2.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
  \includegraphics[alt={},max width=\textwidth]{044c5866-0a12-4309-8ced-b463e1615fb0-2_389_601_1362_693}
\end{center}
\end{figure}

A light inextensible string of length $8 l$ has its ends fixed to two points $A$ and $B$, where $A$ is vertically above $B$. A small smooth ring of mass $m$ is threaded on the string. The ring is moving with constant speed in a horizontal circle with centre $B$ and radius 3l, as shown in Fig. 2. Find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string,
\item the speed of the ring.
\item State briefly in what way your solution might no longer be valid if the ring were firmly attached to the string.\\
(1)

\section*{3.}
\section*{Figure 3}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{044c5866-0a12-4309-8ced-b463e1615fb0-3_564_1051_438_541}
\end{center}

A child's toy consists of a uniform solid hemisphere attached to a uniform solid cylinder. The plane face of the hemisphere coincides with the plane face of the cylinder, as shown in Fig. 3. The cylinder and the hemisphere each have radius $r$, and the height of the cylinder is $h$. The material of the hemisphere is 6 times as dense as the material of the cylinder. The toy rests in equilibrium on a horizontal plane with the cylinder above the hemisphere and the axis of the cylinder vertical.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2003 Q2 [9]}}