Four masses a, b, c and d are attached to a shaft and revolve in the same plane. the masses are 12kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm and 30 mm. the angular position of the masses b, c and d are 60°, 135° and 270° from the mass a. find the magnitude and position of the balancing mass at a radius of 100 mm.