7. One end of a light inextensible string of length \(l\) is attached to a particle \(P\) of mass \(m\). The other end is attached to a fixed point \(A\). The particle is hanging freely at rest with the string vertical when it is projected horizontally with speed \(\sqrt { \frac { 5 g l } { 2 } }\).

1. Find the speed of \(P\) when the string is horizontal. When the string is horizontal it comes into contact with a small smooth fixed peg which is at the point \(B\), where \(A B\) is horizontal, and \(A B < l\). Given that the particle then describes a complete semicircle with centre \(B\),
2. find the least possible value of the length \(A B\).