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The figure shows an isosceles triangle p...

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 `z-`axis is

A

`(ML^(2))/(12)`

B

`(ML^(2))/(24)`

C

`(ML^(2))/(6)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`dI (dm(2y)^(2))/(12) + dmy^(2) rArr dI = (4)/(3) dmy^(2)`
.
`I_(z) = int (4)/(3) dmy^(2)` ….(1)
`dm = (m)/((1)/(2) L xx (L)/(2)) 2ydy rArr dm = (8m)/(L^(2)) ydy` ....(2)
From (1) and (2)
`I_(z) = (4)/(3) xx(8)/(L^(2)) int_(0)^(L//2) y^(3)dy rArr I_(z) =(4)/(3) xx (8)/(L^(2)) xx((y^(4))/(4))_(0)^(L//2) rArr I_(z) = (mL^(2))/(6)`.
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