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.`

Answer

2

Explanation

`2Tsin((triangletheta)/(2))=dmomega^(2)r`

`2T((/_\theta)/2)=rhoxxAxxr^(2)omega^(2)`
`sigma=T/A=rhor^(2)omega^(2)`
`:. Omega=1/r sqrt((sigma)/(rho))=2rad//s`