A rectangular plate of dimensions `l xx b` is in `x -y` plane as shown in Fig. If the portion of this plate lying in quadrant `I` is removed, find the position of centre of mass of remaining part of plate.

Explanation

In Fig. we have chosen `O` as origin. length `l` of rectangular plate along X-axis and its breadth `b` along Y-axis. The plate is divided into four equal quadrants each of mass `m` say. The shaded quadrant is removed. If removed. If `C_(2), C_(3), C_(4)` are the centres of mass of quardants indicated, then their co-ordinates are :
`C_(2) (-l//4, b//4), C_(3) (-l//4, - b//4), C_(4) (l//4, - b//4)`.
The co-ordinates of centre of mass of `L` shaped lamina are
`x_(cm) = (m (x_(1) + x_(2) + x_(3)))/(m_(1) + m_(2) + m_(3)) = (x_(1) + x_(2) + x_(3))/(3)`
`= (-l//4 - l//4 + l//4)/(3) = (l)/(12)`
Similarly,
`y_(cm) =(y_(1) + y_(2) + y_(3))/(3) = (b//4 - b//4 - b//4)/(3) = (-b)/(12)`