7 One end of a light inextensible string of length 0.15 m is attached to a fixed point which is above a smooth horizontal surface. A particle of mass 0.5 kg is attached to the other end of the string. The particle moves with constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a horizontal circle, with the string taut and making an angle of \(\theta ^ { \circ }\) with the downward vertical.

1. Given that \(\theta = 60\) and that the particle is not in contact with the surface, find \(v\).
2. Given instead that \(\theta = 45\) and \(v = 0.9\), and that the particle is in contact with the surface, find
   (a) the tension in the string,
   (b) the force exerted by the surface on the particle.