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\includegraphics[max width=\textwidth, alt={}, center]{e5d70ccb-cec0-4390-a500-b550957a4ac6-4_503_805_260_671} A light inextensible string passes through a small smooth bead \(B\) of mass 0.4 kg . One end of the string is attached to a fixed point \(A 0.4 \mathrm {~m}\) above a fixed point \(O\) on a smooth horizontal surface. The other end of the string is attached to a fixed point \(C\) which is vertically below \(A\) and 0.3 m above the surface. The bead moves with constant speed on the surface in a circle with centre \(O\) and radius 0.3 m (see diagram).

1. Given that the tension in the string is 2 N , calculate
   (a) the angular speed of the bead,
   (b) the magnitude of the contact force exerted on the bead by the surface.
2. Given instead that the bead is about to lose contact with the surface, calculate the speed of the bead.