6. A uniform rod, PQ, of length \(2 a\), rests with one end, \(P\), on rough horizontal ground and a point \(T\) resting on a rough fixed prism of semi-circular cross-section of radius \(a\), as shown in the diagram. The rod is in a vertical plane which is parallel to the prism's cross-section. The coefficient of friction at both \(P\) and \(T\) is \(\mu\).
\includegraphics[max width=\textwidth, alt={}, center]{069a48ca-5453-4549-8a9a-0b0eeb2f08af-24_531_1291_577_331} The rod is on the point of slipping when it is inclined at an angle of \(30 ^ { \circ }\) to the horizontal.
Find the value of \(\mu\).
[0pt] [8]
[0pt] [Question 6 Continued]
[0pt] [Question 6 Continued]
[0pt] [Question 6 Continued]