6
\includegraphics[max width=\textwidth, alt={}, center]{68acf474-5da2-4949-b3b2-fc42cd73bd4a-3_504_878_1557_632} One end of a light inextensible string of length 0.7 m is attached to a fixed point \(A\). The other end of the string is attached to a particle \(P\) of mass 0.25 kg . The particle \(P\) moves in a circle on a smooth horizontal table with constant speed \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The string is taut and makes an angle of \(40 ^ { \circ }\) with the vertical (see diagram). Find

1. the tension in the string,
2. the force exerted on \(P\) by the table.
   \(P\) now moves in the same horizontal circle with constant angular speed \(\omega \operatorname { rad~s } ^ { - 1 }\).
3. Find the maximum value of \(\omega\) for which \(P\) remains on the table.