2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fd8bc7b5-adee-4d67-b15d-571255b00b83-04_529_794_246_639}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A thin hollow hemisphere, with centre \(O\) and radius \(a\), is fixed with its axis vertical, as shown in Figure 2.
A small ball \(B\) of mass \(m\) moves in a horizontal circle on the inner surface of the hemisphere. The circle has centre \(C\) and radius \(r\). The point \(C\) is vertically below \(O\) such that \(O C = h\).
The ball moves with constant angular speed \(\omega\)
The inner surface of the hemisphere is modelled as being smooth and \(B\) is modelled as a particle. Air resistance is modelled as being negligible.
- Show that \(\omega ^ { 2 } = \frac { g } { h }\)
Given that the magnitude of the normal reaction between \(B\) and the surface of the hemisphere is \(3 m g\)
- find \(\omega\) in terms of \(g\) and \(a\).
- State how, apart from ignoring air resistance, you have used the fact that \(B\) is modelled as a particle.