5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b070338-1de4-4c33-be29-d37ac06c9fed-16_730_442_223_877}
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\caption{Figure 3}
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A uniform lamina \(O A B\) is modelled by the finite region bounded by the \(x\)-axis, the \(y\)-axis and the curve with equation \(y = 9 - x ^ { 2 }\), for \(x \geqslant 0\), as shown shaded in Figure 3. The unit of length on both axes is 1 m .
The area of the lamina is \(18 \mathrm {~m} ^ { 2 }\)
- Show that the centre of mass of the lamina is 3.6 m from \(\boldsymbol { O B }\).
[0pt]
[ Solutions relying on calculator technology are not acceptable.]
A light string has one end attached to the lamina at \(O\) and the other end attached to the ceiling. A second light string has one end attached to the lamina at \(A\) and the other end attached to the ceiling.
The lamina hangs in equilibrium with the strings vertical and \(O A\) horizontal.
The weight of the lamina is \(W\)
The tension in the string attached to the lamina at \(A\) is \(\lambda W\) - Find the value of \(\lambda\)