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Question
A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.
Solution
Let a0 be the acceleration with which U-tube is accelerated horizontally. So, the horizontal part will experience some inertial force.
Also,
pa = Atmospheric pressure
A = Area of cross section
h = Increase in height of the liquid
According to the question,
\[p_a A + A \times l \times \rho \times a_0 = p_a A + h\rho g \times A\]
\[ \Rightarrow hg = a_0 l\]
\[ \Rightarrow h = \frac{a_0 l}{g}\]
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