Discussion
A disk and a sphere of same radius but different masses roll on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?
Answer: B
The sphere reaches the bottom first.
For a body rolling without slipping, \[a = \frac{g\sin\theta}{1 + k^2/R^2}\] The ratio \(k^2/R^2\) is \(2/5\) for a solid sphere and \(1/2\) for a disc, so the sphere has the larger acceleration. Mass and radius cancel out entirely - only the shape matters.
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