5. A cone of semi-vertical angle \(60 ^ { \circ }\) is fixed with its axis vertical and vertex upwards. A particle of mass \(m\) is attached to one end of a light inextensible string of length \(l\). The other end of the string is attached to a fixed point vertically above the vertex of the cone. The particle moves in a horizontal circle on the smooth outer surface of the cone with constant angular speed \(\omega\), with the string making a constant angle \(60 ^ { \circ }\) with the horizontal, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{5f9a87c6-2255-4178-ab04-441bb0cc4ce0-10_538_648_456_664}

1. Find the tension in the string, in terms of \(m , l , \omega\) and \(g\). The particle remains on the surface of the cone.
2. Show that the time for the particle to make one complete revolution is greater than $$2 \pi \sqrt { \frac { l \sqrt { 3 } } { 2 g } } .$$ [Question 5 Continued]
   [0pt] [Question 5 Continued]