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  • The vertical limbs of a U shaped tube are filled with a liquid of density  upto a he

The vertical limbs of a U shaped tube are filled with a liquid of density \mathrm{\rho} upto a height h on each side. The horizontal portion of the U tube having length \mathrm{2 h} contains a liquid of density . The U tube is moved horizontally with an accelerator \mathrm{\mathrm{g} / 2} parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs, at steady state will be

Option: 1

\mathrm{2 \mathrm{~h} / 7}


Option: 2

\mathrm{8 \mathrm{~h} / 7}


Option: 3

\mathrm{4 \mathrm{~h} / 7}


Option: 4

\mathrm{None}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \rho x g / 2+2(2 h-x) g / 2=P_B-P_A \\\\ & P_A=(h-x) \rho g \\\\ & P_B=h \rho g+2 \rho x g \\\\ & \rho x g / 2+2 \rho(2 h-x) g / 2=h \rho g+2 \rho x g-h \rho g+x \rho g \\\\ & \frac{4 \rho h g}{2}-\frac{2 \rho x g}{2}=2 \rho x g+\rho x g / 2 \\\\ & 2 \rho h g-\rho x g=5 P x g / 2 \\\\ & \Rightarrow x=\frac{4 h}{7} \end{aligned}}

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Irshad Anwar

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