1.
\begin{figure}[h]
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\caption{Figure 1}
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A uniform rod of length \(72 a\) is cut into pieces. The pieces are used to make two rigid squares, \(A B C D\) and \(P Q R S\), with sides of length \(10 a\) and \(8 a\) respectively. The two squares are joined to form the rigid framework shown in Figure 1.
The squares both lie in the same plane with the rod \(A B\) parallel to the rod \(P Q\).
Given that
- \(A D\) cuts \(P Q\) in the ratio \(3 : 5\)
- \(D C\) cuts \(Q R\) in the ratio 5:3
- explain why the centre of mass of square \(A B C D\) is at \(Q\).
- Find the distance of the centre of mass of the framework from \(B\).