6. A particle \(P\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point. The particle is hanging freely at rest, with the string vertical, when it is projected horizontally with speed \(U\). The particle moves in a complete vertical circle.

1. Show that \(U \geqslant \sqrt { 5 a g }\) As \(P\) moves in the circle the least tension in the string is \(T\) and the greatest tension is \(k T\). Given that \(U = 3 \sqrt { a g }\)
2. find the value of \(k\).