5 A particle of mass \(m\) is suspended from a fixed point \(O\) by a light inextensible string of length \(l\). The particle hangs in equilibrium at the point \(R\) vertically below \(O\). The particle is set into motion with a horizontal velocity \(u\) so that it moves in a complete vertical circle with centre \(O\). The point \(T\) on the circle is such that angle \(R O T\) is \(30 ^ { \circ }\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{7c2c50e0-4976-4301-9898-61b2760a2aee-12_766_736_644_651}

1. Find, in terms of \(g , l\) and \(u\), the speed of the particle at the point \(T\).
2. Find, in terms of \(g , l , m\) and \(u\), the tension in the string when the particle is at the point \(T\).
3. Find, in terms of \(g , l , m\) and \(u\), the tension in the string when the particle returns to the point \(R\).
4. The particle makes complete revolutions. Find, in terms of \(g\) and \(l\), the minimum value of \(u\).
   [0pt] [4 marks]