Question

A ring of radius R is made of a thin wire of material of density rho, having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is omega. The tension in the ring will be

Answer 1

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,