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\includegraphics[max width=\textwidth, alt={}, center]{d6cb7a28-e8d7-4239-b9d3-120a284d7353-3_259_890_584_630} One end of a light inextensible string of length 0.2 m is attached to a fixed point \(A\) which is above a smooth horizontal table. A particle \(P\) of mass 0.3 kg is attached to the other end of the string. \(P\) moves on the table in a horizontal circle, with the string taut and making an angle of \(60 ^ { \circ }\) with the downward vertical (see diagram).

1. Calculate the tension in the string if the speed of \(P\) is \(1.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. For the motion as described, show that the angular speed of \(P\) cannot exceed \(10 \mathrm { rad } \mathrm { s } ^ { - 1 }\), and hence find the greatest possible value for the kinetic energy of \(P\).