A uniform square plate of side a has a circul | vedclass

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(A) Let the side of the square plate be $a$. The area of the square plate is $A_1 = a^2$. The centre of mass of the square plate is at its geometric c

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At the centre of the square

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(A) Let the side of the square plate be $a$. The area of the square plate is $A_1 = a^2$. The centre of mass of the square plate is at its geometric centre $(0,0)$.The circular hole has a diameter $a$,so its radius is $r = a/2$. The area of the circular hole is $A_2 = \pi r^2 = \pi (a/2)^2 = \pi a^2 / 4$.The centre of mass of the circular hole is also at the centre of the square $(0,0)$.The centre of mass of the remaining part is given by the formula:$X_{cm} = \frac{A_1 X_1 - A_2 X_2}{A_1 - A_2}$Since both $X_1$ and $X_2$ are $0$ (as the hole is cut from the centre),the centre of mass of the remaining part is:$X_{cm} = \frac{A_1(0) - A_2(0)}{A_1 - A_2} = 0$Therefore,the centre of mass of the remaining part remains at the centre of the square.

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The centre of the hole is at the centre of the square. The centre of mass of the remaining part is:

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