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\includegraphics[max width=\textwidth, alt={}, center]{7fcedc6d-8dc1-4159-8a72-be0f6a3f659b-2_698_737_484_703} A particle \(P\) travels on a smooth surface whose vertical cross-section is in the form of two arcs of circles. The first arc \(A B\) is a quarter of a circle of radius \(\frac { 1 } { 8 } a\) and centre \(O\). The second arc \(B C\) is a quarter of a circle of radius \(a\) and centre \(Q\). The two arcs are smoothly joined at \(B\). The point \(Q\) is vertically below \(O\) and the two arcs are in the same vertical plane. The particle \(P\) is projected vertically downwards from \(A\) with speed \(u\). When \(P\) is on the \(\operatorname { arc } B C\), angle \(B Q P\) is \(\theta\) (see diagram). Given that \(P\) loses contact with the surface when \(\cos \theta = \frac { 5 } { 6 }\), find \(u\) in terms of \(a\) and \(g\).