7 Particles \(P\) and \(Q\), of masses 0.8 kg and 0.5 kg respectively, are attached to the ends of a light inextensible string which passes through a small hole in a smooth horizontal table of negligible thickness. \(P\) moves with constant angular speed \(6.25 \mathrm { rad } \mathrm { s } ^ { - 1 }\) in a circular path on the surface of the table.

1. It is given that \(Q\) is stationary and that the part of string attached to \(Q\) is vertical. Calculate the radius of the path of \(P\), and find the speed of \(P\).
2. It is given instead that the part of string attached to \(Q\) is inclined at \(60 ^ { \circ }\) to the vertical, and that \(Q\) moves in a horizontal circular path below the table, also with constant angular speed \(6.25 \mathrm { rad } \mathrm { s } ^ { - 1 }\). Calculate the total length of the string.
   [0pt] [6]