Answer:
Initial levels of water in two cylindrical vessels
are at A and B.
As total volume of water is constant,
therefore, after interconnection, the height of water in each
vessel becomes \[\frac{{{h}_{1}}+{{h}_{2}}}{2}\], Fig.
4(HT).7.
In the left vessel, level falls through
\[AC=\left( {{h}_{1}}-\frac{{{h}_{1}}+{{h}_{2}}}{2}
\right)=\frac{{{h}_{1}}-{{h}_{2}}}{2}\]
In the right vessel, level rises through
\[BD=\frac{{{h}_{1}}-{{h}_{2}}}{2}\]
Mass of water moved \[(m)=\rho A\left(
\frac{{{h}_{1}}-{{h}_{2}}}{2} \right)\]
Work done = \[mgh=\left[ \rho A\frac{\left( {{h}_{1}}-{{h}_{2}}
\right)}{2} \right]g\left( \frac{{{h}_{1}}-{{h}_{2}}}{2} \right)=\rho
Ag{{\left( \frac{{{h}_{1}}-{{h}_{2}}}{2} \right)}^{2}}\]
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