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Q7. Four masses m₁, m₂, m₃ and m₄ on a common axis of rotation are 20 kg, 30 kg, 24 kg and 26 kg respectively. Their radii from the centre of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m, with the angles separating the masses measured as 45°, 75° and 135°.

(a) Determine the magnitude of the balance mass if its radius of rotation is 0.2 m. (10)

(b) Calculate the angular position of the balance mass in relation to m₁. (6)