2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{176ae8f8-7de9-4993-825a-6067614526ae-04_351_563_296_751}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A thin hemispherical shell, with centre \(O\) and radius \(a\), is fixed with its open end uppermost and horizontal.
A particle \(P\) of mass \(m\) moves in a horizontal circle on the smooth inner surface of the shell. The vertical distance of \(P\) below the level of \(O\) is \(d\), as shown in Figure 2.
- Find, in terms of \(m , g , d\) and \(a\), the magnitude of the force exerted on \(P\) by the inner surface of the hemisphere.
The particle moves with constant speed \(v\).
- Find \(v\) in terms of \(g , a\) and \(d\).