Question

Two squares of size $(a\times a)$ each are removed from a bigger square of size $(2a\times 2a)$ as shown in the figure. Removed parts are unshaded in the figure given below. Find the coordinates of the $COM$ w.r.t the origin $\text{O}$.

• A. $(\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}})$
• B. $(\frac{a}{2},\frac{a}{2})$
• C. $(0,0)$
• D. $(a,a)$

Answer 1

The correct option is C $(0,0)$

Given: areas and $COMs$ of the shapes, taing $\text{O}$ as the origin.
$\begin{array}{ccc}& \text{Area}& \text{COM}\\ \text{parent square}& 2a\times 2a=4a^2& (0,0)\\ \text{removed squares}& a\times a=a^2& (a/2,a/2)\\ & a\times a=a^2& (-a/2,-a/2)\end{array}$

As we know,
$x_{COM}=\frac{4a^2\times \left(0\right)+(-a^2)\times \left(a/2\right)+(-a^2)\times (-a/2)}{4a^2-a^2-a^2}$
(Take removed areas as negative)
$\Rightarrow x_{COM}=0$

Similarly
$y_{COM}=\frac{4a^2\times \left(0\right)+(-a^2)\times \left(a/2\right)+(-a^2)\times (-a/2)}{4a^2-a^2-a^2}$
$\Rightarrow y_{COM}=0$

Hence, the $COM$ will be at $(0,0)$.