Centre of mass of uniform bodies — A/L Combined Mathematics

How do I practise Centre of mass of uniform bodies?

1 question with a worked solution

Check before you answer: Symmetry Argument Justification: Stating the existence of axes or planes of symmetry explicitly to locate coordinates of G without redundant calculations.

1. Where is the center of mass of a uniform thin semicircular wire of radius r located along its axis of symmetry from the center of the bounding diameter?
   1. A) r / 2
   2. B) 4r / (3π)
   3. C) 2r / π
   4. D) 3r / 8
   Check my answer

   Correct answer: C) 2r / π

   By integration over the wire element dm = λ r dθ from θ = 0 to π: y_cm = (∫ r sin θ · λ r dθ) / (λ π r) = r² [-cos θ]₀^π / (π r) = r (1 - (-1)) / π = 2r / π. (Note: 4r/(3π) is for a uniform semicircular lamina).

   Show worked solution

   Step 1: Formula for semicircular wire: y_cm = 2r / π. Answer: 2r / π.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Centre of mass of uniform bodies fit in the syllabus?

Year 2 · Term 2