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\includegraphics[max width=\textwidth, alt={}, center]{85402f4a-8d55-47d8-ba48-5b837609b0f4-3_581_903_267_621} Two uniform rods \(X A\) and \(X B\) are freely jointed at \(X\). The lengths of the rods are 1.5 m and 1.3 m respectively, and their weights are 150 N and 130 N respectively. The rods are in equilibrium in a vertical plane with \(A\) and \(B\) in contact with a rough horizontal surface. \(A\) and \(B\) are at distances horizontally from \(X\) of 0.9 m and 0.5 m respectively, and \(X\) is 1.2 m above the surface (see diagram).

1. The normal components of the contact forces acting on the rods at \(A\) and \(B\) are \(R _ { A } \mathrm {~N}\) and \(R _ { B } \mathrm {~N}\) respectively. Show that \(R _ { A } = 125\) and find \(R _ { B }\).
2. Find the frictional components of the contact forces acting on the rods at \(A\) and \(B\).
3. Find the horizontal and vertical components of the force exerted on \(X A\) at \(X\), stating their directions.