A cube of ice whose edge is 20.0 mm is floating in a glass of ice-cold water wit

Question

A cube of ice whose edge is 20.0 mm is floating in a glass of ice-cold water with one
of its faces parallel to the water’s surface.
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 surface to form a layer 5.00
mm thick above the water. When the ice cube attains hydrostatic equilibrium
again, what will be 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 surface until the top surface
of the alcohol coincides with the top surface of the ice cube (in hydrostatic
equilibrium).
d) How thick is the required layer of ethyl alcohol?

Explanation / Answer

its is given that the length of one edge ofthe ice cubeis s = 20.0 mm so the area of one face of the cube will be s^2 andvolume will be s^3 (a) as the ice cube is floating the weight ofthe diasplaced water must be equal to the weight of the cube so from the figure weget ?w (s^2 .xa) g = ?ice s^3 g xa = ........ mm (b) in this case the buoyant forces exerted by thealcohol and the water must equal the weight of thye floating ice cube so from the figure weget ?alcohol [s^2(5.00 mm)] g + ?w (s^2 . xb) g= ?ice s^3 g xb = ........... mm (c) in this case the sum of buoyant forces exerted bythe alcohol and water must equal the weight of the floating ice cube so we get ?alcohol [s^2xc] g + ?w s^2 [(s -xc)] g = ?ice s^3 g xc = ......... mm

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