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

Options

A. `I_(AD) = 3I_(EF)`
B. `I_(AC) = I_(EF)`
C. `I_(AC) = sqrt(2)I_(EF)`
D. `sqrt(2)I_(AC) = I_(EF)`

Answer

B

Explanation

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`