2
\includegraphics[max width=\textwidth, alt={}, center]{84a2b2eb-a750-4047-864b-4a165fc66b2a-2_812_1218_479_468} A uniform solid cone with height 0.8 m and semi-vertical angle \(30 ^ { \circ }\) has weight 20 N . The cone rests in equilibrium with a single point \(P\) of its base in contact with a rough horizontal surface, and its vertex \(V\) vertically above \(P\). Equilibrium is maintained by a force of magnitude \(F \mathrm {~N}\) acting along the axis of symmetry of the cone and applied to \(V\) (see diagram).

1. Show that the moment of the weight of the cone about \(P\) is 6 Nm .
2. Hence find \(F\).