4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{916543cb-14f7-486c-ba3c-eda9be134045-10_633_1237_258_356}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\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 $T$
\begin{enumerate}[label=(\alph*)]
\item By considering particle $C$, find $T$ in terms of $m , g$ and $\beta$
\item 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.
\item Find the value of $\tan \beta$\\

\includegraphics[max width=\textwidth, alt={}, center]{916543cb-14f7-486c-ba3c-eda9be134045-11_2255_50_314_34}\\

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIXV SIHIANI III IM IONOO & VIAV SIHI NI JYHAM ION OO & VI4V SIHI NI JLIYM ION OO \\
\hline
\end{tabular}
\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2020 Q4 [10]}}