7.

A non-uniform rod $A B$ has length 6 m and mass 8 kg . The rod rests in equilibrium, in a horizontal position, on two smooth supports at $C$ and at $D$, where $A C = 1 \mathrm {~m}$ and $D B = 1 \mathrm {~m}$, as shown in Figure 3. The magnitude of the reaction between the rod and the support at $D$ is twice the magnitude of the reaction between the rod and the support at $C$. The centre of mass of the rod is at $G$, where $A G = x \mathrm {~m}$.
\begin{enumerate}[label=(\alph*)]
\item Show that $x = \frac { 11 } { 3 }$.

The support at $C$ is moved to the point $F$ on the rod, where $A F = 2 \mathrm {~m}$. A particle of mass 3 kg is placed on the rod at $A$. The rod remains horizontal and in equilibrium. The magnitude of the reaction between the rod and the support at $D$ is $k$ times the magnitude of the reaction between the rod and the support at $F$.
\item Find the value of $k$.\\
7.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
  \includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-20_223_1262_127_338}
\end{center}
\end{figure}

\begin{center}

\end{center}

\begin{center}

\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2018 Q7 [12]}}