5.
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\caption{Figure 2}
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A horizontal uniform \(\operatorname { rod } A B\) has mass \(m\) and length \(4 a\). The end \(A\) rests against a rough vertical wall. A particle of mass \(2 m\) is attached to the rod at the point \(C\), where \(A C = 3 a\). One end of a light inextensible string \(B D\) is attached to the rod at \(B\) and the other end is attached to the wall at a point \(D\), where \(D\) is vertically above \(A\). The rod is in equilibrium in a vertical plane perpendicular to the wall. The string is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 3 } { 4 }\), as shown in Figure 2.
- Find the tension in the string.
- Show that the horizontal component of the force exerted by the wall on the rod has magnitude \(\frac { 8 } { 3 } m g\).
The coefficient of friction between the wall and the rod is \(\mu\). Given that the rod is in limiting equilibrium,
- find the value of \(\mu\).
\includegraphics[max width=\textwidth, alt={}, center]{7ae16b00-d388-4c1b-a195-c785a3900548-08_158_136_2595_1822}