4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{88731f1c-5177-4096-841b-cd9c3f87782b-12_510_1082_269_438}
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\caption{Figure 3}
\end{figure}
A uniform rod \(A B\), of mass \(m\) and length \(2 a\), rests with its end \(A\) on rough horizontal ground. The rod is held in limiting equilibrium at an angle \(\theta\) to the horizontal by a light string attached to the rod at \(B\), as shown in Figure 3. The string is perpendicular to the rod and lies in the same vertical plane as the rod.
The coefficient of friction between the ground and the rod is \(\mu\).
Show that \(\mu = \frac { \cos \theta \sin \theta } { 2 - \cos ^ { 2 } \theta }\)