A cube of ice whose edge measures 21.3 mm is floating in a glass of ice-cold wat

Question

A cube of ice whose edge measures 21.3 mm is floating in a glass of ice-cold water with one of its faces parallel to the water's surface. (assumes a density of ethanol of about 805 kg/m^3. )

(a)How far below the water surface is the bottom face of the block?

(b)Ice-cold ethyl alcohol is gently poured onto the water's surface to form a layer 5.30 mm thick above the water. The alcohol does not mix with the water. When the ice cube again attains hydrostatic equilibrium, what is the distance from the top of the water to the bottom face of the block?

(c)Additional cold ethyl alcohol is poured onto the water's surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol?

Explanation / Answer

density of ice = 917 kg/m^3

density of water = 1000 kg/m^3

0.0213*0.0213* 0.0213 * 917 = 0.0213*0.0213 * x * 1000

x = 0.0195 m is below the water surface

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