What does mass, volume and density of displaced water mean?

Homework Statement

I was having a lecture of buoyancy and I am confused about the meaning of displaced water. I asked my classmates about it and they said it is essentially the volume of the object when you put the object into the water. So now the question comes.

There are three objects placed into three different cups of water. Object A floats. Object B sits in the middle of the water and object C sinks. Compare the mass, volume, density of each object to the mass, volume and density of the "displaced water" they are sitting in, respectively?

F = PA
P = pgh
B = pgV

The Attempt at a Solution

Okay, I think I just do not get what the question is talking about. If the displaced water is the volume of the object, what does mass, volume, and density of the displaced water mean? Volume of displaced water should simply mean volume of the object, and density of displaced water should just be density of water (I am guessing here, correct me if I am wrong). But what is the mass of the displaced water? Does that mean mass of the volume of object, which means mass of the object? I am comparing the mass of object to mass of displaced water. If they are the same, how do I compare!!!

Alright, for starters...volume of displaced water does not necessarily mean volume of object. You have to compare the density of the object vs. the density of water....if the density of the object > density of water, what would happen to the object? How about if density of the object < density of water? Finally, what about density of the object = density of water?

okay, youve got three objects. You need to undertand this basic concept about bouyancy: When an object is placed in water, it displaces a certain volume of water. This volume is equal to the volume of the part of the obect inside of the water (the volume where water would be were there no object). Now , if the water that is displaced has greater weight than the object itself (of course the entire object, not just the part in water) then the object will float. Think about this--if the weight of the object were greater, then the object would sink, so what does that say about the density of the object compared to water? If two volumes are equal but one has greater mass, you should see that the density of the one of greater mass had better be greater.

okay, youve got three objects. You need to undertand this basic concept about bouyancy: When an object is placed in water, it displaces a certain volume of water. This volume is equal to the volume of the part of the obect inside of the water (the volume where water would be were there no object). Now , if the water that is displaced has greater weight than the object itself (of course the entire object, not just the part in water) then the object will float. Think about this--if the weight of the object were greater, then the object would sink, so what does that say about the density of the object compared to water? If two volumes are equal but one has greater mass, you should see that the density of the one of greater mass had better be greater.
wow, THANKS. I finally got what displaced water means. You just answered my question that I've been thinking for 2 hours!!!

I have an extension of this question,but posed a different way.

What will displace more water- an object with greater mass, or greater volume?

For instance, if you have a glass of water and you drop an object in that is heavy (mass), but relatively small in size versus dropping an item that is much larger in size (volume), but not nearly as heavy, which item would displace more?

The second part of the question.

Assume you had two items of the same size (volume), but two different weights or mass.

Would the displacement be the same based on volume, or greater based on mass?