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Question

A right circular cylinder of specific gravity σ floats in water with its axis vertical, one third volume being above the water. If ρ is the specific gravity of air then select the correct option.

A
3σ=3+ρ
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B
3σ=2+ρ
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C
2σ=2+ρ
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D
3σ=1+2ρ
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Solution

The correct option is B 3σ=2+ρ
From archimedes's principle
Weight of the cylinder is equal to the sum of weight of the fluids displaced( air and water)
Weight of the cylinder: mg=πr2hρg=πr2hσρwg
Weight of the water displaced: mwg=πr223hρwg
Weight of the air displaced: mairg=πr213hρρwg
mg=mwg+mairg
πr2hσρwg=πr223hρwg+πr213hρρwg
3σ=2+ρ

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