of the element. The net inward force is 2T ( d 2 ) T d since d is very small. Equating t