A particle \(P\) of mass \(m\) is free to move on the smooth inner surface of a fixed hollow sphere of radius \(a\). The centre of the sphere is \(O\) and the point \(C\) is on the inner surface of the sphere, vertically below \(O\). The points \(A\) and \(B\) on the inner surface of the sphere are the ends of a diameter of the sphere. The diameter \(A O B\) makes an acute angle \(\alpha\) with the vertical, where \(\cos \alpha = \frac { 4 } { 5 }\), with \(A\) below the horizontal level of \(B\). The particle is projected from \(A\) with speed \(u\), and moves along the inner surface of the sphere towards \(C\). The normal reaction forces on the particle at \(A\) and \(C\) are in the ratio \(8 : 9\).

1. Show that \(u ^ { 2 } = 4 a g\).
2. Determine whether \(P\) reaches \(B\) without losing contact with the inner surface of the sphere. [6]