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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.`

Text Solution

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The correct Answer is:
2
`omega = (1)/(r) sqrt((sigma)/(rho)) = 2rad//s`
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Knowledge Check

  • 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

    A
    `1//2MR^(2)`
    B
    `MR^(2)`
    C
    `1//4MR^(2)`
    D
    `3//4 MR^(2)`

  • A ring of mass 10 kg and diameter 0.4m is rotated about an axis passing through its centre and perpendicular to its plane moment of inertia of the ring is

    A
    `1.4kg m^(2)`
    B
    `2.4kg m^(2)`
    C
    `0.4kg m^(2)`
    D
    `2kg m^(2)`

  • A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity omega . Its kinetic energy is

    A
    `1/2mr^(2)omega^(2)`
    B
    `mromega^(2)`
    C
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    D
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