4.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{e5998843-0bec-4b64-bba4-0e2212e4929b-3_700_743_354_740}
\end{figure}
A hollow cone, of base radius \(3 a\) and height \(4 a\), is fixed with its axis vertical and vertex \(V\) downwards, as shown in Figure 1. A particle moves in a horizontal circle with centre \(C\), on the smooth inner surface of the cone with constant angular speed \(\sqrt { \frac { 8 g } { 9 a } }\).
Find the height of \(C\) above \(V\).