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.

Four particles of masses 1 kg, 2 kg, 3 kg and 4 kg are placed at the f

1.	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.
Answer» SOLUTION :ASSUMING A as the origin, AB as 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)=0.5 m` 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(0)+2(0)+3(1)+4(1))/(1+2+3+4)=0.7 m` `therefore` Co-ordinates of centre of mass `(X_(CM), y_(CM))=(0.5 m, 0.7 m)`