3.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{2273ca38-1e16-44ab-ae84-f4c576cbb8f9-08_583_549_210_760}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

A light inextensible string of length $7 l$ has one end attached to a fixed point $A$ and the other end attached to a fixed point $B$, where $A$ is vertically above $B$ and $A B = 5$ l. A particle of mass $m$ is attached to the string at the point $C$ where $A C = 4 l$, as shown in Figure 1. The particle moves in a horizontal circle with constant angular speed $\omega$. Both parts of the string are taut.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $m , g , l$ and $\omega$,
\begin{enumerate}[label=(\roman*)]
\item the tension in $A C$,
\item the tension in $B C$.

The time taken by the particle to complete one revolution is $R$.\\
Given that $R \leqslant k \pi \sqrt { \frac { l } { 5 g } }$
\end{enumerate}\item find the least possible value of $k$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2018 Q3 [12]}}