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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

l

B

`lsin^(2)theta`

C

`lcos^(2)theta`

D

`lcos^(2)""(theta)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I_(Z)` is the moment of inertia of square plate about the axis which is passing through the centre and perpendicular to the plane.
`I_(Z)=I_(AB)+I_(A.B.)=I_(CD)+I_(C.D.)` [By the theorem of perpendicular axis]
`I_(Z)=2I_(AB)=2I_(A.B.)=2I_(CD)=2I_(C.D.)` [As AB, A. B. and CD, C. D. are symmetric axis]
Hence `I_(CD)=I_(AB)=l`
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