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Let I be the moment of interia of a unif...

Let `I` be the moment of interia of a uniform square plate about an axis `AB` that passses through its centre and is parallel to two its sides. `CD` is a line in the plane of the plate that passes through the centre of the plate and makes an angle `theta` with `AB`. The moment of inertia of the plate about the axis `CD` is then equal to-

A

I

B

`I sin^(2) theta`

C

`I cos^(2) theta`

D

`I cos^(2) (theta//2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`I_(AB) = I_(AB) = I_(CD) + I_(CD)`
`2I_(AB) = 2I_(CD)`
`I_(AB) = I_(CD)`
`I_(CD) = I`
.
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Knowledge Check

  • Let l be the moment of inertia of an uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle theta with AB . The moment of inertia of the plate about the axis CD is then equal to

    A
    l
    B
    `lsin^(2)theta`
    C
    `lcos^(2)theta`
    D
    `lcos^(2)""(theta)/(2)`

  • The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

    A
    increases if its temperature is increased
    B
    changes if its axis of rotation is changed
    C
    increases if its angular velocity is increased
    D
    both (a) and (b) are correct

  • Moment of inertia of a circular ring about an axis through its centre and perpendicular to its plane is

    A
    `I = (1)/(2) MR^2`
    B
    `I = MR^2`
    C
    `I = (3)/(2) MR^2`
    D
    `I = (5)/(2) MR^2`

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