1.
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\caption{Figure 1}
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Five identical uniform rods are joined together to form the rigid framework \(A B C D\) shown in Figure 1. Each rod has weight \(W\) and length 4a. The points \(A , B , C\) and \(D\) all lie in the same plane.
The centre of mass of the framework is at the point \(G\).
- Explain why \(G\) is the midpoint of \(A C\).
The framework is suspended from the ceiling by two vertical light inextensible strings. One string is attached to the framework at \(A\) and the other string is attached to the framework at \(B\). The framework hangs freely in equilibrium with \(A B\) horizontal.
- Find
- the tension in the string attached at \(A\),
- the tension in the string attached at \(B\).
A particle of weight \(k W\) is now attached to the framework at \(D\) and a particle of weight \(2 k W\) is now attached to the framework at \(C\). The framework remains in equilibrium with \(A B\) horizontal and the strings vertical.
Either string will break if the tension in it exceeds \(6 W\).
- Find the greatest possible value of \(k\).