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.
.

Options

A. `4.8Ma^(2)`
B. `2.6Ma^(2)`
C. `1.8Ma^(2)`
D. `7.2Ma^(2)`

Explanation

`I_(z)=1.6Ma^(2)=I_(x)+I_(y)` (`bot^(ar)` axis theorem)
`I_(x)=I_(y)=0.8Ma^(2)` (due to symmetry)
`I_(AB)=I_(x)+M(2a)^(2)` (parallel axes theorem)
`=0.8Ma^(2)+4Ma^(2)=4.8Ma^(2)`