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.

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

1.	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.
Answer» Solution :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)`