Four particles of masses 1kg, 2kg, 3kg and 4kg are placed at the four vertices A, B, C and D of a square of side 1m. Find the position of centre of mass of the particles. Assume that D is situated at the origin.

Explanation

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)`
and `m_(4)=4kg, (x_(4), y_(4))=(0,0)`
Co-ordinates of their COM are
`X_(COM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)m_(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)/(2)m`
`=0.5 m`
Similarly, `y_(COM)= (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)/(10)=0.3m`

`therefore (x_(COM), y_(COM))=(0.5m, 0.3m)`
Thus, position of COM of the four particles is as shown in figure.