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\includegraphics[max width=\textwidth, alt={}, center]{6503ebb1-5649-4ca5-9500-da4fb28009dd-3_540_537_255_804} A particle \(P\) of mass 0.2 kg is attached to a fixed point \(A\) by a light inextensible string of length 0.4 m . A second light inextensible string of length 0.3 m connects \(P\) to a fixed point \(B\) which is vertically below \(A\). The particle \(P\) moves in a horizontal circle, which has its centre on the line \(A B\), with the angle \(A P B = 90 ^ { \circ }\) (see diagram).

1. Given that the tensions in the two strings are equal, calculate the speed of \(P\).
2. It is given instead that \(P\) moves with its least possible angular speed for motion in this circle. Find this angular speed.