What is the moment of inertia of a disc about one of its diameter?

Explanation

Suppose a disc of mass M and radius R in XY plane as shown in figure. Z is perpendicular axis to the plane passing through the centre of disc.
Moment of inertia of disc about Z-axis
`I_(Z)=(MR^(2))/(2)`
According to perpendicular axis theorem
`I_(z)=I_(x)+I_(y)" "....(1)`
Since disc is symmetrical with axis x and y,
`I_(x)=I_(y)`
`therefore` From eqn. (1), `I_(z)=2I_(x)" "........(2)`
but `I_(z)=(MR^(2))/(2)`
`(MR^(2))/(2)=2I_(x)`
`therefore I_(x)=(MR^(2))/(4)andI_(x)=I_(y)`
`therefore I_(y)=(MR^(2))/(4)`