Question

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?

Answer 1

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`