5 A uniform rod AB , of mass \(3 m\) and length \(2 a\), rests with the end A on a rough horizontal surface. A small object of mass \(m\) is attached to the rod at B . The rod is maintained in equilibrium at an angle of \(60 ^ { \circ }\) to the horizontal by a force acting at an angle of \(\theta\) to the vertical at a point C , where the distance \(\mathrm { AC } = \frac { 6 } { 5 } a\). The force acting at C is in the same vertical plane as the rod (see Fig. 5).
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\caption{Fig. 5}
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- On the copy of Fig. 5 in the Printed Answer Booklet, mark all the forces acting on the rod. [2]
- Show that the magnitude of the force acting at C can be expressed as \(\frac { 25 m g } { 6 ( \cos \theta + \sqrt { 3 } \sin \theta ) }\).
- Given that the rod is in limiting equilibrium and the coefficient of friction between the rod and the surface is \(\frac { 3 } { 4 }\), determine the value of \(\theta\).