The centre of mass of three particles of masses 10 kg, 20 kg and 30 kg is on origin (0, 0, 0). Now where should one place a mass of 40 kg, so that centreof mass of system is equal to (3, 3, 3)?

The centre of mass of three particles of masses 10 kg, 20 kg and 30 kg

1.	The centre of mass of three particles of masses 10 kg, 20 kg and 30 kg is on origin (0, 0, 0). Now where should one place a mass of 40 kg, so that centreof mass of system is equal to (3, 3, 3)?
Answer» `(0,0,0)` `(7.5,7.5,7.5)` `(1,2,3)` `(4,4,4)` SOLUTION :`m_(1)(x_(1),y_(1),z_(1))+m_(2)(x_(2),y_(2),z_(2))+` `(x,y,z)=(m_(3)(x_(3),y_(3),z_(3))+m_(4)(x_(4),y_(4),z_(4)))/(m_(1)+m_(2)+m_(3)+m_(4))` `therefore (x,y,z)=(0+m_(4)(x_(4),y_(y),z_(4)))/(10+20+30+40)` `therefore (3,3,3)=(40(x_(4),y_(4),z_(4)))/(100)` `therefore ((300)/(40),(300)/(40),(300)/(40))=(x_(4),y_(4),z_(4))` `therefore (7.5,7.5,7.5)=(x_(4),y_(4),z_(4))` `therefore (x_(4),y_(4),z_(4))=(7.5,7.5,7.5)` unit