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[Tellemurius]

Actually, it does depend.
If the cube is completely submerged, even if it still is floating in the glass, then the water will go down and stay the same, if it is not completely submerged (Halfway out of the water?) then it may go up the stay the same.

The question, as stated, leaves unknowns that can change the answer, at which point it becomes a guessing game.  I don't think that was the intent.

ice has a density of .97 but displaces the same amount of water that is frozen, it shouldn't overflow.

[Il Palazzo]

Oh god, this is hillarious.
A great presentation on the issues other countries are having with our language.
I remember my father telling me about this, but since I ignore any advice or recommendations he gives me and have a poor opinion on polish television, I've never looked into it.

Now I want to get this.
Considering that I understand both languages, this should be fun.

Isn't it great?  I'd love to watch it, too, but I'm not sure where to find it with subtitles yet...

Ah, well, I can enjoy it without completely understanding

(Also, I am glad to see that at least one person followed the link)

Hehehe. Classic.
Google "subtitles" + "jak rozpętałem drugą wojnę światową" (i.e."How I unleashed World War II")and you should find some English subtitles. I don't have to tell you how to find the movie itself on the internet.

[Tellemurius]

got my mother hooked on thai movies online, my bandwidth is dieing now >.>

[G-Flex]

A piece of ice floats in a glass filled with water.  The ice contains a small stone, so that when the ice has all melted, the stone sinks to the bottom of the glass.  What will happen to the level of water in the glass, firstly as the ice melts, and secondly as the stone is released from the ice and sinks to the bottom?
The water in the glass will

A. Remain the same then rise
B. Rise and fall
C. Fall then remain the same
D. Remain the same then fall

If the piece of ice+stone is floating, as the question states, then the weight of the ice+stone is equivalent to the weight of the displaced water. As the ice melts, there isn't a change in water level. For every gram of ice that melts, you're displacing one less gram of water, but another gram of water is added from the melting ice. In other words, no change. When the stone slips out of the ice and sinks, however, the ice becomes more buoyant, more of it being exposed to the air, causing the water level to fall to some extent.

In other words, D.

Actually, it does depend.
If the cube is completely submerged, even if it still is floating in the glass, then the water will go down and stay the same, if it is not completely submerged (Halfway out of the water?) then it may go up the stay the same.

The question, as stated, leaves unknowns that can change the answer, at which point it becomes a guessing game.  I don't think that was the intent.

This is only true if the ice isn't actually floating. If the ice is floating, then some (even a very small) portion of it is above the water, and the question specifically states that the ice is floating.

Of course, there's a third option: Let's say the ice+stone is floating. As it melts, the water level doesn't change. However, if the ice+stone becomes overall less dense than the water (and sinks), something else happens: The water level actually starts to go down, and keeps going down as the ice melts, since the entirety of the ice is submerged and melts into higher-density water (in this case, this is not compensated for by anything because none of the ice is floating above the water).

However, I don't think this latter case is really possible, since the question seems to indicate that the stone only sinks when it's released by the ice, implying that the entire thing is floating up until that point.

[Earthquake Damage]

What did it intend then? There are far to many things that can affect this...

Reasonable assumptions:  Inert container, ordinary pressures (and temperatures, but that naturally follows since liquid water is present), pure ice floating in pure water (e.g. not freshwater ice floating in saltwater), and a dense (i.e. denser than the water) inert (i.e. doesn't react with the water) stone.  Also, gravity keeps everything in the container.  Also, the ice and stone are solid, so no hollow floating stones.

Point:  They're testing for the level of understanding shown in G-Flex's answer, not your ability to outguess the tester given limited information.

[iceball3]

A piece of ice floats in a glass filled with water.  The ice contains a small stone, so that when the ice has all melted, the stone sinks to the bottom of the glass.  What will happen to the level of water in the glass, firstly as the ice melts, and secondly as the stone is released from the ice and sinks to the bottom?
The water in the glass will

A. Remain the same then rise
B. Rise and fall
C. Fall then remain the same
D. Remain the same then fall

If the piece of ice+stone is floating, as the question states, then the weight of the ice+stone is equivalent to the weight of the displaced water. As the ice melts, there isn't a change in water level. For every gram of ice that melts, you're displacing one less gram of water, but another gram of water is added from the melting ice. In other words, no change. When the stone slips out of the ice and sinks, however, the ice becomes more buoyant, more of it being exposed to the air, causing the water level to fall to some extent.

In other words, D.

WELL,
Water looses density when it freezes up, making the water in the ice takes up more space when it melts, and may make the level rise at first.
But at this point I'm lost on what I'm trying to get at.

[G-Flex]

Point:  They're testing for the level of understanding shown in G-Flex's answer, not your ability to outguess the tester given limited information.

I must say, however, that poking and prodding for inconsistencies (and whether or not enough information is given, or what assumptions you can or cannot make, and how they may change the results) is a very, very good idea when encountering any sort of question or problem. In this case, however, I think the intent is pretty clear, even if it's fun or enlightening to ponder how the results would change if some assumptions are broken.

Water looses density when it freezes up, making the water in the ice takes up more space when it melts, and may make the level rise at first.
But at this point I'm lost on what I'm trying to get at.

That's not true. Yes, water is more dense than ice. This does not matter. Archimedes' Principle states that a buoyant object displaces its own weight in the fluid in which it is buoyant. In other words, if the floating block of ice melts off 10 grams of its mass, it adds that 10 grams of liquid water to the water it's floating in, but it also displaces 10 less grams of water, so nothing changes. In other words, the volume of water added by the melting ice is equivalent to the volume of water the ice is no longer displacing below the water line. This is basic buoyancy, and probably explained better than I'm doing it elsewhere on the internet.

[Earthquake Damage]

I must say, however, that poking and prodding for inconsistencies (and whether or not enough information is given, or what assumptions you can or cannot make, and how they may change the results) is a very, very good idea when encountering any sort of question or problem. In this case, however, I think the intent is pretty clear, even if it's fun or enlightening to ponder how the results would change if some assumptions are broken.

No argument here.  Doubly so for the bit I bolded.

[Mindmaker]

Oh god, this is hillarious.
A great presentation on the issues other countries are having with our language.
I remember my father telling me about this, but since I ignore any advice or recommendations he gives me and have a poor opinion on polish television, I've never looked into it.

Now I want to get this.
Considering that I understand both languages, this should be fun.

Isn't it great?  I'd love to watch it, too, but I'm not sure where to find it with subtitles yet...

Ah, well, I can enjoy it without completely understanding

(Also, I am glad to see that at least one person followed the link)

Hehehe. Classic.
Google "subtitles" + "jak rozpętałem drugą wojnę światową" (i.e."How I unleashed World War II")and you should find some English subtitles. I don't have to tell you how to find the movie itself on the internet.

I could use some help finding it.
Amazon and some other places, where I normally get stuff, yielded no results.

[Il Palazzo]

As the ice melts, there isn't a change in water level. For every gram of ice that melts, you're displacing one less gram of water, but another gram of water is added from the melting ice. In other words, no change.

Incorrect. While mass of the systems remains the same, the volume changes. 1 gram of water takes up less space than 1 gram of ice(which is why it floats).

1.If not for the stone, the water level would remain constant as the cube melts, due to the excess volume of ice being above water, and so, not contributing to the water displacement.
For the sake of easiness of calculations, let's assume that Vi(volume of ice cube)=2liters, Di(density of ice)=50%Dw(density of water). It is unimportant for the resolution of the problem that the real water vs ice density ratio is different.
2 liters of ice weight as much as 1 liter of water. However, only 1 liter of ice is submerged, with the rest sticking out above the water level. As it melts by half, it adds 1/2 liter of water, while shrinking by 1 liter, of which only 1/2 was under water. The amount of water added and the amount of volume freed is the same, so the water level remains constant.

2.Now, if there is a stone in the ice cube.
Let's assume it weights just as much as 1 liter of water(1kg). In this case, the cube is fully submerged. As it melts by half, it adds 1/2 liter of water, while shrinking by 1 liter, of which 100% was under water. The amount of water added is 1/2 of the vloume of space freed by melting, so the water level goes down as the cube melts.

3.When the stone is released, the remaining ice resurfaces, putting half of its volume above water, causing the water level to fall again.
As it settles on the surface, we've got the same situation as described in 1., meaning that the water level remains the same.

The answer is: Water level will fall, then remain the same.

If you want to play with real densities of water and ice, you'll get the same answer.

[ToonyMan]

Oh my god, you're arguing about water melting.

[Aklyon]

Ms Olschner: Your honor, I wish to swat Mr. Buck in the head with his client's [deposition transcript].
Judge: You mean read it?
Ms Olschner: No, I wish to swat him in the head with it. The [Rules of Procedure] clearly state that a deposition may be used for "any purpose" in court, and this is the purpose for which I want to use it.
Judge: Well, it does say that. (he pauses)
Judge: There being no objection, you may proceed.
Ms Olschner: Thank you your honor. (she swats Mr. Buck in the head with a copy of deposition.)
Mr. Buck: But Judge...
Judge: Next witness.
Mr. Buck: We object!
Judge: Sustained. Next witness.

[Darvi]

2.Now, if there is a stone in the ice cube.
Let's assume it weights just as much as 1 liter of water(1kg). In this case, the cube is fully submerged.

Which it isn't, as stated by the question.

[G-Flex]

As the ice melts, there isn't a change in water level. For every gram of ice that melts, you're displacing one less gram of water, but another gram of water is added from the melting ice. In other words, no change.

Incorrect. While mass of the systems remains the same, the volume changes. 1 gram of water takes up less space than 1 gram of ice(which is why it floats).

Ergh. I already stated Archimedes' Principle. If something is buoyant, then the mass it displaces is equal to the mass of the object itself. If the object melts and contributes to the volume of the liquid it's in, the level of that liquid remains the same. Period. Unless, of course, the liquid being added is some other substance, but that isn't the case.

If the ice+stone weighs 1kg and is floating, then it displaces 1kg of water. If 10g of ice melt off of it, that contributes an additional 10g of water to the surrounding fluid, but also means that the object displaces 10g less water. In other words, nothing changes, because the volume of fluid added by the object melting is the same as the volume of fluid the object was displacing but no longer is.

Let's assume it weights just as much as 1 liter of water(1kg). In this case, the cube is fully submerged.

It's not fully submerged. Period. The ice+stone object is floating. It is defined as floating in the question. This means that some finite amount of it is above the water. The only time at which it's floating but without anything sticking above the water is when its density is exactly equal to that of the water it's floating in, which is a state that cannot even last a finite amount of time. It is impossible for something to be buoyant yet completely submerged at the same time, as that would imply that the overall density of the object is strictly equal to the density of the fluid it's in, meaning that it's not buoyant, it's just free-floating. And the instant more of that object melts, it isn't even doing that anymore, and in this case will sink.

[ToonyMan]

I have a challenge.

Eat a coffee cake without having one crumb fall off of it.  I tried like 4 times, but it's impossible for me.  Completely impossible.