6.
\begin{figure}[h]
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\caption{Figure 3}
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\end{figure}
A uniform rod \(A B\) has length 3 m and weight 120 N . The rod rests in equilibrium in a horizontal position, smoothly supported at points \(C\) and \(D\), where \(A C = 0.5 \mathrm {~m}\) and \(A D = 2 \mathrm {~m}\), as shown in Fig. 3. A particle of weight \(W\) newtons is attached to the rod at a point \(E\) where \(A E = x\) metres. The rod remains in equilibrium and the magnitude of the reaction at \(C\) is now twice the magnitude of the reaction at \(D\).
- Show that \(W = \frac { 60 } { 1 - x }\).
- Hence deduce the range of possible values of \(x\).