The figure shows an isosceles triangle plate of mass `M` and base `L`.
The angle at the apex is `90^@`. The apex lies at the origin and the base is parallel to `X-`axis.

The moment of inertia of the plate about the `x-`axis is

Options

A. `(ML^(2))/(8)`
B. `(ML^(2))/(32)`
C. `(ML^(2))/(24)`
D. `(ML^(2))/(6)`

Answer

A

Explanation

`dm = (m)/((1)/(2) xx L xx (L)/(2)) xx 2y dy`
`dm = (8m)/(L^(2)) ydy` ....(1)
`I_(x) = int_(0)^(L//2) dmy^(2)` …..(2)

`I_(x) = int_(0)^(L//2) (8m)/(L^(2)) ydy.y^(2) rArr I_(x) = (8m)/(L^(2)) [(y^(4))/(4)]_(0)^(L//2)`
`I_(x) = (2m)/(L^(2)) xx (L^(4))/(16) rArr I_(x) = (ML^(2))/(8)`.