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\(A B\) is the diameter of a uniform semicircular lamina which has radius 0.3 m and mass 0.4 kg . The lamina is hinged to a vertical wall at \(A\) with \(A B\) inclined at \(30 ^ { \circ }\) to the vertical. One end of a light inextensible string is attached to the lamina at \(B\) and the other end of the string is attached to the wall vertically above \(A\). The lamina is in equilibrium in a vertical plane perpendicular to the wall with the string horizontal (see diagram).

1. Show that the tension in the string is 2.00 N correct to 3 significant figures.
2. Find the magnitude and direction of the force exerted on the lamina by the hinge.
   \includegraphics[max width=\textwidth, alt={}, center]{5a2248f6-3ef9-4e69-90cf-4d6a2351be14-3_956_540_258_804} A small ball \(B\) of mass 0.4 kg is attached to fixed points \(P\) and \(Q\) on a vertical axis by two light inextensible strings of equal length. Both strings are taut and each is inclined at \(30 ^ { \circ }\) to the vertical. The ball moves in a horizontal circle (see diagram).