4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{b4065fe1-55fa-4a01-8ae2-006e0d529c50-10_787_814_246_566}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

The uniform lamina $L$, shown shaded in Figure 1, is formed by removing a circular disc of radius $2 a$ from a uniform circular disc of radius $4 a$. The larger disc has centre $O$ and diameter $A B$. The radius $O D$ is perpendicular to $A B$. The smaller disc has centre $C$, where $C$ is on $A B$ and $B C = 3 a$
\begin{enumerate}[label=(\alph*)]
\item Show that the centre of mass of $L$ is $\frac { 13 } { 3 } a$ from $B$.

The mass of $L$ is $M$ and a particle of mass $k M$ is attached to $L$ at $B$. When $L$, with the particle attached, is freely suspended from point $D$, it hangs in equilibrium with $A$ higher than $B$ and $A B$ at an angle $\theta$ to the horizontal, where $\tan \theta = \frac { 3 } { 4 }$
\item Find the value of $k$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2019 Q4 [9]}}