A shaft rotating at 1000 rpm carries two unbalances of magnitudes 0.2 kg m and 0.1 kg m in planes A and B respectively. The planes A and B are 0.5 m apart and the directions of the unbalances are at 90°. A third unbalances has to be attached to the shaft at a location C so that the shaft is statically balanced and the magnitude of the bearing reactions is minimum possible. The bearings are 0.6 m from A and B. Determine

(a) location of C with respect to A and B,

(b) the magnitude of unbalance at C,

(c) the angular position of unbalance at C with respect to A and B.