A ring of radius r made of wire of densi...

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.`

Verified by Experts

The correct Answer is:

`omega = (1)/(r) sqrt((sigma)/(rho)) = 2rad//s`

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Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is

`1//2MR^(2)`

`MR^(2)`

`1//4MR^(2)`

`3//4 MR^(2)`

`1.4kg m^(2)`

`2.4kg m^(2)`

`0.4kg m^(2)`

`2kg m^(2)`

`1/2mr^(2)omega^(2)`

`mromega^(2)`

`mr^(2)omega^(2)`

`1/2mromega^(2)`