A 1.1 kg block of ice floats in a salt solution of density 1100 kg/m³. After the ice melts completely, the meltwater has density 1000 kg/m³ and remains in a vessel of uniform horizontal cross-sectional area 1000 cm². Ignoring mixing-volume changes, the liquid level rises by N mm. Find N.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

A 1.1 kg block of ice floats in a salt solution of density 1100 kg/m³. After the ice melts completely, the meltwater has density 1000 kg/m³ and remains in a vessel of uniform horizontal cross-sectional area 1000 cm². Ignoring mixing-volume changes, the liquid level rises by N mm. Find N.

Physics · Fluid Mechanics · pascal law and buoyant force

G1 Physics · Accepted Answer

Initially the floating ice displaces salt solution whose weight equals the weight of the ice. Initial displaced volume: V(initial) = m/ρ(salt) = 1.1/1100 = 0.0010 m³ = 1000 cm³. After melting, the ice becomes water of volume V(melt) = 1.1/1000 = 0.0011 m³ = 1100 cm³. Increase in occupied liquid volume: ΔV = 1100−1000 = 100 cm³. Vessel area: A = 1000 cm². Therefore, Δh = ΔV/A = 100/1000 = 0.1 cm = 1 mm. Hence, N = 1.