Challenge 7 Distinguishing two nearly identical spheres

[PritamDamania]

You are given two spheres that are identical in size, weight, appearance, and touch but one sphere is hollow while the other is solid. (As an example, the solid sphere could be made out of a light wood and the hollow sphere made out of a denser wood, then both spheres carefully painted to look and feel the same.) Using only simple items that you might find at home (no fancy equipment, no drills), determine which sphere is hollow.

[ket]

Spin em.

[PritamDamania]

yep or place them on an incline plane and see which one comes down first

[Sir_Zerp]

It takes less force to accelerate the rotation of a solid sphere vs. hollow sphere of the same size and mass?

Sounds right.

[PritamDamania]

yep it is due to the diff. in moment of inertias of the two spheres.

[Ardeocalidus]

I guess the easiest answer would be to knock or drop them.

Even with denser wood, the \"echo\" to the sound made by the force of the drop would be able to identify the hollow one. Pure speculation though.

Rolling them down the inclined plane would and would not work. It would if there was a weight difference, because gravity will pull the heavier one downwards faster than the lighter one, but the author said that one is made out of light wood, and one is made out of heavier wood (which is the hollow one) indicating a tendency for both spheres to be the same weight. This would allow you to not be able to \'feel\' the difference.

The author did specify that the lighter one would be solid, the heavier to be hollow to allow for no weight discrimination. Therefore simple appearences may allow for an answer. By chipping away at the paint, one could in theory identify the two spheres.

But for the sake of being right, I\'ll go with PritamDamania\'s explanation. :)

[Bella]

Whichever one floats! :eyebrow:

[gyani]

Whichever one floats!

i think this test will fail. Both have same mass and volume. So both will have same \"Effective Density\". So both will float in the water to the same extent.


I guess the easiest answer would be to knock or drop them.

That\'s a brilliant idea! The air cavity in the hollow ball will produce a different sound than the solid sphere.


Rolling them down the inclined plane would and would not work.

Moment of Inertia will come into play only when the sphere rolls down the inclined plane. Rolling is possible only when there is friction between the sphere and the inclined plane. The friction force will provide the torque which will be same for both spheres(since they have the same weight). But torque = I*(alpha) so if the I is different, the angular acceleration will be different. For the solid sphere, I = (2/5)*M*R^2 but for the hollow spherical shell, I = (2/3)*M*R^2. Since the moment of inertia of the solid sphere is lesser, its angular acceleration is greater and so it reaches the bottom of the inclined plane first.

But if the friction force was zero, then both balls will just slide down the inclined plane instead of rolling. Then only weight matters, and since that\'s the same for both, both spheres will reach the bottom at the same time.

[lysdexia]

It\'s only a challenge after all the obvious answers have been taken away...

Place each ball onto an electric stove or hotplate, on of course. Then place a palm on each ball. The palm that yanks away first is on the hollow one. Even easier, squeeze a ball in each hand. The chillier is the hollow one.

Massively denser materials have lower specific heats due to nuclear deadheft, not to mention that the thinner shell allows faster heat transport. I invite ye to think of other ways.

[Edited on 11,Fri.02,Feb.2005 by lysdexia]

[kghose]

Originally posted by lysdexia
It\'s only a challenge after all the obvious answers have been taken away...

Place each ball onto an electric stove or hotplate, on of course. Then place a palm on each ball. The palm that yanks away first is on the hollow one.

Why ? We are told nothing about specific heats and conductivity of these materials

-kg

[lysdexia]

edited, happy now?

[Xanadu]

put them in a vacuum see which one explodes first?? :grin:

[editor]

\"Ardeocalidus
Rolling them down the inclined plane would and would not work. It would if there was a weight difference, because gravity will pull the heavier one downwards faster than the lighter one,\"

Have you learned nothing about physics ??
Galileo, 500 years ago rolled balls down an incline and dropped weights from the leaning tower.
Astonaut on the moon dropped a feather and a hammer at the same time and they hit the floor together.

It upsets me that such nonsense is posted and nobody comments that it is rubbish. Well, here you go \"It\'s rubbish.\"

[Sir_Zerp]

Originally posted by editor
It upsets me that such nonsense is posted and nobody comments that it is rubbish.

Even if it is true rubbish, Editor surely you see error of not rethinking even the the most basic facts that we hold dear.

The quote I heard the other day was, \"When you change your thinking about a problem, you change the problem\"

The more we learn now, to more we have to go back and rethink the basics from the past.

Not that it applies to this thread, but in general one should be open minded about rubbish.

There may be treasure in that trash :fresh:

BTW, I\'ll post my answer to this thread next week. I got a good one, that may just work, based on my zerp conjecture.

[Bella]

True, thats why it is a brain teaser... anyways I changed my idea from last years answer \"whichever floats\" cuz I found out that was stupid..

So how about put them in a pressure chamber in whichever collapses upon itself is the hollow one!

[Bella]

Or how about freeze them both then drop them from a tower and when they break whichever has the least pieces was the hollow one!