A cube of ice whose edge is 24.5 mm is floating in a glass of ice-cold water wit

Question

A cube of ice whose edge is 24.5 mm is floating in a glass of ice-cold water with one of its faces parallel to the water surface. (a) How far below the water surface is the bottom face of the block? ___mm (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? ___mm (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). How thick is the required layer of ethyl alcohol? ___mm

Explanation / Answer

a. Buoyant force= Weight of the cube. (Volume of water displaced)*(Density of water)*(acceleration due to gravity)=(Mass of Ice)*(acceleration due to gravity) (A*l)*1*9.8=(A*24.5 * 0.9167)*9.8 A=cross sectional area l=length of ice cube submerged. l=22.46 mm b. Buoyant force= Weight of the cube { (Volume of water displaced)*(Density of water)+(Volume of ethyl alcohol displaced)*(Density of ethyl alcohol)}*(acceleration due to gravity)=(Mass of Ice)*(acceleration due to gravity) {(A*l)*1+(A*5*0.789)}9.8=(A*24.5 * 0.9167)*9.8 l+5*0.789=24.5*0.9167 l=18.5 mm c. Buoyant force= Weight of the cube { (Volume of water displaced)*(Density of water)+(Volume of ethyl alcohol displaced)*(Density of ethyl alcohol)}*(acceleration due to gravity)=(Mass of Ice)*(acceleration due to gravity) Let x be the required layer of ethyl alcohol {(A*(24.5-x))*1+(A*x*0.789)}9.8=(A*24.5 * 0.9167)*9.8 24.5-x+(0.789)x=24.5*0.9167 x=9.67 mm The required layer of ethyl alcohol = 9.67 mm

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