One is made of gold and hollow, other is not hollow and made of titanium. Both balls are identical in size and weight, and covered with a shell made of non-transparent, electricity/heat/cold non conducting material. Find a way to determine which ball is made of what, without damaging the shell (you are not allowed to burn it, place in liquid, etc.) and without using any external measurement equipment.

Ratch

 

Would a spoon count as external test equipment?

 

I want the sphere with the moment of inertia greater than 2/5mr^2..

 

is it equal mass as well? cause weight and mass are different, would finding them out have anything to do with changing the gravitational force? i.e going to the moon?

 

If they have equal weight here, then they have equal mass, and will be equally weighted and massive anywhere..

 

If the spoon is allowed, and not considered external test equipment, I will use the spoon. Tap, tap, tap. Hollow gold and solid titanium have drastically different acoustical properties.

 

thingmaker3,

If the spoon is allowed, and not considered external test equipment, I will use the spoon. Tap, tap, tap. Hollow gold and solid titanium have drastically different acoustical properties.

No hand sonar or radar. You don't need it anyway. There is a much simpler way.

I want the sphere with the moment of inertia greater than 2/5mr^2..

Fine, how does that help you determine which is which?

vane,

The method I have in mind works fine on the moon. Ratch

 

How about this:

Bring a magnet close to the shell with the Au ball. Bring the same magnet close to the shell with the Ti ball. Au is a better metal. You can feel the stronger magnetic force with the Au shell, and there you are!

 

No hand sonar or radar. You don't need it anyway. There is a much simpler way.

Spoon = hand sonar? Never would have called it that, but I like it.

Guess I'll just have to sit at the bench and spin my balls, watching them slow to a stop. I'll keep doing such to stay out of trouble while others here do more interesting things with their pair.

 

How about this:

Bring a magnet close to the shell with the Au ball. Bring the same magnet close to the shell with the Ti ball. Au is a better metal. You can feel the stronger magnetic force with the Au shell, and there you are!

HEY! No fair! I get my spoon taken away as "test equipment" and Terp gets to use a magnet strong enough to bring paramagnetic differences into play?

 

Yea, thingmaker3 got the shaft if paramagnetism is on the table..
What I was getting at is that the moment of inertia for a solid sphere is I = 2/5mr^2, while for an infinitely thin shelled sphere it is 2/3mr^2.. So a real world hollow sphere will have a moment of inertia greater than the solid sphere, and therefore you simply need to spin them and see which spins easier..

 

One is made of gold and hollow, other is not hollow and made of titanium. Both balls are identical in size and weight, and covered with a shell made of non-transparent, electricity/heat/cold non conducting material. Find a way to determine which ball is made of what, without damaging the shell (you are not allowed to burn it, place in liquid, etc.) and without using any external measurement equipment.

Ratch

How about being more precise than "etc." in what is or isn't allowed?

 

terp,

Bring a magnet close to the shell with the Au ball. Bring the same magnet close to the shell with the Ti ball. Au is a better metal. You can feel the stronger magnetic force with the Au shell, and there you are!

Those are not ferromagnetic materials. What if I said the materials were glass and balsa wood? What if the size of your balls were very small? The method I have in mind can determine the ball with the highest density material regardless of the size within reason. Ratch

 

Mark44,

How about being more precise than "etc." in what is or isn't allowed?

I would be all day writing what is and isn't allowed. It is nothing exotic, and can be implemented relatively easily. Ratch

 

triggernum5,

So a real world hollow sphere will have a moment of inertia greater than the solid sphere, and therefore you simply need to spin them and see which spins easier..

You are getting close. How do you implement such a scheme? Especially if you have very large balls. Ratch

 

Gold has more mass, correct? So if you were to roll both spheres down an incline across a semi-liquid/gel surface, the gold sphere should roll further.

Or, as mentioned before, spinning...you simply put lines or dots across the diameter, and judge which one slows down first.

 

Same mass, remember? I like the spinning idea, since the mass isn't evenly distributed there should be a difference in moment of inertia.

 

he said same weight..but weight and mass aren't the same... gravity will always pull down at the same speed... but i would think deceleration of a denser item would take longer. it's been a while since i've had physics

I do know a pound of gold is heavier than a pound of lead

 

Release both balls simultaneously to roll down an inclined plane. The ball with the lower moment of inertia (the titanium ball) gets to the bottom first.

 

Yea, but what if these balls are planet sized?.. He doesn't define the problem precisely at all, and then makes us play a guessing game as to feasibility/allowability..
Personally I was thinking spinning them at a specific speed, and seeing which one stops first with equal frictional resistance applied, but methodology depends on the size, so until he ponies up some numbers, I have no idea..