6.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{3847deb8-d86e-4254-828f-5d62f20c186f-09_442_689_292_632}
\end{figure}
A uniform pole \(A B\), of mass 30 kg and length 3 m , is smoothly hinged to a vertical wall at one end \(A\). The pole is held in equilibrium in a horizontal position by a light rod CD. One end \(C\) of the rod is fixed to the wall vertically below \(A\). The other end \(D\) is freely jointed to the pole so that \(\angle A C D = 30 ^ { \circ }\) and \(A D = 0.5 \mathrm {~m}\), as shown in Figure 2. Find
- the thrust in the rod \(C D\),
- the magnitude of the force exerted by the wall on the pole at \(A\).
The rod \(C D\) is removed and replaced by a longer light rod \(C M\), where \(M\) is the mid-point of \(A B\). The rod is freely jointed to the pole at \(M\). The pole \(A B\) remains in equilibrium in a horizontal position.
- Show that the force exerted by the wall on the pole at \(A\) now acts horizontally.