4.
\begin{figure}[h]
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\caption{Fig. 1}
\end{figure}
Figure 1 shows a uniform rod \(A B\) of mass 2 kg and length \(2 a\). The end \(A\) is attached by a smooth hinge to a fixed point on a vertical wall so that the rod can rotate freely in a vertical plane. A mass of 6 kg is placed at \(B\) and the rod is held in a horizontal position by a light string joining the midpoint of the rod to a point \(C\) on the wall, vertically above \(A\). The string is inclined at an angle of \(60 ^ { \circ }\) to the wall.
- Show that the tension in the string is \(28 g\).
- Find the magnitude and direction of the force exerted by the hinge on the rod, giving your answers correct to 3 significant figures.