3. The diagram below shows a hollow cone, of base radius 5 m and height 12 m , which is fixed with its axis vertical and vertex \(V\) downwards. A particle \(P\), of mass \(M \mathrm {~kg}\), moves in a horizontal circle with centre \(C\) on the smooth inner surface of the cone with constant speed \(v = 3 \sqrt { g } \mathrm {~ms} ^ { - 1 }\).
\includegraphics[max width=\textwidth, alt={}, center]{b6b77d92-acb6-4cc3-8328-1899ed4a87cd-4_940_695_598_683}

1. Show that the normal reaction of the surface of the cone on the particle is \(\frac { 13 M g } { 5 } \mathrm {~N}\).
2. Calculate the length of \(C P\) and hence determine the height of \(C\) above \(V\).