17 A uniform rod is resting on two fixed supports at points \(A\) and \(B\).
\(A\) lies at a distance \(x\) metres from one end of the rod.
\(B\) lies at a distance \(( x + 0.1 )\) metres from the other end of the rod.
The rod has length \(2 L\) metres and mass \(m\) kilograms.
The rod lies horizontally in equilibrium as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{28ee1134-b938-4c8f-b4ef-f3f9b210fdef-28_332_880_726_644} The reaction force of the support on the rod at \(B\) is twice the reaction force of the support on the rod at \(A\). Show that $$L - x = k$$ where \(k\) is a constant to be found.