A cube of wood whose edge is 12 mm is floating in a liquid in a glass with one o
ID: 2241692 • Letter: A
Question
A cube of wood whose edge is 12 mm is floating in a liquid in a glass with one of its faces parallel to the liquid surface. The density of wood is 835 kg/m^3, that of liquid is 1296 kg/m^3. How far (h) below the liquid surface is the bottom face of the cube? Answer in units of mm
A light oil is gently poured onto the immiscible liquid surface to form a 3.4 mm thick layer above the liquid. The density of the oil is 606 kg/m^3. When the wood cube attains hydrostatic equilibrium again, what will be the distance from the top of the liquid to the bottom face of the cube? Answer in units of mm
Additional light oil is poured onto the liquid surface until the top surface of the oil coincides with the top surface of the wood cube( in hydrostatice equilibrium). How thick is the whole layerr of the light oil? answer in units of mm.
Explanation / Answer
s = 12 mm
Pw = 835 kg/m3
Pl = 1296 kg/m3
According to Archemedes principle
Pw s^3 g = Pl h s^2 g
h = s [Pw / Pl]
= 12 mm [835 / 1296]
= 7.73 mm
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ha = 3.4 mm
Po = 606 kg/m3
We assume that the top of the cube is still above the oil's surface. If ha is the width of the oil layer, we have that the buoyant force is
= 6.14 mm
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ha = s[Pl - Pw / Pl - Po]
12 [(1296 - 835) / (1296 - 606)]
= 8.02 mm
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