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Q. A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then

AIPMTAIPMT 1993System of Particles and Rotational Motion

Solution:

For solid sphere, $\frac{K^2}{R^2}=\frac{2}{5}$
For disc and solid cylinder, $\frac{K^2}{R^2}=\frac{1}{2}$
As $\frac{K^2}{R^2}$ for solid sphere is smallest, it takes minimum time to reach the bottom of the incline, disc and cylinder reach together later.