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

1.	Four particles of masses 1kg, 2kg, 3kg and 4kg 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 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)`