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\includegraphics[max width=\textwidth, alt={}, center]{68acf474-5da2-4949-b3b2-fc42cd73bd4a-3_405_545_630_799} A uniform lamina \(A O B\) is in the shape of a sector of a circle with centre \(O\) and radius 0.5 m , and has angle \(A O B = \frac { 1 } { 3 } \pi\) radians and weight 3 N . The lamina is freely hinged at \(O\) to a fixed point and is held in equilibrium with \(A O\) vertical by a force of magnitude \(F \mathrm {~N}\) acting at \(B\). The direction of this force is at right angles to \(O B\) (see diagram). Find

1. the value of \(F\),
2. the magnitude of the force acting on the lamina at \(O\).