Two cylindrical vessels of equal cross-sectional area $16\,cm ^{2}$ contain water upto herghts $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is $......J$ [Take density of water $=10^{3}\,kg / m ^{3}$ and $g =10\,ms ^{-2}$ ]
JEE MAIN 2022, Diffcult
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$h =\frac{ h _{1}+ h _{2}}{2}$
Now,
$W = U _{1}- U _{f}$
$W =\left(\rho A h_{1}\right) g \frac{h_{1}}{2}+\left(\rho A h_{2}\right) g \frac{h_{2}}{2}-\rho A \left( h _{1}+h_{2}\right) g$
$\left(\frac{h_{1}+h_{2}}{4}\right)$
$W =\frac{\rho Ag }{2}\left[ h _{1}^{2}+ h _{2}^{2}-\frac{\left( h _{1}+ h _{2}\right)^{2}}{2}\right]$
$W =1\,J$
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