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A particle \(P\) of mass 0.5 kg is attached to the vertex \(V\) of a fixed solid cone by a light inextensible string. \(P\) lies on the smooth curved surface of the cone and moves in a horizontal circle of radius 0.1 m with centre on the axis of the cone. The cone has semi-vertical angle \(60 ^ { \circ }\) (see diagram).
- Calculate the speed of \(P\), given that the tension in the string and the contact force between the cone and \(P\) have the same magnitude.
- Calculate the greatest angular speed at which \(P\) can move on the surface of the cone.