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

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Solution

The correct option is **D** 14(h1∼h2)2gAp

given that, density =P

let, h2<h1

let at equilibrium the height of liquid = h

since, volume of water is constant

So,Ah1+Ah2+V0=V0+2Ah

V0=volume of water in pipe

h=h1+h22

potential energy of the system, initially

Ui=m1gh12+m2gh22=A⋅h1⋅P⋅h12g+A⋅h2⋅P⋅h22⋅g=APh21g2+APh222g=APg2(h21+h22)

potential energy at equilibrium

Uf=mgh2+mgh2=mgh=Aρgh2

=APgh24(h1+h2)2

∴ work done w=vi−vf

or w=APg2(h21+h22−h21+h22+2h1h22)

or w=APg(h1−h2)24

Correct option is (C).

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