6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b070338-1de4-4c33-be29-d37ac06c9fed-20_611_782_210_660}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A hollow right circular cone, of internal base radius 0.6 m and height 0.8 m , is fixed with its axis vertical and its vertex \(V\) pointing downwards, as shown in Figure 4.
A particle \(P\) of mass \(m \mathrm {~kg}\) moves in a horizontal circle of radius 0.5 m on the rough inner surface of the cone.
The particle \(P\) moves with constant angular speed \(\omega\) rads \(^ { - 1 }\)
The coefficient of friction between the particle \(P\) and the inner surface of the cone is 0.25
Find the greatest possible value of \(\omega\)