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  4. For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

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Q. For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

AIPMTAIPMT 2000System of Particles and Rotational Motion

Solution:

Solid sphere reaches the bottom first because for solid cylinder$\frac{K^2}{R^2}=\frac{1}{2},$
and for hollow cylinder$\frac{K^2}{R^2}=1$.
Acceleration down the inclined plane $\propto \frac{1}{K^2/R^2}$.
Solid cylinder has greater acceleration, so it reaches the bottom first.