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NEET 2010 (AIPMT, Mains) · Rolling Motion

Rolling Motion question from NEET 2010 (AIPMT, Mains)

Q82NEET 2010 · AIPMT · MAINSEasy

Rolling Motion

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

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Answer: (d)

$a = \frac{g\sin\theta}{1 + k^2/R^2}$ : smaller $\frac{k^2}{R^2}$ gives larger acceleration.
Solid cylinder: $\frac{k^2}{R^2} = \frac{1}{2}$ ; hollow cylinder: $\frac{k^2}{R^2} = 1$ .
The solid cylinder accelerates faster, independent of mass and angle.
So the answer is (d) solid cylinder.

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