Physics - Center of Mass Question with Solution | TestHub

Let the origin be at the center of the square plate. The square plate is symmetric about the origin, and the circular hole is also symmetric about the origin.

When a part is removed from a body, the center of mass of the remaining body can be found using the formula: $${\vec{R}}_{CM}=\frac{M{\vec{R}}_{original}-m{\vec{r}}_{hole}}{M-m}$$ Here, the original square plate has its center of mass at the origin, ${\vec{R}}_{original}=0$. The circular hole is also cut from the center, so its center of mass is also at the origin, ${\vec{r}}_{hole}=0$.

Therefore, the center of mass of the remaining plate will be at the origin. The system remains symmetric about the original center.