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Topic: Equilibrium of rigid bodies, rigid body rotation, equations of rotational motion· Rotational Motion

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

1. Disk

2. Sphere

3. Both reach at the same time

4. Depends on their masses

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Answer: 2. Sphere

Key idea: for rolling down an incline, \(a=\dfrac{g\sin\theta}{1+k^2/R^2}\). Smaller \(k^2/R^2\) means larger acceleration and less time.

  • Disk: \(k^2/R^2=\tfrac12\), so \(a=\tfrac23g\sin\theta\).
  • Solid sphere: \(k^2/R^2=\tfrac25\), so \(a=\tfrac57g\sin\theta\).

The sphere accelerates faster and reaches the bottom first. Mass does not matter.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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