Question

A thin ring of radius R is made of a wire of density rho and Young’s modulus Y. It is spun in its own plane, about an axis through its centre, with angular velocity w. Determine the amount (assumed small) by which its circumference increases.

Answer 1

Answer:

Consider an element PQ of length dl. Let T be the tension and A the area of cross-section of the wire. Mass of element dm = volume x density The component of T, towards the centre provides the necessary centripetal force Substituting in Eq. (i), we have Let ΔR be the increase in radius,