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\includegraphics[max width=\textwidth, alt={}, center]{6ae57fe9-3b6f-46c2-95b8-d48903ed796b-4_794_735_264_705} A particle \(P\) of mass 0.5 kg is attached to points \(A\) and \(B\) on a fixed vertical axis by two light inextensible strings of equal length. Both strings are taut and each is inclined at \(60 ^ { \circ }\) to the vertical (see diagram). The particle moves with constant speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a horizontal circle of radius 0.4 m .

1. Calculate the tensions in the two strings. The particle now moves with constant angular speed \(\omega\) rad s \(^ { - 1 }\) and the string \(B P\) is on the point of becoming slack.
2. Calculate \(\omega\).