$AOB$ is a uniform lamina in the shape of a quadrant of a circle with centre $O$ and radius $0.6{\text{ }}m$ (see diagram).
a) Calculate the distance of the centre of mass of the lamina from $A$.
The lamina is freely suspended at $A$ and hangs in equilibrium.
b) Find the angle between the vertical and the side $AO$ of the lamina.

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