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

Explanation

Assuming A as the origin , AB x-axis and AD as y-axis we have

Co-ordinates of their CM are
`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)=0.5m`
Similarly, `y_(CM)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`=(1(0)+2(0)+3(1)+4(1))/(1+2+3+4)=0.7m`
`:.` Co-ordinate of centre of mass
`(X_(CM),y_(CM))=(0.5m,0.7m)`