3
\includegraphics[max width=\textwidth, alt={}, center]{0cb05368-9ddf-4564-8428-725c77193a1e-2_892_412_1217_865} A hollow cylinder of radius 0.35 m has a smooth inner surface. The cylinder is fixed with its axis vertical. One end of a light inextensible string of length 1.25 m is attached to a fixed point \(O\) on the axis of the cylinder. A particle \(P\) of mass 0.24 kg is attached to the other end of the string. \(P\) moves with constant speed in a horizontal circle, in contact with the inner surface of the cylinder, and with the string taut (see diagram).

1. Find the tension in the string.
2. Given that the magnitude of the acceleration of \(P\) is \(8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find the force exerted on \(P\) by the cylinder.