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\includegraphics[max width=\textwidth, alt={}, center]{9951c978-37e6-4d89-9fe3-c1e5e28b221e-3_670_613_274_767} A particle \(P\) of mass 0.3 kg is attached to one end of each of two light inextensible strings. The other end of the longer string is attached to a fixed point \(A\) and the other end of the shorter string is attached to a fixed point \(B\), which is vertically below \(A\). \(A P\) makes an angle of \(30 ^ { \circ }\) with the vertical and is 0.4 m long. \(P B\) makes an angle of \(60 ^ { \circ }\) with the vertical. The particle moves in a horizontal circle with constant angular speed and with both strings taut (see diagram). The tension in the string \(A P\) is 5 N . Calculate

1. the tension in the string \(P B\),
2. the angular speed of \(P\),
3. the kinetic energy of \(P\).