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When cubes of ice floating on water melt, will the level of water change?

According to the Archimedes Principle, a body fully or partially immersed in a liquid will experience an upward force which will be equal to the amount of liquid displaced by the body.


This means that a floating cube of ice displaces a volume of water that has exactly the same mass as that of the cube. Since mass is conserved when the melting of ice occurs, the melted ice will make up for the displaced water mass and hence the water level will remain the same.


Another way to think about the problem is this: an ice cube of mass m will displace a volume of water equal to m/d, where d is the density of water. When the ice cube melts, it will convert to a volume of water equal to m/d. That is, the displaced water volume is same as the water volume obtained from ice melting. Thus, the water level will stay the same. 


Hope this helps. 

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