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Question

For the rotating container shown in figure, differences in the heights of the fluid between the centre and the sides (in cm) is-
[Take π2=10 & g=10 m/s2 for calculation]


A
12.5 cm
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B
18 cm
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C
15 cm
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D
20 cm
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Solution

The correct option is A 12.5 cm
Let the difference in the heights between the centre and the sides be h.


For a rotating fluid, the pressure difference can be given as
Δp=12ρω2x2
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.
i.e pB>pO
Δp=pBp0=12ρω2x2 ...(1)
The pressure variation along vertical direction is,
pB=pA+ρgh
pBp0=ρgh ...(2)
[pA=p0= atmospheric pressure]

From Eq.(1) and (2), on equating, we get
ρgh=12ρω2x2
h=ω2x22g
h=(5π)2×(0.1)22×10
(x=10 cm=0.1 mω=5π rad/s)

h=0.125 m=12.5 cm

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