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NEET 2016 (Phase 1) · Rolling Motion

Rolling Motion question from NEET 2016 (Phase 1)

Q74NEET 2016 · PHASE 1Medium

Rolling Motion

A disc 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?

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Answer: (d)

Rolling acceleration $a = \dfrac{g\sin\theta}{1 + k^2/R^2}$ does not depend on mass.
Disc: $k^2/R^2 = \frac{1}{2}$ ; sphere: $k^2/R^2 = \frac{2}{5}$ (smaller), so the sphere has larger $a$ .
Same length, larger $a$ means less time: the sphere reaches first, answer (d).

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