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

Centre of mass of 3 particles 10 kg, 20 kg and 30 kg is at (0, 0, 0).

1.	Centre of mass of 3 particles 10 kg, 20 kg and 30 kg is at (0, 0, 0). Where should a particle of mass 40 kg be placed so that the combined centre of mass will be at (3, 3, 3)?
Answer» (0,0,0) (7.5 , 7.5 , 7.5) (1 , 2 , 3) (4 , 4 , 4) SOLUTION :LET the position COORDINATES of 40 kg be (x , y , z) `therefore X_(CM) = sum_(m_(i) x_(i))/(sum m_(i)) or 3 = (10 xx 0 + 20 xx 0 + 30 xx 0 + 40 xx x)/(10 + 20 + 30 + 40)` `therefore x = (300)/(40) = 7.5` `Y_(CM) = (sum m_(i) y_(i))/(sum m_(i))` `3 = (10 xx 0 + 20 xx 0 + 30 xx 0+ 40 xx y)/(10 + 20 + 30 + 40) = y = (300)/(40) = 7.5` `Z_(CM) = (sum m_(i) z_(i))/(sum m_(i))` `3=(10 xx 0 + 20 xx 0 + 30 xx 0 + 40 xx z)/(10 + 20 + 30 + 40) implies z = (300)/(40) = 7.5`