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Using perpendicular axes theorem, find t...

Using perpendicular axes theorem, find the M.I. of a disc about an axis passing through its diameter.

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According to perpendicular axis theorem, `I_(Z) = I_(X) + I_(Y)`
We know that `I_(X) = I_(Y)` due to the geometrical symmetry of the disc, where `I_(X) and I_(Y)` are M.I. of the disc about an axis passing through its diameter.
`rArr" "I_(Z) = I_(X) + I_(Y) rArr I_(X) = I_(Y) = (I_(Z))/(2)`
where, `I_(Z) =` M.I. of the disc about Z-axis passing through its center perpendicular to its plane `= mr^(2)//2`
M.I. about diameter `= I_(X) = I_(Y) = (1)/(4) mr^(2)`
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