Centre of mass of 3 particles of 10 kg, 20 kg and 30kg is at (0, 0, 0). Where should a particle of 40 kg be placed so that the combined centre of mass will be at (3, 3, 3) ?

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In the first case, ​ x cm ​ = 60 10 x 1 ​ + 20 x 2 ​ + 30 x 3 ​ ​ = 0 ​ or 10 x 1 ​ + 20 x 2 ​ + 30 x 3 ​ = 0 ​ In the second case, ​ x c m ​ = 100 10 x 1 ​ + 20 x 2 ​ + 30 x 3 ​ + 40 x 4 ​ ​ = 3 ​ or 100 40 x 4 ​ ​ = 3 ⇒ x 4 ​ = 7.5 units ​ Similarly y 4 ​ = z 4 ​ = 7.5 units

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