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A symmetrical square lamina of mass $M$ has uniform semi-circular plates attached to it on its four sides as shown in the figure. Each plate has the same mass $M$ , and the disc of a square is equal to $a$ . The moment of inertia of system about an axis passing through the centre $O$ , perpendicular to the plane of the lamina is:

$\frac{13}{6} M a^{2}$
$\frac{25}{12} M a^{2}$
$\frac{25}{6} M a^{2}$
$N o n e o f t h e s e$

A

\frac{25}{12} M a^{2}

B

\frac{25}{6} M a^{2}

C

N o n e o f t h e s e

D

\frac{13}{6} M a^{2}

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