3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c9d14ac-0757-4cdd-9534-337e6b3acee0-05_454_835_239_548}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A particle \(P\) of mass \(m\) moves on the smooth inner surface of a hemispherical bowl of radius \(r\). The bowl is fixed with its rim horizontal as shown in Figure 2. The particle moves with constant angular speed \(\sqrt { } \left( \frac { 3 g } { 2 r } \right)\) in a horizontal circle at depth \(d\) below the centre of the bowl.
- Find, in terms of \(m\) and \(g\), the magnitude of the normal reaction of the bowl on \(P\).
- Find \(d\) in terms of \(r\).