4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-05_241_794_219_575}
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\caption{Figure 1}
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A non-uniform \(\operatorname { rod } A B\), of mass \(m\) and length \(5 d\), rests horizontally in equilibrium on two supports at \(C\) and \(D\), where \(A C = D B = d\), as shown in Figure 1. The centre of mass of the rod is at the point \(G\). A particle of mass \(\frac { 5 } { 2 } m\) is placed on the rod at \(B\) and the rod is on the point of tipping about \(D\).
- Show that \(G D = \frac { 5 } { 2 } d\).
The particle is moved from \(B\) to the mid-point of the rod and the rod remains in equilibrium.
- Find the magnitude of the normal reaction between the support at \(D\) and the rod.