3.
\begin{figure}[h]
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\caption{Figure 1}
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Nine uniform rods are joined together to form the rigid framework \(A B C D E F A\), with \(A B = B C = D F = 3 a , B F = C D = D E = 4 a\) and \(A F = F E = C F = 5 a\), as shown in Figure 1. All nine rods lie in the same plane.
The mass per unit length of each of the rods \(B F , C F\) and \(D F\) is twice the mass per unit length of each of the other six rods.
- Find the distance of the centre of mass of the framework from \(A C\)
The mass of the framework is \(M\). A particle of mass \(k M\) is attached to the framework at \(E\) to form a loaded framework.
When the loaded framework is freely suspended from \(F\), it hangs in equilibrium with \(C E\) horizontal.
- Find the exact value of \(k\)