4. A uniform yoke \(A B\), of mass 4 kg and length \(4 a \mathrm {~m}\), rests on the shoulders \(S\) and \(T\) of two oxen.
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\(A S = T B = a \mathrm {~m}\). A bucket of mass \(x \mathrm {~kg}\) is suspended from \(A\).

1. Show that the vertical force on the yoke at \(T\) has magnitude \(\left( 2 - \frac { 1 } { 2 } x \right) g \mathrm {~N}\) and find, in terms of \(x\) and \(g\), the vertical force on the yoke at \(S\).
2. If the ratio of these vertical forces is \(5 : 1\), find the value of \(x\).
3. Find the maximum value of \(x\) for which the yoke will remain horizontal.