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PhysicsFluidPressureMedium3 minQB

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Passage / Comprehension

A U-tube with liquids of densities $ρ$ and $2 ρ$ stands vertically on a rotating table.
Its rotation axis passes through the table centre. Initially the interface is at A, the liquid column above A is $8 a /3$ , and $A B = 2 a$ .
The tube has cross-sectional area S. At angular speed $ω$ , the interface shifts $2 a /3$ toward B. Use the shown geometry for Q16 to Q18.

Find the force exerted by liquid of $ρ$ on liquid of $2 ρ$ at the interface.

Options:

Answer:

Solution:

After the interface shifts toward B, the light-liquid column above A is 2a.
$P_{A} = 2 ρ g a$
The radial segment of light liquid runs from r=a to r=5a/3.
$S (P_{x} - P_{A}) = \int_{a}^{5 a /3} ρS ω^{2} r d r$
$S (P_{x} - P_{A}) = \frac{8}{9} ρS ω^{2} a^{2}$
Using the angular speed found in Q18:
$ω^{2} = \frac{9 g}{32 a}$
$S (P_{x} - P_{A}) = \frac{1}{4} ρS a g$
$F_{x} = S P_{x} = S P_{A} + S (P_{x} - P_{A})$
$F_{x} = \frac{9}{4} ρS a g$

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Pressure

⏱ 3mℹ️ Source: QB

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