Question:
Three different liquids are filled in a U-tube as shown. Their densities are \( \rho_1, \rho_2, \rho_3 \) respectively. From the figure we may conclude that
Three different liquids are filled in a U-tube as shown. Their densities are \( \rho_1, \rho_2, \rho_3 \) respectively. From the figure we may conclude that
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U-tube problems:
Compare pressures at same level.
Use \( \rho g h \).
Compare pressures at same level.
Use \( \rho g h \).
Updated On: Mar 2, 2026
- \( \rho_3 = 4(\rho_2 - \rho_1) \)
- \( \rho_3 = 4(\rho_1 - \rho_2) \)
- \( \rho_3 = 2(\rho_2 - \rho_1) \)
- \( \rho_3 = \frac{\rho_1+\rho_2}{2} \)
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The Correct Option is C
Solution and Explanation
Concept:
Hydrostatic equilibrium:
\[
P = \rho g h
\]
Pressures at same horizontal level are equal.
Step 1: {\color{red}Equate pressures at dotted line.}
Left side:
\[
\rho_1 g h + \rho_3 g \frac{h}{2}
\]
Right side:
\[
\rho_2 g h
\]
Step 2: {\color{red}Cancel \( g \).}
\[
\rho_1 h + \rho_3 \frac{h}{2} = \rho_2 h
\]
Step 3: {\color{red}Simplify.}
\[
\rho_1 + \frac{\rho_3}{2} = \rho_2
\Rightarrow \rho_3 = 2(\rho_2 - \rho_1)
\]
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