Question

Two cylindrical vessels of equal crosssectional area $16 \,cm ^2$ contain water upto heights $100 \, cm$ 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 [Take density of water $=10^3 \,kg / m ^3$ and $\left.g =10 \, ms ^{-2}\right]$

• A. 0.25 J
• B. 1 J
• C. 8 J
• D. 12 J

Answer 1

Answer: (B)

$h =\frac{ h _1+ h _2}{2}$
Now,
$ W = U _{ i }- U _{ f } $
$ W =\left(\rho Ah _1\right) g \frac{ h _1}{2}+\left(\rho Ah _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 $