2
\includegraphics[max width=\textwidth, alt={}, center]{e004bbb5-f9e1-4ea2-8357-39db9392cb8c-2_403_999_982_575} Two uniform rods \(A B\) and \(A C\), of lengths 3 m and 4 m respectively, have weights 300 N and 400 N respectively. The rods are freely jointed at \(A\). The mid-points of the rods are joined by a light inextensible string. The rods are in equilibrium in a vertical plane with the string taut and \(B\) and \(C\) in contact with a smooth horizontal surface. The point \(A\) is 2.4 m above the surface (see diagram).

1. Show that the force exerted by the surface on \(A B\) is 374 N and find the force exerted by the surface on \(A C\).
2. Find the tension in the string.
3. Find the horizontal and vertical components of the force exerted on \(A B\) at \(A\) and state their directions.