A piece of pure ice floats freely in a vessel containing pure water. No water is lost from the vessel. After the ice melts completely, what happens to the water level?
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Question

A piece of pure ice floats freely in a vessel containing pure water. No water is lost from the vessel. After the ice melts completely, what happens to the water level?

G1 Physics · Accepted Answer

Let the mass of the floating ice be m. While floating, the ice displaces water whose weight equals the weight of the ice. Therefore, ρ(water)V(displaced)g = mg. Hence, V(displaced) = m/ρ(water). After the ice melts, it becomes water of volume V(melt) = m/ρ(water). Thus, V(melt) = V(displaced). Therefore the water level remains unchanged. Correct option: C.