1.
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\caption{Figure 1}
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A uniform rod of length \(24 a\) is cut into seven pieces which are used to form the framework \(A B C D E F\) shown in Figure 1.
It is given that
- \(A F = B E = C D = A B = F E = 4 a\)
- \(B C = E D = 2 a\)
- the rods \(A F , B E\) and \(C D\) are parallel
- the rods \(A B , B C , F E\) and \(E D\) are parallel
- \(A F\) is perpendicular to \(A B\)
- the rods all lie in the same plane
The distance of the centre of mass of the framework from \(A F\) is \(d\).
- Show that \(d = \frac { 19 } { 6 } a\)
- Find the distance of the centre of mass of the framework from \(A\).