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\includegraphics[max width=\textwidth, alt={}, center]{3e7472a8-df1e-45c4-81fb-e4397bddf5ad-3_576_826_258_662} A hollow cone with semi-vertical angle \(45 ^ { \circ }\) is fixed with its axis vertical and its vertex \(O\) downwards. A particle \(P\) of mass 0.3 kg moves in a horizontal circle on the inner surface of the cone, which is smooth. \(P\) is attached to one end of a light inextensible string of length 1.2 m . The other end of the string is attached to the cone at \(O\) (see diagram). The string is taut and rotates at a constant angular speed of \(4 \mathrm { rad } \mathrm { s } ^ { - 1 }\).

1. Find the acceleration of \(P\).
2. Find the tension in the string and the force exerted on \(P\) by the cone.