7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{7ba14d10-1b57-4930-8d65-f21088c5d513-12_292_897_278_415}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Two particles $A$ and $B$, of mass $m$ and $2 m$ respectively, are attached to the ends of a light inextensible string. The particle $A$ lies on a rough horizontal table. The string passes over a small smooth pulley $P$ fixed on the edge of the table. The particle $B$ hangs freely below the pulley, as shown in Figure 3. The coefficient of friction between $A$ and the table is $\mu$. The particles are released from rest with the string taut. Immediately after release, the magnitude of the acceleration of $A$ and $B$ is $\frac { 4 } { 9 } g$. By writing down separate equations of motion for $A$ and $B$,
\begin{enumerate}[label=(\alph*)]
\item find the tension in the string immediately after the particles begin to move,
\item show that $\mu = \frac { 2 } { 3 }$.

When $B$ has fallen a distance $h$, it hits the ground and does not rebound. Particle $A$ is then a distance $\frac { 1 } { 3 } h$ from $P$.
\item Find the speed of $A$ as it reaches $P$.
\item State how you have used the information that the string is light.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2008 Q7 [15]}}