4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1f39620e-c10f-4344-89f1-626fff36d187-12_640_645_258_699}
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\caption{Figure 2}
\end{figure}
A small smooth ring \(R\) of mass \(m\) is threaded onto a light inextensible string. One end of the string is attached to a fixed point \(A\) and the other end of the string is attached to the fixed point \(B\) such that \(B\) is vertically above \(A\) and \(A B = 6 a\)
The ring moves with constant angular speed \(\omega\) in a horizontal circle with centre \(A\). The string is taut and \(B R\) makes a constant angle \(\theta\) with the downward vertical, as shown in Figure 2.
The ring is modelled as a particle.
Given that \(\tan \theta = \frac { 8 } { 15 }\)
- find, in terms of \(m\) and \(g\), the magnitude of the tension in the string,
- find \(\omega\) in terms of \(a\) and \(g\)