a A shaft has five masses \( m_{1}, m_{2}, m_{3}, m_{4} \) and \( m_{5} \) which revolves with same radius in planes which are equidistant from one another. The magnitudes of masses in planes 1,3 and 4 are \( 50 \mathrm{~kg}, 40 \mathrm{~kg} \) and 80 kg respectively. The position of masses 3 and 4 with respect to mass 1 are \( 60^{\circ} \) and \( 120^{\circ} \) respectively. Determine the weight in planes 2 and 5 and their positions with respect to plane in order to put the shaft in completely rotary balanced.