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Asked in JEE Main 22nd July 2nd Shift 2021 · Rolling on an incline
Rolling without slipping from rest through a height h: v=√(2gh)/(1+k) with k=I/(MR²).
The speed depends on the shape only, through k, and it falls as k rises.
Ring: k=1, so v=√gh.
Solid cylinder: k=1/2, so v=√(4gh)/3.
Solid sphere: k=2/5, so v=√(10gh)/7.
Putting gh=1: ring 1.00, cylinder 1.15, sphere 1.20.
The sphere is fastest and the ring slowest.
Mass and diameter never appear, which is the point of saying they are identical: it removes them as an explanation and leaves shape as the only one.
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