Fig. shown a three particle system with masses `m_(1) = 3.0 kg, m_(2) = 4.0kg` and `m_(3) = 8.0 kg`. The scales on the axes are set by `x_(s) = 2.0 m` and `y_(s) = 2.0m`. What are the co-ordinates of centre if mass ? If `m_(3)` is gradually increased, does the centre of mass of the system shift towards or away from that particle or does it remain stationary ?

Explanation

In Fig. co-ordinates of mass `m_(1) = 3.0 kg` are `x_(1) = 0, y_(1) = 0`.
For mass `m_(2) = 4.0 kg , x_(2) = 2.0m, y_(2) = 1.0 m`.
For mass `m_(3) = 8.0 kg, x_(3) = 1.0, y_(3) = 2.0 m`.
The co-ordinate of centre of mass is
`x_(cm) = (m_(1)x_(1) + m_(2)x_(2) + m_(3)x_(3))/(m_(1) + m_(2) + m_(3))`
`= (0 + 4.0(2.0) + (8.0)(1.0))/(3.0 + 4.0 + 8.0) = (16)/(15) = 1.1m`
`y_(cm) = (m_(1)y_(1) + m_(2)y_(2) + m_(3)y_(3))/(m_(1) + m_(2) + m_(3))`
`= (3.0 xx 0 + 4.0 xx 1.0 + 8.0 xx 2.0)/(3.0 + 4.0 + 8.0) = (20)/(15) = 1.3 m`
When the mass `m_(3)` is gradually increased, the centre of mass shifts towards `m_(3)`.