Identifying the Gold & Titanium Balls

[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 let's 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..[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, want to 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 ) 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 ) 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.