GATE ME 2019 Set 1 — Question 56
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Fluid Mechanics → Fluid Properties & Statics → Buoyancy & Stability
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Question
A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m. Liquid of density 1000 kg/m is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is ______ mm.
Correct answer
80 to 80
Solution
Let mm be the side of the cube.
Density of the cube kg/m.
Density of the liquid kg/m.
For the cube to just lift up, the upward buoyancy force must equal the weight of the cube.
Assuming the liquid seeps under the cube, the upward force is due to the pressure at the bottom: .
The weight of the cube is .
Equating the two:
.
Since , the cube is partially submerged when it lifts, and the calculation is consistent.
Density of the cube kg/m.
Density of the liquid kg/m.
For the cube to just lift up, the upward buoyancy force must equal the weight of the cube.
Assuming the liquid seeps under the cube, the upward force is due to the pressure at the bottom: .
The weight of the cube is .
Equating the two:
.
Since , the cube is partially submerged when it lifts, and the calculation is consistent.
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