4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ad09e19e-c4f3-4b93-9e9a-4987def62f26-07_542_700_219_628}
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\caption{Figure 1}
\end{figure}
A uniform lamina \(A B C D\) is formed by removing the isosceles triangle \(A D C\) of height \(h\) metres, where \(h < 2 \sqrt { 3 }\), from a uniform lamina \(A B C\) in the shape of an equilateral triangle of side 4 m , as shown in Figure 1. The centre of mass of \(A B C D\) is at \(D\).
- Show that \(h = \sqrt { } 3\)
The weight of the lamina \(A B C D\) is \(W\) newtons. The lamina is freely suspended from \(A\). A horizontal force of magnitude \(F\) newtons is applied at \(B\) so that the lamina is in equilibrium with \(A B\) vertical. The horizontal force acts in the vertical plane containing the lamina.
- Find \(F\) in terms of \(W\).