Question

# Two identical cylenderical vessels with their bases at same level contains liquid of density p to different height h1 and h2. The work done by gravity in equalising the levels, when two vessels are connected by a small tube is

A
A(h1h2)gp
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B
(h1h2)pg
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C
14(h1h2)2gAp
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D
14(h1h2)gAp
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Solution

## The correct option is D 14(h1∼h2)2gApgiven that, density =P let, h2<h1let at equilibrium the height of liquid = hsince, volume of water is constantSo,Ah1+Ah2+V0=V0+2AhV0=volume of water in pipeh=h1+h22potential energy of the system, initiallyUi=m1gh12+m2gh22=A⋅h1⋅P⋅h12g+A⋅h2⋅P⋅h22⋅g=APh21g2+APh222g=APg2(h21+h22)potential energy at equilibriumUf=mgh2+mgh2=mgh=Aρgh2=APgh24(h1+h2)2∴ work done w=vi−vfor w=APg2(h21+h22−h21+h22+2h1h22)or w=APg(h1−h2)24Correct option is (C).

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