Find the `M.I.` of thin uniform rod of mass `M` and length `L` about the axis as shown.

Explanation

Here mass is distributed on length. Taking an element of small length `dx` at distance `x` as shown.
`dm=(M)/(L)dx`
`dI=r^(2)dm=(xsinalpha)^(2)(M)/(L)dx`
`I=(M)/(L)sin^(2)alpha int_(0)^(L) x^(2) dx`
` =(M)/(L)sin^(2)alpha|(x^(3))/(3)|_(0)^(L)`
` =(M)/(L)sin^(2)alpha(L^(3))/(3)`
`(1)/(3)ML^(2)sin^(2)alpha`
If `alpha=90^(@), I=(1)/(3)ML^(2)`