6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4fe54579-ac77-46f9-85e1-2e95963d6b3e-4_288_1275_201_410}
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\caption{Fig. 2}
\end{figure}
Figure 2 shows a uniform plank \(A B\) of length 8 m and mass 50 kg suspended horizontally by two light vertical inextensible strings attached at either end of the plank. The maximum tension that either string can support is 40 gN .
A rock of mass \(M \mathrm {~kg}\) is placed on the plank at \(A\) and rolled along the plank to \(B\) without either string breaking.
- Explain, with the aid of a sketch-graph, how the tension in the string at \(A\) varies with \(x\), the distance of the rock from \(A\).
- Show that \(M \leq 15\).
The first rock is removed and a second rock of mass 20 kg is placed on the plank.
- Find the fraction of the plank on which the rock can be placed without one of the strings breaking.