Braingle: 'Opaque Marble Balls' Brain Teaser

Opaque Marble Balls

Science brain teasers require understanding of the physical or biological world and the laws that govern it.

Puzzle ID:	#5443
Fun:	(2.93)
Difficulty:	(2.3)
Category:	Science
Submitted By:	im_para_noid
Corrected By:	boodler

Lost in the woods, you come upon a mysterious stranger who hands you two large spheres made of two kinds of opaque marble. The spheres look the same, are the same size and have the same weight and apparent density; however, one is solid and the other hollow. The hollow sphere contains a tiny map that will enable you to navigate your way home. Unfortunately, you cannot break the spheres. The stranger agrees to open the sphere that contains the map only if you can determine which sphere is hollow. How do you determine which sphere is hollow?

Answer

Roll the spheres on a level flat surface. The hollow sphere will roll further because its mass is distributed away from the center giving it a higher moment of inertia. Alternatively, you could spin them and see which is harder to stop.
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Comments

mad-ade Jul 22, 2002	exactly where would you find a level flat surface in the woods. Since the balls have equal diameter and equal mass, their volume and density are also equal. However, the mass distribution is not equal, so they will have different moments of inertia - the hollow sphere has its mass concentrated at the outer edge, so its moment of inertia will be greater than the solid sphere. Applying a known torque and observing which sphere has the largest angular acceleration will determine which is which. An easy way to do this is to "race" the spheres down an inclined plane with enough friction to prevent the spheres from sliding. Then, by conservation of energy:
mad-ade Jul 22, 2002	mgh = 1/2 mv^2 + 1/2 Iw^2 Since the spheres are rolling without sliding, there is a relationship between velocity and angular velocity: w = v / r so mgh = 1/2 mv^2 + 1/2 I (v^2 / r^2) = 1/2 (m + I/r^2) v^2 and v^2 = 2mgh / (m + I / r^2) From this we can see that the sphere with larger moment of inertia (I) will have a smaller velocity when rolled from the same height, if mass and radius are equal with the other sphere. Thus the solid sphere will roll faster.
mad-ade Jul 22, 2002	i have no idea why the comment above has split in two?
farrell2k Jul 23, 2002	You could look for hours for a flat surface, then work on rolling both balls with equal force, which would be impossible to determine without instrumentation. In this situation, your best bet would be to knock on them with something. You'd probably be able to pick out the hollow one.
SkinnySpace Jul 24, 2002	stares at the above comments um.......... what does that mean (retorical question dont write even more stuff that will makr my head hurt)
bronze Jul 26, 2002	there is a easier way to find out. Just let, a few drops of lemon juice get into contact with the surface of the marble. You will see the acid in the lemon will leave a deep mark on the marble surface in 10-15 minutes time.
4sH_n_7ay_t4y Jul 30, 2002	this comment is for the mad, it's just a riddle dude, don't get your panties in a wad, lol
cathalmccabe Aug 07, 2002	Mad-Ades "comment" is copied directly from a maths site which explains the maths behind if you roll or push the balls. But the problem is he just copied it and can't do it because then he would understand that the answer given is the same as the one he has copied. Its one thing to copy all your puzzle but to criticise someone else's by copying answers ......
mad-ade Aug 12, 2002	Posted by cathalmccabe Aug 07, 2002 Mad-Ades "comment" is copied directly from a maths site which explains the maths behind if you roll or push the balls. But the problem is he just copied it and can't do it because then he would understand that the answer given is the same as the one he has copied. Its one thing to copy all your puzzle but to criticise someone else's by copying answers ...... ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZz.......yawn oh, have you finished Cathal, hmmm, as usual very riviting and flattering that once again you have took the time to chase up my answers. I really don't understand this attraction you have for me, but hey if it means so much to you, then please, carry on, be my guest. After all we are all adults, we understand. What ever floats your boat! No need to be ashamed of your "supressed" proclivities. The world accepts people like you now, its ok, trust me. ;)
farrell2k Aug 21, 2002	LMAO. Come on now! How many ORIGINAL, non-copied teasers are there here. I'd wager one or two, maybe!!!
(user deleted) Oct 03, 2002	Never talk to a stranger in the woods!
speedyg1000 Nov 16, 2002	how can you guys be such babies over a riddle? jesus...
speedyg1000 Dec 08, 2002	But she is right, mad-ade. Why do you take the time to fill out two comments explaining exactly what they have already said when nobody has questioned it and nobody (I doubt even you) understands the equation the you posted??? Does it give you some sort of pleasure to imagine that you are smart?
glyn1wood Dec 31, 2002	you could tap them both on the same surface. one would sound hollow!!!!!!!!!!!!!
OD-1 Apr 04, 2003	hey paranoid you could have just asked your alien buddies to stick you in the hollow one.. oh wait those are your other teasers. never mind
Jerrythellama May 20, 2006	Hit on them! The hollow one will be easy to tell =D
cyberstar5150 Jul 31, 2006	First off, the solid sphere would roll further. Another option would be plausible if you had a thermometer of some sort. If you heat both balls for the same amount of time, then wouldn't the hollow one get hotter slower? Even if you heat them too long and they both become equal temperature, the faster cooling one would be the solid sphere.
oxymoronish Feb 13, 2009	Or, you could just shake each of them, the one that seems to have some movement at all is the hollow one!
mousechicks Feb 13, 2009	Anyone who thinks within the box would strike them. The one that sounds hollow would be the hollow one. So easy.
Cubano Feb 13, 2009	Or you could drop them both into water and see which one floats? But wouldn't it just be easier to take either sphere and knock the stranger out? Then you could do whatever you wanted with the spheres.
rabhingm Feb 13, 2009	My first thought was indeed whacking the marble spheres with a stick or stone and listen for the one that is hollow.
gaylewolf Feb 13, 2009	Is it roll "further" or roll "farther"
emu77alu02 Feb 13, 2009	I thought about shaking or banging on them to see which was hollow, but I think I like Cubano's answer best!
craniac Feb 13, 2009	Even when I studied physics years ago, I don't think I could have solved this teaser.
lsmith Feb 13, 2009	so confused
kwelchans Feb 13, 2009	For those who have suggested tapping the spheres and listening for an echo (and I admit I had the same thougth), it would depend on the thickness of the "shell". If for instance, the sphere is 12 inches in diameter and has, say, a 1-inch hollow space inside (it does say that the map is "tiny"), then the thickness of the outer shell would likely muffle any echo.
narmo3 Feb 13, 2009	yeah and where would you find a flat surface in the woods? You could simply nock each sphere on a rock and listen to see which sounds hollow.
FatHead Feb 13, 2009	Hmp. I would have tried dipping them in water, but I guess we don't "know" if there's water nearby.
gghali Feb 13, 2009	If you're in a magical woods where there are tiny maps inside of perfectly sealed marble spheres and perfectly frictionless ramps where you can conduct your experiment, then I'm guessing that you can find water somewhere to float the balls. And lemon juice to burn through them. And a saw that will cut through marble...
kwelchans Feb 13, 2009	Dipping them in water wouldn't do any good. If they have the same density, they will both either sink or float, even if one of them is hollow.
dodgerh8ter Feb 13, 2009	I'd pull out my uzi and make the stranger guide me out of the woods. You can get more of what you want with a kind word and a gun then you can with just a kind word. --Al Capone
tamjp Feb 13, 2009	I had the same thought as cubano! The floating bit not the violent bit
Viper Feb 13, 2009	To add to the answer, Just knock on the marbles. The one that sounds more hollow is the one.
avonma Feb 13, 2009	I was also thinking about knocking on them for a hollow sound, and also seeing if one of them would float; but I don't know how you would figure it out. Some of the solutions just make my head spin. It was an interesting teaser, though.
(user deleted) Feb 13, 2009	I second the float test. Irrespective of the fact that the density/mass of both balls is the same, the presence of any air in the hollow will provide buoyancy.
UptheHill Feb 13, 2009
Cubano Feb 18, 2009	The teaser said "apparent density" probably because if one of them is solid and the other isn't and they weight the same, then one of them isn't marble. Most importantly, hopefully your map isn't ruined after you submerge it.
cacepc Mar 30, 2009	One: If one marble is hollow, how can it be the same density? That being said brings me to number Two: Archemedes principle: Sink both marbles, obstensably, the solid one will displace more water than the hollow one.
choirgirl926 Apr 25, 2009	Just a question, even if you did find the map, how would you know where you were on it? To use a map, you have to know where you are, and the teaser specifically tells us we're lost.
kwelchans Apr 25, 2009	Look for the "You are here" icon on the map
(user deleted) May 13, 2009	since you said the hollow one had the map, i would guess that the one with the map in it was the hollow one.
Babe Feb 13, 2012	I am like a lot of others. Just rap on them and listen, or find a stream and see which one floats. If you have to find a flat surface you can certainly find a stream in the woods. Not a very good teaser with so many ways to tell without all the figuring. Simple solutions work best.
gaylewolf Feb 13, 2012	Once again, love the comments! This teaser sure got a lot of wild responses! Thanks!
eamon Feb 13, 2012	The second (alternative) answer is the obvious solution to me. It's the same basic way you test an egg to see if it's raw or cooked. Spin them. Just by applying a torque to each one you can feel the different way the angular momentum is being transferred. No need to bother with all the physics really. If you know the two possible constructions (hollow/solid or raw cooked for eggs) you can "feel" the spin of the object. As long as the two examples being tested are distinct as described in the puzzle (or the eggs thing), there's no need for instruments or precision, just a reasonably flat bit of wood or rock. Now, where DID I pack my perfectly level surface...
Chobuck Feb 13, 2012	If these balls are both made of marble and weigh the same wouldn't the hollow one be larger in diameter? Unless of course the map is made of lead. LOL . I too enjoy the comments.
dsjt Feb 13, 2012	The physical description of the balls as proposed by the teaser does not make sense. One of the balls would have to be larger than the other if the densities were the same and the weights were the same. I understand the physical phenomena that the author is trying to demonstrate. It is a very measurable event. But just stating that one of the spheres is hollow does not descriptive enough. Is the hollow sphere 12" in diameter with a 1" hollow core? Or does it have an 11" hollow core? Does the weight of the map make up for the lost mass? If the hollow core were very small and the mass of the map sufficient enough, I'm not sure one could measure the rotational inertia to a significant degree. If the hollow sphere has a relavively large hollow core, could one try to float them on a liquid? How did the map get inside the marble sphere? How was the sphere hollowed out? Whould there be a seam or a detectible drill hole? I would closely inspect the spheres for surface defects.
dodgerh8ter Feb 13, 2012	Just a question.... Would the resonance be different? I was thinking of hitting them with rocks or bottles and listening for the sound they make. The solid one would sound deeper than the hollow one.
auntiesis Feb 14, 2012	The las time I was lost in the woods and a strange man came up and offered me a way out......... I just ran til I found a genie with a lamp and wished my way out.