8 A smooth wire is fixed in a vertical plane so that it forms a circle of radius \(a\) metres and centre \(O\). A bead, \(B\), of mass 0.3 kg , is threaded on the wire and is set in motion with a speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the lowest point of its circular path, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-6_364_378_466_845}

1. Show that, if the bead is going to make complete revolutions around the wire, $$u > 2 \sqrt { a g }$$
2. At time \(t\) seconds, the angle between \(O B\) and the horizontal is \(\theta\), as shown in the diagram.
   \includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-6_330_328_1231_858} It is given that \(u = \sqrt { \frac { 9 } { 2 } a g }\).
   1. Find the reaction of the bead on the wire, giving your answer in terms of \(g\) and \(\theta\).
   2. Find \(\theta\) when this reaction is zero.