Consider a rectangular plate of dimensions `axxb`. If this plate is considered to be made up of four rectangles of dimensions `a/2xxb/2` and we now remove one out of four rectangles. Find the position where the centre of mass of the remaining system will lie?

Explanation

The rectangular plate is shown in the figure of is removed. We can find the `x` and `y` coordinates of the centre of mas of this system, taking origin at the centre of plate. The coordinates of the three remaining rectangles are `(a/4, b/4), ((-a)/4 (+b)/4)` and `((-a)/4, (-b)/4)`. By geometry, masses of these rectangles can be taken as `M/4`. Now `x`-coordinate of the centre of mass:
`X_(CM)=(M/4 a/4 M/4 a/4-M/4 a/4)/(3M/4)=a/12`
and `y`-coordinate of the centre of mass:
`y_(CM)=(M/4b/4+M/4b/4-M/4b/4)/(3M/4)=b/12`