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\includegraphics[max width=\textwidth, alt={}, center]{3243c326-a51c-462f-a57c-a150d0044ea9-3_510_716_662_676} Two uniform rods \(A B\) and \(B C\), each of length \(4 L\), are freely jointed at \(B\), and rest in a vertical plane with \(A\) and \(C\) on a smooth horizontal surface. The weight of \(A B\) is \(W\) and the weight of \(B C\) is \(2 W\). The rods are joined by a horizontal light inextensible string fixed to each rod at a point distance \(L\) from \(B\), so that each rod is inclined at an angle of \(60 ^ { \circ }\) to the horizontal (see diagram).

1. By considering the equilibrium of the whole body, show that the force acting on \(B C\) at \(C\) is \(1.75 W\) and find the force acting on \(A B\) at \(A\).
2. Find the tension in the string in terms of \(W\).
3. Find the horizontal and vertical components of the force acting on \(A B\) at \(B\), and state the direction of the component in each case.