Rolling on an Inclined Plane – Rankers Physics

Rolling on an Inclined Plane

For a hollow cylinder & a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier on the ground: (2000)

Solid cylinder
Hollow cylinder
Both simultaneously
Can't say anything

Solution:

Acceleration of a rolling body is given by $$a = \frac{g \sin\theta}{1 + I/MR^2}$$. Since the solid cylinder has a smaller moment of inertia ratio than the hollow cylinder, its acceleration is greater, so it reaches the bottom first.

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