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The centre of mass of three particles of...

The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (2, 2, 2). The position of the fourth mass of 4 kg of be placed in the system as that the new centre of mass is at (0, 0, 0) is

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Total mass of system of given three particles is `m_(1)` = 1+ 2 +3 = 6 kg
All this mass can be assumed to be existing as a point mass at `(x_(1),y_(1),z_(1))=(2,2,2)`.
Let second mass `m_2 = 4` kg be located at a position with co-ordinates `(x_(2),y_(2),z_(2))`
CM of the system will be at (0,0,0)
`X_(cm) =(m_(1)x_(1) + m_(2)x_(2))/(m_(1) + m_(2)), 0= (6(2) + 4(x_(2)))/(6+4) rArr x_(2)=-3`
Similarly `y_(2)=-3, z_(2)=-3`
`therefore` 4 kg mass should be placed at `(-3,-3,-3)`
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