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Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and have identical diameters. The correct statement for this situation is

Asked in JEE Main 22nd July 2nd Shift 2021 · Rolling on an incline

Answer: (3) The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.

Step-by-step solution

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.

Why the other options are wrong

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