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Four particles of masses 1 kg, 2kg, 3kg ...

Four particles of masses `1 kg, 2kg, 3kg` and `4kg` are placed the four vertices `A,B,C` and `D`, respectively, of a square of side `1m`. Find the position of centre of mass of the particles.

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Assuming `D` as the origin, `DC` as `x`-axis and `DA` as `y`-axis, we have
`m_(1)=1kg, (x_(1), y_(1))=(0,1m)`
`m_(2)=2kg, (x_(2),y_(2))=(1m,1m)`
`m_(3)=3kg, (x_(3),y_(3))=(1m,0)`
`m_(4)=3kg, (x_(4),y_(4))=(0,0)`
coordinates of their `CM` are calculted as follows
`x_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`

`=((1)(0)+2(1)+3(1)+4(0))/(1+2+3+4)`
`=5/10=1/2m=0.5m`
Similarly `y_(CM)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`=((1)(1)+2(1)+3(0)+4(0))/(1+2+3+4)=3/10m=0.3m`
`:. x_(CM), y_(CM)=(0.5m, 0.3m)`
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