Question

The centre of mass of three particles of masses `1 kg, 2kg and 3 kg` lies at the point `(3m, 3m, 3m)` where should a fourth particles of mass `4 kg` be positioned so that centre of mass of the four particle system at `(1m, 1m, 1m)`?

Answer 1

Suppose particle of `4 kg` mass is aplced at point `(x,y,z)`. Then the centre of mass of `6 kg (1 kg + 2 kg + 3 kg)` mass and `4 kg` mass must lie at the point `(1 m, 1m, 1m)`.
`:. X_(cm) = (6 xx 3 + 4x)/(6+ 4)= 1 or x = - 2m`
`y_(cm) = (6 xx 3+ 4 y)/(6 + 4) = 1 or y =- 2m`
`z_(cm) = (6xx 3 + 4 z)/(6 + 4) = 1 or z = - 2m`