Phase change question

[heylollipop]

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I chose B. Here is my reasoning: According to Archimedes' Principle, if an object floats in a fluid, then the mass of the fluid displaced equals the mass of the object submerged in the fluid. The question says that the ice cube sticks out ABOVE the level of the water, so only a portion of the ice cube is submerged. So when the ice cube melts and becomes water, the portion of the ice cube above the water, in addition to the exiting water in the glass,will make it overflow.

Not sure if I explained myself clearly... Could someone please help me understand this question? Am I understand the Archimedes' Principle correctly ?

Many thanks.

 

[inasensegone]

The ice cube does displace an equal mass... but the thing is is that ice is less dense than liquid water. This is why the ice floats in the first place. So the amount of the ice that is submerged, has a less density than the volume of the water that it displaces. The mass of ice above the surface of the water, combined with the amount submerged, equals a mass equivalent to the liquid displaced.

The problem with your reasoning is that you are viewing Archimede's principle with the thought of something being completely submerged (like the King's "Gold" crown). Archimede's principle still works here, but you need to take into account that part of the ice is not submerged. This part that is not submerged is still acting to displace some of the liquid mass.

 

[heylollipop]

The ice cube does displace an equal mass... but the thing is is that ice is less dense than liquid water. This is why the ice floats in the first place. So the amount of the ice that is submerged, has a less density than the volume of the water that it displaces. The mass of ice above the surface of the water, combined with the amount submerged, equals a mass equivalent to the liquid displaced.

The problem with your reasoning is that you are viewing Archimede's principle with the thought of something being completely submerged (like the King's "Gold" crown"). Archimede's principle still works here, but you need to take into account that part of the ice is not submerged. This part that is not submerged is still acting to displace some of the liquid mass.

I see what you mean. I didn't take into consideration the density difference, considering the object is an ice cube. Thank you!