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For the given uniform square lamina ABCD...

For the given uniform square lamina ABCD, whose centre is O

A

`I_(AD) = 3I_(EF)`

B

`I_(AC) = I_(EF)`

C

`I_(AC) = sqrt(2)I_(EF)`

D

`sqrt(2)I_(AC) = I_(EF)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the side of square be a. `I_(EF) = (Ma^(2))/12`
By perpendicular axes theorem, the moment of inertia of lamina about an axis passing through O and perpendicular to plane of lamina `I_(2) = (Ma^(2))/12 +(Ma^(2))/12 = (Ma^(2))/6`.
Again by perpendicular axes theorem, `I_(AC) + I_(BD)= I_(Z) rArr I_(AC) = I_(z)/2 =(Ma^(2))/12`
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