4 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 \(P\) vertically below \(O\). The particle is then set into motion with a horizontal velocity \(U\) so that it moves in a complete vertical circle with centre \(O\). The point \(Q\) on the circle is such that \(\angle P O Q = 60 ^ { \circ }\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{c02cf013-365b-44e2-8c16-aa8209cbe250-3_566_540_1797_751}

1. Find, in terms of \(g , l\) and \(U\), the speed of the particle at \(Q\).
2. Find, in terms of \(g , l , m\) and \(U\), the tension in the string when the particle is at \(Q\).
3. Find, in terms of \(g , l , m\) and \(U\), the tension in the string when the particle returns to \(P\).
   (2 marks)