A thin uniform circular disc of radius R and mass M is placed on the x y -plane with its center at the origin. A square hole of side length a = R /2 is cut from the disc such that centre of the square

Question

A thin uniform circular disc of radius R and mass M is placed on the x y -plane with its center at the origin. A square hole of side length a = R /2 is cut from the disc such that centre of the square coincides with the center of the disc and its sides are parallel to the x and y axes. Find the coordinates of the center of mass of the remaining portion of the disc.

TestHub · Accepted Answer

The full disc is uniform with its centre at the origin O, so its COM is at (0, 0).

The square hole is concentric with the disc and its sides are parallel to the axes, so the removed square's own COM is also at (0, 0).

Negative-mass method: $x_{COM} = \frac{M \cdot 0 - m _{s q} \cdot 0}{M - m _{s q}} = 0$ , and similarly $y_{COM} = 0$ .

(Equivalently: the remaining figure is symmetric under both $x \to - x$ and $y \to - y$ reflections, so the COM must lie on both axes.)

Answer: (D) (0, 0)

Physics - Center of Mass Question with Solution | TestHub

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