2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a7901165-1679-4d30-9444-0c27020e32ea-04_572_889_246_589}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A small smooth ring \(P\), of mass \(m\), is threaded onto a light inextensible string of length 4a. One end of the string is attached to a fixed point \(A\) on a smooth horizontal table. The other end of the string is attached to a fixed point \(B\) which is vertically above \(A\). The ring moves in a horizontal circle with centre \(A\) and radius \(a\), as shown in Figure 2.
The ring moves with constant angular speed \(\sqrt { \frac { 2 g } { 3 a } }\) about \(A B\).
The string remains taut throughout the motion.
- Find, in terms of \(m\) and \(g\), the magnitude of the normal reaction between \(P\) and the table.
The angular speed of \(P\) is now gradually increased.
- Find, in terms of \(a\) and \(g\), the angular speed of \(P\) at the instant when it loses contact with the table.
- Explain how you have used the fact that \(P\) is smooth.