It is assumed that a shaft caries four masses A, B, C and D which revolve in the same plane. The radii of rotations for these masses are 40 mm, 50 mm, 60 mm, and 30 mm. respectively. The given masses are 12 kg, 10 kg, 18 kg and 15 kg and the angular position of the masses B, C and D are 60°, 135º and 270° with respect to the mass A. Find the magnitude and position of the balancing mass. It is given that the balancing mass should rotate at a radius of 100 mm