6 A light inextensible string, of length \(a\), has one end attached to a fixed point \(O\). A small bead, of mass \(m\), is attached to the other end of the string. The bead is moving in a vertical circle, centre \(O\). When the bead is at \(B\), vertically below \(O\), the string is taut and the bead is moving with speed \(5 v\).
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1. The speed of the bead at the highest point of its path is \(3 v\). Find \(v\) in terms of \(a\) and \(g\).
2. Find the ratio of the greatest tension to the least tension in the string, as the bead travels around its circular path.
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