4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d4fc2ea6-3ffc-42f2-b462-9694adfe2ec1-14_682_817_246_625}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
One end of a light inextensible string of length \(2 l\) is attached to a fixed point \(A\). A small smooth ring \(R\) of mass \(m\) is threaded on the string and the other end of the string is attached to a fixed point \(B\). The point \(B\) is vertically below \(A\), with \(A B = l\). The ring is then made to move with constant speed \(V\) in a horizontal circle with centre \(B\). The string is taut and \(B R\) is horizontal, as shown in Figure 4.
- Show that \(B R = \frac { 31 } { 4 }\)
Given that air resistance is negligible,
- find, in terms of \(m\) and \(g\), the tension in the string,
- find \(V\) in terms of \(g\) and \(l\).