Four bodies have been arranged at the co...

Four bodies have been arranged at the corners of a rectangle shown in Fig. Find the centre of mass of the system.

Text Solution

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The masses at the corners O,A, B and C of the rectangle Fig are respectively `m_(1)= m, m_(2) =2m, m_(3)=3m " ""and"" " m_(4)=2m.` x-axis is chosen along OC and y-axis along OA. So the coordinates of the masses are respectively (0,0), (0,b), (a,b) and (a,0). If (x,y) are the coordinates of the centre of mass then
`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))`
=`(m.0+2m.0+3m.a+2m.a)/(m+2m+3m+2m)`
`=(5ma)/(8m)=(5)/(8)a`
Similarly , `y=(m.0+2m.b+3m.b+2m.0)/(m+2m+3m+2m)`
`(5mb)/(8m)=(5)/(8)b`
So the centre of mass is at `((5)/(8)a,(5)/(8)b).`

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