5
\includegraphics[max width=\textwidth, alt={}, center]{39282b82-5229-484a-beb9-7a845dbb5727-2_478_867_1816_641} Two uniform rods \(A B\) and \(B C\) are smoothly jointed at \(B\) and rest in equilibrium with \(C\) on a rough horizontal floor and with \(A\) against a rough vertical wall. The rod \(A B\) is horizontal and the rods are in a vertical plane perpendicular to the wall. The rod \(A B\) has mass \(3 m\) and length \(3 a\), the rod \(B C\) has mass \(5 m\) and length \(5 a\), and \(C\) is at a distance \(6 a\) from the wall (see diagram). Show that the normal reaction exerted by the floor on the rod \(B C\) at \(C\) has magnitude \(\frac { 13 } { 2 } m g\). The coefficient of friction at both \(A\) and \(C\) is \(\mu\). Find the least possible value of \(\mu\) for which the rods do not slip at either \(A\) or \(C\).