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A unifor4m equilateral triangular lamina...

A unifor4m equilateral triangular lamina of side a has mass m. Its moment of inertia about the axis passing through the centroid and prependicular to the plane of the lamina is :-

A

`(2ma^(2))/(3)`

B

`(ma^(3))/(3)`

C

`(ma^(2))/(6)`

D

`(ma^(2))/(12)`

Text Solution

Verified by Experts

The correct Answer is:
A
Any uniform triangular lamina can be represented by three point masses for purpose of calculation of moment of inertia.

Required moment of inertia
`=3xx[(m)/(3)((a)/(2sqrt(3)))^(2)]=(ma^(2))/(12)`
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Knowledge Check

  • Three particles each of 'm' are kept at the three vertices of an equilateral triangle of side 'a' . Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is

    A
    `3 ma^(2)`
    B
    `ma^(2)`
    C
    `ma^(2)//3`
    D
    `2//3 ma^(2)`

  • Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is

    A
    `1//2MR^(2)`
    B
    `MR^(2)`
    C
    `1//4MR^(2)`
    D
    `3//4 MR^(2)`

  • A thin ring has mass 0.25 kg and radius 0.5 m. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is ………… .

    A
    `0.0625 kg m^(2)`
    B
    `0.625 kg m^(2)`
    C
    `6.25 kg m^(2)`
    D
    `62.5 kg m^(2)`

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