Balls puzzle.

[Sakha]

You have 2 balls. Both are identical in size and mass, but one is made of gold and is hollow,the other is not hollow and made from titanium. Find out which is which ball, and lets say both are covered with a black paint that is anti reflective, heat/electricity insulator. You can't use any measurement device, nor hitting, damaging or breaking the ball..

P.S: There's a really simple way.

[DaveC426913]

Knock them? One will sound hollow?

[Sakha]

Mmm.. lets say the paint is anti-acoustics.

[lisab]

Roll the balls side-by-side down a ramp. The solid ball will roll faster.

[Sakha]

wheew.. you're fast..

[DaveC426913]

wheew.. you're fast..Around here, we like our women that way. :devil:

[regor60]

drop them in water. the hollow one will bob higher.

oh..same mass, never mind

[Sakha]

drop them in water. the hollow one will bob higher.

oh..same mass, never mind

Nice try.

[arildno]

Remove the paint?
(This as an alternative to lisab's suggestion)

[some_one]

oohh rigid bodies thats realy good

[some_one]

put them in a bucket of water
they vary in density
the gold will pull out more water
am i correct?

[Sakha]

Remove the paint?
(This as an alternative to lisab's suggestion)
As I said, you can't damage nor break the ball, and removing the paint would be considered damaging. But yeah, lisab's answer is right.
put them in a bucket of water
they vary in density
the gold will pull out more water
am i correct?
Both would pull same amount of water because both are same size and mass, so they have same volume and density.

[arildno]

I think black is a damaging colour, I'm merely prettifying the balls..

[some_one]

aaahhh disregard it
you sayed that the gold ball is hollow

[Sakha]

No, imagine a gold sphere as an "o" the black line is gold and the white is hollow... The titanium sphere is all solid.

[some_one]

if you shoot them out of a cannon
the gold ball will not fly in a steady trajectory
because its hollow

in order to fly in a steady way you need to have a full ball

because from my knowledge
the AK bullets have a shifted center of mass
which make them highly unstable
and when they hit a person
instead of going forward
they are starting to swirl inside the victim

am i correct?

[arildno]

The middle of the gold ball is empty, some one, it is hollow.

The hollowed gold ball can perfectly well have the same size and mass as the compact titanium ball

[Sakha]

if you shoot them out of a cannon
the gold ball will not fly in a steady trajectory
because its hollow

in order to fly in a steady way you need to have a full ball
Actually I don't know. I didn't went that far.

[LowlyPion]

Titanium is paramagnetic.

[some_one]

i am not a physicist but i had some small experience with fire arms

and i know for a fact that bullets with a shifted center of mass
are swirling inside the victim instead of going threw him

the question is whether the hollow ball considered to have a shifted center of mass

[Sakha]

No, the center of gravity is the center of the ball (geometric). For both balls.

[some_one]

these materials have different electric resistance

so plug it threw an electric circuit
and mesure the resistance using ohms law
i know that the gold in a pretty good conductor so it should have less ressistanse

[Sakha]

You have 2 balls. Both are identical in size and mass, but one is made of gold and is hollow,the other is not hollow and made from titanium. Find out which is which ball, and lets say both are covered with a black paint that is anti reflective, heat/electricity insulator. You can't use any measurement device, nor hitting, damaging or breaking the ball..

P.S: There's a really simple way.

anti reflective, heat/electricity insulator.

[some_one]

there are particles called miuons which go threw any thing
and they will go faster threw the hollow ball

[DaveC426913]

The OP has stated that no measurement device can be used.

To which I will make 2 qualifiers for you picky types:
1] He means no man-made measurement device, i.e. eyes and such are allowed.
2] He is indicating that this can be solved without resorting to any man-made measurement. The test is easy, the results are obvious.

[some_one]

the only solution is this rigid body property
i cant think of any better answer

[DaveC426913]

if you shoot them out of a cannon
the gold ball will not fly in a steady trajectory
because its hollow

in order to fly in a steady way you need to have a full ball

because from my knowledge
the AK bullets have a shifted center of mass
which make them highly unstable
and when they hit a person
instead of going forward
they are starting to swirl inside the victim

am i correct?

The balls do not have a shifted centre of mass though. Thery are symmetrical.

Good try though. You're getting warmer.

[LowlyPion]

Titanium is paramagnetic.

... and gold is diamagnetic.

Enough clues yet?

[DaveC426913]

... and gold is diamagnetic.
How will you know without an instrument to measure it?

[LowlyPion]

How will you know without an instrument to measure it?

You will know by utilizing the paramagnetic quality of the titanium. You place the ball in a magnetic field and then use another magnet to detect which one exhibits an attractive force. No measurement involved.

[DaveC426913]

use another magnet to detect which one exhibits an attractive force. That would be a measurement device, albeit a simple one, making a measurement, albeit a simple one.

[LowlyPion]

Alternatively you can use a penny or a copper stylus and try to scratch it.

The copper is harder than gold but not as hard as titanium.

[LowlyPion]

That would be a measurement device, albeit a simple one, making a measurement, albeit a simple one.

I would claim that it is detection, not measurement. And if detection is not allowed ... then what is?

[DaveC426913]

Alternatively you can use a penny or a copper stylus and try to scratch it.

The copper is harder than gold but not as hard as titanium.
PLEASE READ THE CRITERIA BEFORE CONTINUALLY OFFERING INVALID RESPONSES. :grumpy:
- both are covered with a black paint that is anti reflective, heat/electricity insulator.
- You can't use any measurement device,
- nor hitting, damaging or breaking the ball

[DaveC426913]

I would claim that it is detection, not measurement. And if detection is not allowed ... then what is?It is detection with a device. There is a naked eye obvious way of telling the difference, (if you know what do with the ball :wink:)...

[LowlyPion]

PLEASE READ THE CRITERIA BEFORE CONTINUALLY OFFERING INVALID RESPONSES. :grumpy:
- both are covered with a black paint that is anti reflective, heat/electricity insulator.
- You can't use any measurement device,
- nor hitting, damaging or breaking the ball

Ohhh. So grumpy.

It is detection with a device. There is a naked eye obvious way of telling the difference, (if you know what do with the ball :wink:)...

I still think a magnet is not a measuring device if you are testing merely for a qualitative property of the material. The paint mentioned in the OP is not magnetically reflective after all.

But that said I'd say you can also exploit the difference in the moment of inertia. A shell ball will have a higher moment than a solid ball. You can spin them and the gold ball will either spin slower for the same torque or longer if you get them spinning at the same speed. There's about a 50% difference in the moments.

[lisab]

Ohhh. So grumpy.



I still think a magnet is not a measuring device if you are testing merely for a qualitative property of the material. The paint mentioned in the OP is not magnetically reflective after all.

But that said I'd say you can also exploit the difference in the moment of inertia. A shell ball will have a higher moment than a solid ball. You can spin them and the gold ball will either spin slower for the same torque or longer if you get them spinning at the same speed. There's about a 50% difference in the moments.

See post #4.

[LowlyPion]

See post #4.

It just says spoiler.

I've already been accused of not reading the OP carefully enough.

[lisab]

It just says spoiler.

I've already been accused of not reading the OP carefully enough.

Ah - run your cursor over the text box under 'Spoiler.'

You've read the OP perfectly well :wink: !

[LowlyPion]

Ah - run your cursor over the text box under 'Spoiler.'

LOL. Thanks. I didn't know what that was.

Now there is a puzzle I didn't get.

Thanks for the tip.

Oh and good answer. I like yours better.

[Hurkyl]

Isn't the ramp a device for measuring rotational inertia? :tongue:

[DaveC426913]

Isn't the ramp a device for measuring rotational inertia? :tongue:Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.

[DaveC426913]

I've already been accused of not reading the OP carefully enough.:wink:

[Hurkyl]

Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.
My eyes are all I need if I set them down next to a strong magnet too. :tongue: (Or if I place the balls in any sort of object one might label as a 'measuring device')

[LowlyPion]

Nope. Your eyes are all that is needed to see the difference. There was no restriction on what you could do with the ball to cause the difference.

I don't know ...

I think he's got a point. A ramp is as much a device that detects a property of the ball (moment of inertia) as a magnet (paramagnetism).

I'd say in the future the OP would want to insure that the statement would say something like no chemical, electrical or magnetic property of the material can be used to differentiate. ... You know for those of us so easily misled.

[DaveC426913]

I don't know ...

I think he's got a point. A ramp is as much a device that detects a property of the ball (moment of inertia) as a magnet (paramagnetism).

Granted, it's a hazy line. You guys are pretty resourceful.

[LowlyPion]

Granted, it's a hazy line. You guys are pretty resourceful.

HAZY???

Progress is slow.

[DaveC426913]

HAZY???

Progress is slow.
OK, well, how about:

I'm at a loss to see a difference between a ramp being used to cause two objects to move in visibly distinguishable ways and a magnet being used to cause two objects to move in visibly distinguishable ways.

So, I must concede the point.


(Of course, I'm not out yet. I'll bet there is a way to show the angular momentum effect without needing a ramp. Thus, all devices could be verboten.)

[LowlyPion]

I'll bet there is a way to show the angular momentum effect without needing a ramp. Thus, all devices could be verboten.

In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...

We'll have to just decide to live with the imprecision.

But I still think lisab's solution is the best.

[Sakha]

I'd say in the future the OP would want to insure that the statement would say something like no chemical, electrical or magnetic property of the material can be used to differentiate. ... You know for those of us so easily misled.
I'll try next time :rolleyes:

[Phrak]

You have 2 balls. Both are identical in size and mass, but one is made of gold and is hollow,the other is not hollow and made from titanium. Find out which is which ball, and lets say both are covered with a black paint that is anti reflective, heat/electricity insulator. [i]You can't use any measurement device, nor hitting, damaging or breaking the ball..[i/]

P.S: There's a really simple way.

take them to a goldsmith. tell him that he can have one sphere. you'll sell it to him for half the price of it's weight in gold.

[Sakha]

take them to a goldsmith. tell him that he can have one sphere. you'll sell it to him for half the price of it's weight in gold.

And how can you say which is the gold ball by doing that?

[Phrak]

And how can you say which is the gold ball by doing that?

I'll bet my gold ball against your titanium ball i walk away with the titanium.

no, wait a minute. I sold the gold ball.

but then again. If you think its gold, wanna buy it?

[DaveC426913]

In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...


No. I (on behalf of the OP :redface:) said that your eyes were not considered a device. One can presume that using one's body is not "making use of a device".

[DaveC426913]

In that regard spinning them by hand, should work. The gold will feel "heavier" to spin - resist spinning by about 50%. (I checked the Hyperphysics calculator and it shows a ration of about 20:33 between a solid and a shell sphere.)

Oh but then the hand might be seen as a device ...


1] Giving the balls the same amount of force, one ball will spin slower than the other. This will be visually discernable without need for measurement.

2] I (on behalf of the OP :redface:) said that your eyes were not considered a device. One can presume that using one's body, such as one's hand, is not "making use of a device".

[xtd]

Before getting into too much detail about that and inventing paint that practically works as a force field, how about generalizing the problem like:

You have two balls A and B made from different metals of the same size. The metals only differ in volume, so that although one of the balls is hollow and one is solid they both weigh the same. How do you tell the two apart?

Or maybe that is giving away the starting point as it only gives one information?

[Phrak]

The most austere method I can think of is to bounce the two balls off of each other, in an off-center impact.

[DaveC426913]

The most austere method I can think of is to bounce the two balls off of each other, in an off-center impact.What would that accomplish?

[Phrak]

Re: off-center impact of one ball on another.
What would that accomplish?

All impacts are not perfectly elastic. The angular momentum imparted to one ball will be equal and opposite the angular momentum imparted to the other. The ball with the least angular velocity is hollow.

[DaveC426913]

Re: off-center impact of one ball on another.


All impacts are not perfectly elastic. The angular momentum imparted to one ball will be equal and opposite the angular momentum imparted to the other. The ball with the least angular velocity is hollow.
Oh, OK, a riff on the angular momentum solution.