# What is this mystery sphere?

**URL:** <https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440>\
**Category:** Factual Questions\
**Created:** [September 12, 2020, 5:20pm UTC](https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440 "2020-09-12T17:20:12Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [September 18, 2020, 8:32pm UTC](https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440/21 "2020-09-18T20:32:44Z")

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One could, in principle, test for hollowness non-destructively by measuring its angular momentum. But I’m not sure how precisely one could do so using equipment in a typical home workshop.

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**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\
**Post date:** [September 19, 2020, 1:01pm UTC](https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440/22 "2020-09-19T13:01:54Z")

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A long ramp and a stopwatch would do the trick.

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**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\
**Post date:** [September 19, 2020, 1:14pm UTC](https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440/23 "2020-09-19T13:14:07Z")

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Oh all right, I’ll give more details than that.

If an object of radius R rolls down a ramp inclined at an angle θ to the vertical, one can show that its acceleration along the ramp is

a = g\*sin(θ)/(1 + β),

where β is a factor that depends on the weight distribution of the object. Specifically, for a solid sphere of uniform density, β = 2/5, and for a thin spherical shell, β = 2/3. If the sphere is of uniform density but has “thick” walls, the result is somewhere in between.

So if you release the ball from rest at the top of a ramp of length L, and it takes a time t to get to the end, then you can determine the acceleration via the kinematic equation

L = (1/2) \* a \* t2, or  
a = 2 \* L/t2.

From that, you can figure out the value of β, which will give you a clue as to its internal mass distribution. For the cognoscenti reading this, the factor β is related to the moment of inertia of the object by I = β M R2.

(Also, I hope that none of my students are reading this, because I sometimes give this problem on exams.)

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<div class="post-metadata">

**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [September 19, 2020, 2:22pm UTC](https://boards.straightdope.com/t/what-is-this-mystery-sphere/920440/24 "2020-09-19T14:22:38Z")

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Ooh, yeah, I should have thought of that! The best I was coming up with was to put the sphere on an axle with a spool, and winding a string around the spool with a weight hanging from it. But your way is much simpler.

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