A solid cylinder and a thin hoop of equal mass and equal radius roll without slipping down the same inclined plane from rest. Which object reaches the bottom first?
Answer and explanation
Correct answer: C. The cylinder
- Step 1: Recall rotational inertias: and $I_{hoop} = MR^2.
- Step 2: Objects with smaller rotational inertia convert a larger fraction of potential energy into translational kinetic energy, producing higher linear acceleration. Thus, the cylinder arrives first.
Answer
The cylinder.
Why not the others: The hoop arrives second due to greater rotational inertia; they do not reach simultaneously because inertia fractions differ; both objects successfully roll to the bottom.
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