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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 `x-`axis is

A

`(ML^(2))/(8)`

B

`(ML^(2))/(32)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`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)`.
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Knowledge Check

  • 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 its base parallel to the x- axis is

    A
    `(ML^(2))/(18)`
    B
    `(ML^(2))/(36)`
    C
    `(ML^(2))/(24)`
    D
    none of these

  • A wire of mass m and length l is bent in the form of circular ring. The moment of inertia of the ring about its axis is

    A
    `ml^(2)`
    B
    `(ml^(2))/(4pi^(2))`
    C
    `(ml^(2))/(2pi^(2))`
    D
    `(ml^(2))/(8pi^(2))`

  • A wire of mass 'm' and length 'l' is bent in the form of a circular ring. The moment of inertia of the ring about its axis is-

    A
    `ml^2`
    B
    `( 1 ml^2)/(2pi^2)`
    C
    `(ml^2)/(4 pi)`
    D
    `(ml^2)/(8 pi^2)`

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