5 A bead of mass \(m\) moves on a smooth circular ring of radius \(a\) which is fixed in a vertical plane, as shown in the diagram. Its speed at \(A\), the highest point of its path, is \(v\) and its speed at \(B\), the lowest point of its path, is \(7 v\).
\includegraphics[max width=\textwidth, alt={}, center]{676e753d-1b80-413c-a4b9-21861db8dde5-4_419_317_484_842}

1. Show that \(v = \sqrt { \frac { a g } { 12 } }\).
2. Find the reaction of the ring on the bead, in terms of \(m\) and \(g\), when the bead is at \(A\).