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Question

Two cylindrical tanks of radii r and 2r with their bases at the same level contain a liquid of density p to heights H and 3H, respectively as shown in figure, The tanks are linked through a pipe of very small cross-sectional area A. Due to pressure difference liquid starts flowing from narrower vessel to broader vessel to equalize the pressure.
Based on above information, answer the following questions:
The final common level of liquid in both vessel is
877053_c3993fcd8b5b46809f3a0e609a2b44a3.png

A
2H
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B
7H5
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C
3H2
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D
5H2
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Solution

The correct option is B 7H5
Let P be the final level of the fluid,
The total volume should be same.
Let the amount of fluid contained in the U tube be
Vinitial=C+πr2×3H+4πr2×H
=C+7πr2H
Vfinal=c+πr2×p+4πr2p
=C+5×πr2p
C+πr2H=C+5πr2p
p=75H

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