A symmetric lamina of mass `M` consists of a square shape with a semicircular section over each of the edge of the square as in fig. The side of the square is `2 a`.
The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is `1.6 Ma^(2)`. The moment of inertia of the lamina about the tangent `AB` in the plane of lamina is.
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Answer

`4.8 Ma^(2)`

Explanation

Given that `I_(Z) = 1.6 Ma^(2)`
by perpendicular axis theorem
`I_(Z) = I_(x) + I_(y)` since `I_(x) = I_(y)`
so, `2 I_(x) = I_(Z)`
`I_(x) = 0.8 Ma^(2)`
from parallel axis theorem
`I_(AB) = I_(X) + M (2a)^(2)`
`I_(AB) + 0.8 Ma^(2) + 4Ma^(2) rArr I_(AB) = 4.8 Ma^(2)`.
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