Find the location of the centre of mass of a uniform plate bounded by two concentric semicircular arcs of inner radius R1 and outer radius R2 (a semicircular annulus).

On the symmetry axis, shifted from the centre towards the curved side
At the centre of the bounding circles
At the midpoint of the straight diameter edge
On the symmetry axis, at a distance from the centre exactly equal to (R1+R2)/2

Correct answer: On the symmetry axis, shifted from the centre towards the curved side

Solution

By symmetry the CM lies on the central axis; subtracting the inner semicircular area from the outer one places it at distance (4/(3*pi))*(R2³ - R1³)/(R2² - R1²) from the centre, on the side of the curved boundary.

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