Answer: Option A
:
A
The rectangular plate is shown in the figure of which one part is removed. We can find the x and y coordinates of the centre of mass of this system, taking origin at the centre of the 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:
$x_{CM}=\frac{\frac{Ma}{16}-\frac{Ma}{16}-\frac{Ma}{16}}{3\frac{M}{4}}=-\frac{a}{12}$
and y-coordinate of the centre of mass:
$y_{CM}=\frac{\frac{Mb}{16}-\frac{Mb}{16}-\frac{Mb}{16}}{3\frac{M}{4}}=\frac{b}{12}$