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A non-uniform \(\operatorname { rod } A B\), of length 0.6 m and weight 9 N , has its centre of mass 0.4 m from \(A\). The end \(A\) of the rod is in contact with a rough vertical wall. The rod is held in equilibrium, perpendicular to the wall, by means of a light string attached to \(B\). The string is inclined at \(30 ^ { \circ }\) to the horizontal. The tension in the string is \(T \mathrm {~N}\) (see diagram).
- Calculate \(T\).
- Find the least possible value of the coefficient of friction at \(A\).