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For the given uniform square lamina ABCD...

For the given uniform square lamina `ABCD`, where centre is `O`. Its moment of inertia about an axis `AD` is equal to how many times its moment of inertia about an axis `EF`?

`1 sqrt(2) I_(AC)=I_(EF) " " 2. I_(AD)=3I_(EF)`
`3.I_(AC)=4I_(EF). " " 4. I_(AC)=sqrt(2)I_(EF)`

Text Solution

Verified by Experts

`I_(EF)=I_(GH)` (due to symmetry)
`I_(AC)=I_(BD)` (due to symmetry)
`I_(AC)+I_(BD)=I_(0)`
`rArr2I_(AC)=I_(0).....(1)`
and `I_(EF)+I_(GH)=I_(0)`
`rArr2I_(EF)=I_(0)...(2)`
From eq(1) and (2), we get
`I_(AC)=I_(EF)`
`:. I_(AD)=I_(EF)+(md^(2))/4=(md^(2))/12+(md^(2))/4`
`I_(AD)=(md^(2))/3=4I_(EF)`
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