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

Options

A. `(Ml^(2))/3`
B. `(Ml^(2))/4`
C. `(Ml^(2))/6`
D. none of these

Answer

D

Explanation

`I_("median line")=I_(A)+I_(B)+I_(C)+I_(D)`
`=2xx(Ml^(2))/12+2m(l/2)^(2)`
`=(Ml^(2))/6+(Ml^(2))/2=2/3Ml^(2)`