6. A particle \(P\) of mass 0.4 kg hangs by a light, inextensible string of length 20 cm whose other end is attached to a fixed point \(O\). It is given a horizontal velocity of \(1.4 \mathrm {~ms} ^ { - 1 }\) so that it begins to move in a vertical circle. If in the ensuing motion the string makes an angle of \(\theta\) with the downward vertical through \(O\), show that

1. \(\theta\) cannot exceed \(60 ^ { \circ }\),
2. the tension, \(T \mathrm {~N}\), in the string is given by \(T = 3.92 ( 3 \cos \theta - 1 )\). If the string breaks when \(\cos \theta = \frac { 3 } { 5 }\) and \(P\) is ascending,
3. find the greatest height reached by \(P\) above the initial point of projection.