Question

# Two identical cylindrical vessels, with their bases at the same level, each contain a liquid of density ρ. The height of liquid in one vessel in h1 and that in the other is h2. The area of either base is A. What is the work done by gravity in equalising the levels when the vessels are interconnected?

A
Aρg(h1h22)2
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B
Aρg(h1+h22)2
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C
12Aρg(h1h2)2
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D
None of these
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Solution

## The correct option is A Aρg(h1−h22)2The figure can be shown diagrammatically as shown here.Let us assume that the height is hSo, h=(h1+h22)Hence decrease in height in vessel of height h1Δh=h1−(h1+h22)=(h1−h22)Mass of liquid would be equal tom=(h1−h22)ρAThus we can find the work done equal toW=mgΔh=(h1−h22)ρA(h1−h22)=(h1−h22)2gρA

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