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I came upon this question recently while studying about buoyancy. It goes like this:

If an iron block is covered with ice and floats in a tub of water, what will be the change to the water level when the ice melts and the iron submerges completely?

According to me the the water level should go up because the iron block will displace more water when it submerges. But, the answer is that the level will remain the same. I did not get the reasoning nor the logic behind it. Please explain why the level will remain the same. This question is driving me crazy.

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  • $\begingroup$ I've evaluated OP's problem and I find that the water level $\textit{goes down}$ after the ice melts completely. I suggest the answerers to kindly take this into consideration. $\endgroup$ – Ajay Mohan Dec 7 '19 at 10:06
  • $\begingroup$ Chill although water expands when freezes but just assume the water level in the container is already at the brim initially... 😎 $\endgroup$ – user6760 Dec 7 '19 at 15:13
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The iron will not displace more water when it submerges because its weight is contributing to the total displacement already. An ice-cube alone will not displace as much water as one with some iron in it. The volume of water displaced by the iron/ice-cube combination will weigh as much as the iron/ice-cube combination.

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The water level actually will go down. You can see the ice and the iron as floating separately because the problem is linear. Imagine the iron floating cause it is on top of a weightless material. When the ice melt the volume does not change (this is a classical problem search it). The iron on top of the weightless material displaces more water than the volume of the iron, because the weight of the displaced water ,matches that of the iron. When you "pop" the weightless material, the volume of water that returns is larger than that displaced by the iron, who requires less volume for the same weight.

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