16 A straight uniform rod, \(A B\), has length 6 m and mass 0.2 kg A particle of weight \(w\) newtons is fixed at \(A\).
A second particle of weight \(3 w\) newtons is fixed at \(B\).
The rod is suspended by a string from a point \(x\) metres from \(B\).
The rod rests in equilibrium with \(A B\) horizontal and the string hanging vertically as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-24_410_1148_767_445} Show that $$x = \frac { 3 w + 0.3 g } { 2 w + 0.1 g }$$ \includegraphics[max width=\textwidth, alt={}, center]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-25_2488_1716_219_153}