A ring of radius `r` made of wire of density `rho` is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in the figure. Determine the angular velocity (in rad/s) of ring at which the ring breaks. The wire breaks at tensile stress `sigma`. Ignore gravity. Take `sigma//rho = 4` and `r= 1 m.`

Explanation

`2T sin (Delta theta)/2 =dm xxomega^(2)r`
`2T((Delta theta)/2)=rhoxxAxxr Delta thetaxxomega^(2)xxr`
`sigma =T/A=rho^(2) omega^(2)`
`:. omega=1/rsqrt((sigma)/(rho))` = 2 rad/sec