6.
\begin{figure}[h]
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\caption{Figure 2}
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A plank \(A B\) has mass 12 kg and length 2.4 m . A load of mass 8 kg is attached to the plank at the point \(C\), where \(A C = 0.8 \mathrm {~m}\). The loaded plank is held in equilibrium, with \(A B\) horizontal, by two vertical ropes, one attached at \(A\) and the other attached at \(B\), as shown in Figure 2. The plank is modelled as a uniform rod, the load as a particle and the ropes as light inextensible strings.
- Find the tension in the rope attached at \(B\).
The plank is now modelled as a non-uniform rod. With the new model, the tension in the rope attached at \(A\) is 10 N greater than the tension in the rope attached at \(B\).
- Find the distance of the centre of mass of the plank from \(A\).