1.
\begin{figure}[h]
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\caption{Figure 1}
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A uniform plane lamina is in the shape of an isosceles trapezium \(A B C D E F\), as shown shaded in Figure 1.
- \(B C E F\) is a square
- \(A B = C D = a\)
- \(B C = 3 a\)
- Show that the distance of the centre of mass of the lamina from \(A D\) is \(\frac { 11 a } { 8 }\)
The mass of the lamina is \(M\)
The lamina is suspended by two light vertical strings, one attached to the lamina at \(A\) and the other attached to the lamina at \(F\)
The lamina hangs freely in equilibrium, with \(B F\) horizontal.
Find, in terms of \(M\) and \(g\), the tension in the string attached at \(A\)