8.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{5c3869c7-008f-4131-b68d-8ecdd4da3377-24_369_1200_248_370}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Two particles, $P$ and $Q$, with masses $2 m$ and $m$ respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed at the edge of a rough horizontal table. Particle $Q$ is held at rest on the table and particle $P$ is on the surface of a smooth inclined plane. The top of the plane coincides with the edge of the table. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha = \frac { 3 } { 4 }$, as shown in Figure 4. The string lies in a vertical plane containing the pulley and a line of greatest slope of the plane. The coefficient of friction between $Q$ and the table is $\frac { 1 } { 2 }$. Particle $Q$ is released from rest with the string taut and $P$ begins to slide down the plane.
\begin{enumerate}[label=(\alph*)]
\item By writing down an equation of motion for each particle,
\begin{enumerate}[label=(\roman*)]
\item find the initial acceleration of the system,
\item find the tension in the string.

Suppose now that the coefficient of friction between $Q$ and the table is $\mu$ and when $Q$ is released it remains at rest.
\end{enumerate}\item Find the smallest possible value of $\mu$.

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\hfill \mbox{\textit{Edexcel M1 2017 Q8 [14]}}