Four particles of masses m, 2m, 3m and 4m are placed at the vertices of a rectangle ABCD as shown in the figure. The particles move from A to B, B to C. C to D and D to A respectively. In this process find the displacement of centre of mass of the system.

Four particles of masses m, 2m, 3m and 4m are placed at the vertices o

1.	Four particles of masses m, 2m, 3m and 4m are placed at the vertices of a rectangle ABCD as shown in the figure. The particles move from A to B, B to C. C to D and D to A respectively. In this process find the displacement of centre of mass of the system.
Answer» Solution :We have `vecDeltar_(CM) =(m_(1)(vec(Deltan)) + m_(2)(vec(Deltar_(2))) + m_(3)vec(Deltar_(3)) + m_(4)vec(Deltar_(4)))/(m_(1) + m_(2) + m_(3) + m_(4))` Where `m_(1) = m, m_(2) = 2m, m_(3) =3m, m_(4)= 4m` `vec(Deltar_(1)) = lhatj. vec(Deltar_(2)) = 2lhati.vec(Deltar_(3)) = - lhatj` and `vec(Deltar_(4)) =-2hati` This GIVES : `vec(DELTAR)cm =((m)(lhatj) + 2m(2lhati) + 3m(-lhatj) + 4m(-2lhati))/(m+2m + 3m + 4m) =-(2L)/5 hati - l/5 HATJ`