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A disc is made to oscillate about a hori...

A disc is made to oscillate about a horizontal axis passing through one of its ends and its behaves like a second's pendulum. Determine its lengths.

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Because ocillating rod behaves as a second's pendulum so its time period will be `2` second.
`T = 2pisqrt((l + (K^(2))/(l))/(g)) = 2s rArr l + (K^(2))/(l) = 1"….."(i)[:' pi^(2) = g]`
Assume length of rod is L, because axis passes through one end So `l = (L)/(2)` and `K^(2) = (L^(2))/(12)`
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Knowledge Check

  • A uniform rod of mass m. length L, area of cross- secticn A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(omega\) in a horizontal plane If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is

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    `(momega^(2)L^(2))/(3AY)`
    D
    `(2momega^(2)L^(2))/(AY)`

  • The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is.

    A
    `l/sqrt 2`
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