3
\includegraphics[max width=\textwidth, alt={}, center]{ece63d46-5e56-4668-939a-9dbbcfc1a77a-3_437_567_269_788} A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to one end of a light inextensible string of length \(L \mathrm {~m}\). The other end of the string is attached to a fixed point \(O\). The particle \(P\) moves with constant speed in a horizontal circle, with the string taut and inclined at \(35 ^ { \circ }\) to the vertical. \(O P\) rotates with angular speed \(2.2 \mathrm { rad } \mathrm { s } ^ { - 1 }\) about the vertical axis through \(O\) (see diagram). Find

1. the value of \(L\),
2. the speed of \(P\) in \(\mathrm { m } \mathrm { s } ^ { - 1 }\).