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Question 30346
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Rigid Body Dynamics: Rotational KE — Yo-Yo MCQ

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Rotational KE — Yo-YoHardQuestion 30346

Question

A yo-yo (treated as a disc, mass M, outer radius R, inner radius r) falls under gravity unrolling from a string wound around r. The acceleration is:
  1. A
    g
  2. B
    g/2
  3. C
    g(1 + R²/2r²)⁻¹
  4. D
    2gr²/(R²+2r²)
    Correct

Correct answer

2gr²/(R²+2r²)

Explanation

For yo-yo: Mg − T = Ma, Tr = Iα = (MR²/2)(a/r). Solving: a = g/(1 + R²/2r²) = 2gr²/(2r²+R²).

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