A block of ice containing a small iron piece floats in water. After the ice melts completely, the iron piece sinks to the bottom. Compared with the initial water level, what happens to the final water level?
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Question

A block of ice containing a small iron piece floats in water. After the ice melts completely, the iron piece sinks to the bottom. Compared with the initial water level, what happens to the final water level?

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G1 Physics · Accepted Answer

Consider the iron piece separately. While the ice-iron combination is floating, the iron contributes to the required displaced-water volume through its weight. Its contribution to displacement is V(initial contribution) = m(iron)/ρ(water). After the ice melts, the iron sinks. A fully submerged iron piece then displaces only its own geometric volume: V(final contribution) = m(iron)/ρ(iron). Since ρ(iron) > ρ(water), we have m(iron)/ρ(iron) < m(iron)/ρ(water). Thus the displaced volume decreases…