5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ad09e19e-c4f3-4b93-9e9a-4987def62f26-09_620_776_219_584}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a uniform rod \(A B\), of mass \(m\) and length \(2 a\), with the end \(B\) resting on rough horizontal ground. The rod is held in equilibrium at an angle \(\theta\) to the vertical by a light inextensible string. One end of the string is attached to the rod at the point \(C\), where \(A C = \frac { 2 } { 3 } a\). The other end of the string is attached to the point \(D\), which is vertically above \(B\), where \(B D = 2 a\).
- By taking moments about \(D\), show that the magnitude of the frictional force acting on the rod at \(B\) is \(\frac { 1 } { 2 } m g \sin \theta\)
- Find the magnitude of the normal reaction on the rod at \(B\).
The rod is in limiting equilibrium when \(\tan \theta = \frac { 4 } { 3 }\)
- Find the coefficient of friction between the rod and the ground.