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A rigid body is made from uniform wire of negligible thickness and is in the form of a square $A B C D$ of mass $M$ enclosed within a circular ring of radius $a$ and mass $2 M$. The centres of the square and the circle coincide at $O$ and the corners of the square are joined to the circle (see diagram). Show that the moment of inertia of the body about an axis through $O$, perpendicular to the plane of the body, is $\frac { 8 } { 3 } M a ^ { 2 }$.

Hence find the moment of inertia of the body about an axis $l$, through $A$, in the plane of the body and tangential to the circle.

A particle $P$ of mass $M$ is now attached to the body at $C$. The system is able to rotate freely about the fixed axis $l$, which is horizontal. The system is released from rest with $A C$ making an angle of $60 ^ { \circ }$ with the upward vertical. Find, in terms of $a$ and $g$, the greatest speed of $P$ in the subsequent motion.

\hfill \mbox{\textit{CAIE FP2 2011 Q11 EITHER}}