A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

Question

Marcelo

Physics

17 December, 00:35

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

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Answers (1)

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Britney Daugherty · Answer 1

Solid sphere will reach the bottom first.

Explanation:

It does not matter having equal masses and radii and uniform density. It's about the shape of object, their rotational inertia and how much the mass is more concentrated towards the center. As we know that the sphere's mass is more towards the center in comparison with hollow pipe and cylinder. As in hollow pipe the mass is towards the edges not towards the center. The moment of inertia for solid sphere is given as follows.

Moment of inertia for sphere = 2/5MR²

Its value is less then those of hollow pipe and cylinder so it will win the race and will reach the bottom first.