One end of a light inextensible string of length \(a\) is attached to a fixed point \(O\). The other end of the string is attached to a particle \(P\) of mass \(m\). The particle \(P\) is held vertically below \(O\) with the string taut and then projected horizontally. When the string makes an angle of \(60^{\circ}\) with the upward vertical, \(P\) becomes detached from the string. In its subsequent motion, \(P\) passes through the point \(A\) which is a distance \(a\) vertically above \(O\).
(a) The speed of \(P\) when it becomes detached from the string is \(V\). Use the equation of the trajectory of a projectile to find \(V\) in terms of \(a\) and \(g\).
(b) Find, in terms of \(m\) and \(g\), the tension in the string immediately after \(P\) is initially projected horizontally.