4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{916543cb-14f7-486c-ba3c-eda9be134045-10_633_1237_258_356}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Two identical small rings, \(A\) and \(B\), each of mass \(m\), are threaded onto a rough horizontal wire. The rings are connected by a light inextensible string. A particle \(C\) of mass \(3 m\) is attached to the midpoint of the string. The particle \(C\) hangs in equilibrium below the wire with angle \(B A C = \beta\), as shown in Figure 2.
The tension in each of the parts, \(A C\) and \(B C\), of the string is \(T\)
- By considering particle \(C\), find \(T\) in terms of \(m , g\) and \(\beta\)
- Find, in terms of \(m\) and \(g\), the magnitude of the normal reaction between the wire and \(A\).
The coefficient of friction between each ring and the wire is \(\frac { 4 } { 5 }\)
The two rings, \(A\) and \(B\), are on the point of sliding along the wire towards each other.
- Find the value of \(\tan \beta\)
\includegraphics[max width=\textwidth, alt={}, center]{916543cb-14f7-486c-ba3c-eda9be134045-11_2255_50_314_34}
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