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\includegraphics[max width=\textwidth, alt={}, center]{833c338f-53c1-436e-a772-0cdaf17fa72d-3_559_1303_255_422} The diagram shows a central cross-section CDEF of a uniform solid cube of weight \(W\) and with edges of length \(2 a\). The cube rests on a rough horizontal plane. A thin uniform \(\operatorname { rod } A B\), of weight \(W\) and length \(6 a\), is hinged to the plane at \(A\). The rod rests in smooth contact with the cube at \(C\), with angle \(C A D\) equal to \(30 ^ { \circ }\). The rod is in the same vertical plane as \(C D E F\). The coefficient of friction between the plane and the cube is \(\mu\). Given that the system is in equilibrium, show that \(\mu \geqslant \frac { 3 } { 25 } \sqrt { } 3\). [6] Find the magnitude of the force acting on the \(\operatorname { rod }\) at \(A\).