Question

A thin ring of radius R is made of a material of density ρ and Young's modulus Y. If the ring is rotated about its centre in its own plane with angular velocity ω , find the small increase in its radius.

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,