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\includegraphics[max width=\textwidth, alt={}, center]{9c82b387-8e5e-48b9-973d-5337b4e56a66-4_553_630_258_753} The diagram shows a container which consists of a bowl of weight 14 N and a handle of weight 8 N . The bowl of the container is in the form of a uniform hemispherical shell with centre \(O\) and radius 0.3 m . The handle is in the form of a uniform semicircular arc of radius 0.3 m and is freely hinged to the bowl at \(A\) and \(B\), where \(A B\) is a diameter of the bowl.

1. Calculate the distance of the centre of mass of the container from \(O\) for the position indicated in the diagram, where the handle is perpendicular to the rim of the bowl.
2. Show that the distance of the centre of mass of the container from \(O\) when the handle lies on the rim of the bowl is 0.118 m , correct to 3 significant figures. In the case when the handle lies on the rim of the bowl, the container rests in equilibrium with the curved surface of the bowl on a horizontal table.
3. Find the angle which the plane containing the rim of the bowl makes with the horizontal.