6.

Figure 3

A uniform pole $A B$, of weight 50 N and length 6 m , has a particle of weight $W$ newtons attached at its end $B$. The pole has its end $A$ freely hinged to a vertical wall.\\
A light rod holds the particle and pole in equilibrium with the pole at $60 ^ { \circ }$ to the wall. One end of the light rod is attached to the pole at $C$, where $A C = 4 \mathrm {~m}$.\\
The other end of the light rod is attached to the wall at the point $D$.\\
The point $D$ is vertically below $A$ with $A D = 4 \mathrm {~m}$, as shown in Figure 3.\\
The pole and the light rod lie in a vertical plane which is perpendicular to the wall.\\
The pole is modelled as a rod.\\
Given that the thrust in the light rod is $60 \sqrt { 3 } \mathrm {~N}$,
\begin{enumerate}[label=(\alph*)]
\item show that $W = 15$
\item find the magnitude of the resultant force acting on the pole at $A$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2023 Q6 [10]}}