A shaft is rotating at a speed of 240 r.p.m. Four masses m₁, m2, m3 and m4 of magnitudes 100 kg, 150 kg, 120 kg and 130 kg respectively are rigidly attached to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are 400 mm, 300 mm, 500 mm and 600 mm respectively. The angles made by these masses with the horizontal are 0°, 45°, 1 120° and 255 and 255° respectively. Find analytically and graphically: (i) the magnitude of the balancing mass and (ii) the position of the balancing mass if its radius of rotation is 400 mm. [Ans. (i) 58 kg (ii) 201.30°)