Derive an expression for the MI. of a disc,
(i) about an axis passing through its centre and perpendicular to its plane. (ii) about its diameter.

Explanation

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)`