7 A light inextensible string, of length \(a\), has one end attached to a fixed point \(O\). A particle, of mass \(m\), is attached to the other end. The particle is moving in a vertical circle, centre \(O\). When the particle is at \(B\), vertically above \(O\), the string is taut and the particle is moving with speed \(3 \sqrt { a g }\).
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1. Find, in terms of \(g\) and \(a\), the speed of the particle at the lowest point, \(A\), of its path.
2. Find, in terms of \(g\) and \(m\), the tension in the string when the particle is at \(A\).