1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ffe0bc72-3136-48d9-9d5b-4a364d134070-02_503_524_121_712}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A hemispherical bowl of internal radius \(2 r\) is fixed with its circular rim horizontal. A particle \(P\) is moving in a horizontal circle of radius \(r\) on the smooth inner surface of the bowl, as shown in Figure 1. Particle \(P\) is moving with constant angular speed \(\omega\).
Show that \(\omega = \sqrt { \frac { g \sqrt { 3 } } { 3 r } }\)