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Question

Difference in height of the liquid columns in the limbs of a rotating U tube as shown in the figure is:
(Neglect the width of each limb and take g=10 m/s2)


A
1 m
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B
0.8 m
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C
0.5 m
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D
0.6 m
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Solution

The correct option is B 0.8 m
Let the difference in heights between the liquid columns in the limbs be x and atmospheric pressure be p0.


For a rotating fluid, the pressure difference can be given as
ΔP=12ρω2x2 ...(1)
where x is the distance between two points in a liquid, measured from the axis of rotation.
The pressure will increase in a direction away from the axis of rotation.
pB>pA
For pressure at A,
pA=p0+ρgh2 ...(2) (due to variation in depth)
For pressure at B:
pB=pA+12ρω2L2 ...(3)
[ we can take AB=xL=2 m]

Also, pB=p0+ρgh1 ...(4) (due to variation in depth)

From Eq.(2), (3) & (4),
p0+ρgh1=p0+ρgh2+12ρω2L2
h1h2=12ω2L2g
Then, difference in heights of the liquid in the limbs
x=h1h2=12×22×2210
x=0.8 m

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