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}
\begin{enumerate}[label=(\alph*)]
\item Show that, if the bead is going to make complete revolutions around the wire,

$$u > 2 \sqrt { a g }$$
\item 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 $u = \sqrt { \frac { 9 } { 2 } a g }$.
\begin{enumerate}[label=(\roman*)]
\item Find the reaction of the bead on the wire, giving your answer in terms of $g$ and $\theta$.
\item Find $\theta$ when this reaction is zero.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA M2 2011 Q8 [10]}}