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\includegraphics[max width=\textwidth, alt={}, center]{3e8248ca-74f1-443f-a5db-d7da532d2815-3_449_442_1281_794} A fixed smooth sphere of radius 0.6 m has centre \(O\) and highest point \(T\). A particle of mass \(m \mathrm {~kg}\) is released from rest at a point \(A\) on the sphere, such that angle \(T O A\) is \(\frac { \pi } { 6 }\) radians. The particle leaves the surface of the sphere at \(B\) (see diagram).

1. Show that \(\cos T O B = \frac { \sqrt { 3 } } { 3 }\).
2. Find the speed of the particle at \(B\).
3. Find the transverse acceleration of the particle at \(B\).