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\includegraphics[max width=\textwidth, alt={}, center]{c85aa042-7b8c-44cc-b579-a5deef91e7e5-3_291_993_1238_575} A uniform solid cone of height 0.6 m and mass 0.5 kg has its axis of symmetry vertical and its vertex \(V\) uppermost. The semi-vertical angle of the cone is \(60 ^ { \circ }\) and the surface is smooth. The cone is fixed to a horizontal surface. A particle \(P\) of mass 0.2 kg is connected to \(V\) by a light inextensible string of length 0.4 m (see diagram).

1. Calculate the height, above the horizontal surface, of the centre of mass of the cone with the particle.
   \(P\) is set in motion, and moves with angular speed \(4 \mathrm { rad } \mathrm { s } ^ { - 1 }\) in a circular path on the surface of the cone.
2. Show that the tension in the string is 1.96 N , and calculate the magnitude of the force exerted on \(P\) by the cone.
3. Find the speed of \(P\).