A symmetrical lamina of mass $M$ consists of a square shape with a semi-circular section over each edge of the square as shown in figure. The side of the square is $2 a .$ The moment of inertia of the lamina about an axis through its center of mass and perpendicular to the plane is $1.6 M a^{2}$ The moment of inertia of the lamina about the tangent $A B$ in the plane of the lamina is :

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$3.6 M a^{2}$

$4.8 M a^{2}$

$2.6 M a^{2}$

$0.8 M a^{2}$

answer is D.

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Detailed Solution

$I_{A B} = I_{C M} + M a^{2} = \frac{1.6 M a^{2}}{2} + M {(2 a)}^{2} = 4.8 M a^{2}$

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