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 a square side 1 m. Find the position of cejitre of mass of the system.

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 a square side 1 m. Find the position of cejitre of mass of the system.
Answer» Solution :ASSUMING A as the origin, AB as x-axis and AD as y-axis we have Mass of FIRST particle, `m_(1)`= 1kg , Mass of SECOND particle, `m_(2)`= 2KG Mass of third particle, `m_3 = 3kg` , Mass of fourth particle, `m_4 = 4`kg Co - ordinates of first particle, (`x_(1),y_(1)`)= (0,0) Co - ordinates of second particle, `(x_2, y_2)` = (1,0) Co - ordinates of third particle `(x_3,y_3) = (1,1)` Co - ordinates of fourth particle `(x_4,y_4) = (0,1)` 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)`