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\includegraphics[max width=\textwidth, alt={}, center]{6b220343-1d64-4dbc-a42d-77967eef9c6d-08_449_890_262_630}
\(O A B\) is a uniform lamina in the shape of a quadrant of a circle with centre \(O\) and radius 0.8 m which has its centre of mass at \(G\). The lamina is smoothly hinged at \(A\) to a fixed point and is free to rotate in a vertical plane. A horizontal force of magnitude 12 N acting in the plane of the lamina is applied to the lamina at \(B\). The lamina is in equilibrium with \(A G\) horizontal (see diagram).
- Calculate the length \(A G\).
- Find the weight of the lamina.