Four particles of masses m_(1) = 1 kg, m_(2) = 2 kg, m_(3) = 3 kg and m_(4) = 4 kg are located at the corners of a rectangle as shown in Fig. Locate the position of centre of mass.

Four particles of masses m_(1) = 1 kg, m_(2) = 2 kg, m_(3) = 3 kg and

1.	Four particles of masses m_(1) = 1 kg, m_(2) = 2 kg, m_(3) = 3 kg and m_(4) = 4 kg are located at the corners of a rectangle as shown in Fig. Locate the position of centre of mass.
Answer» Solution :Here, `m_(1) = 1kg, m_(2) = 2 KG, m_(3) = 3 kg`, `m_(4) = 4kg` As is clear form Fig. `m_(1)` is taken at the origin. Therefore, `x_(1) = 0, y_(1) = 0`. For `m_(2) , x_(2) = a hati, y_(2) = 0` For `m_(3) , x_(3) = a hati , y_(3) = b HATJ` For `m_(4) , x_(4) = 0, y_(4) = b hatj` Co-ordinates of centre of mass of the SYSTEM are `X = (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 xx 0 + 2 (a hati) + 3 (a hati) + 4 xx 0)/(1 + 2+ 3+ 4) = 0.5 a hati` `y = (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 xx 0 + 2 xx 0 + 3 xx b hatj + 4 xx b hatj)/(1 + 2+ 3+ 4) = 0.7 b hatj` Position of centre of mass of the system is `[0.5 a hatj + 0.7 b hatj]`