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  4. 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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Q. 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?

AIPMTAIPMT 2010System of Particles and Rotational Motion

Solution:

Time taken to reach the bottom of inclined plane.
$t=\sqrt{\frac{2 l\left(1+\frac{K^{2}}{R^{2}}\right)}{g \sin \theta}}$
Here, $l$ is length of incline plane
For solid cylinder $K^{2}=\frac{R^{2}}{2}$
For hollow cylinder $K^{2}=R^{2}$
Hence, solid cylinder will reach the bottom first.