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For a homogeneous (uniformly dense) thin circular disc, the centre of mass lies at:
AAny point on the circumference
BIts geometric centre
CA point depending on its orientation
DA point on the axis but outside the plane of the disc
Answer & Solution
Correct answer: B. Its geometric centre
A homogeneous disc has reflection symmetry about its geometric centre: for every mass element at (x, y) there is an equal element at (−x, −y). The symmetry integrals $\int x \, dm$ and $\int y \, dm$ both vanish about that point, so the COM coincides with the geometric centre. This argument holds for all uniformly dense regular shapes (ring, sphere, rod, etc.).
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