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PRACTICE / Floating equilibrium

Test the melting shortcut

Pure ice of mass 0.24 kg floats in a liquid of density 1200 kg/m³. It melts into water of density 1000 kg/m³, forming an unmixed upper layer during the observation. The vessel has vertical sides and area 0.040 m². Neglect evaporation, trapped gas, supporting-liquid thermal expansion and mixing volume changes.

How much does the upper free-surface level change, positive upward?

Organize the givens & assumptions
  • Ice mass = 0.24 kg
  • Supporting density = 1200 kg/m³
  • Melt-water density = 1000 kg/m³
  • Vessel area = 0.040 m²

Settled hydrostatic equilibrium in uniform gravity; stable stated orientation, no contact forces unless stated, negligible air buoyancy and surface tension, no absorption, trapped gas or spilling.

  1. A+6.0 mm+6.0\ \mathrm{mm}
  2. B+1.0 mm+1.0\ \mathrm{mm}
  3. C0 mm0\ \mathrm{mm}
  4. D−1.0 mm-1.0\ \mathrm{mm}

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