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Question

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides, as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s1. The difference in the height, h (in cm) of liquid at the centre of the vessel and at the side will be :


A
2ω225g
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B
5ω22g
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C
25ω22g
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D
ω225g
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Solution

The correct option is C 25ω22g

Along the radius, the pressure due to centrifugal force is related to radius as,

dP=ρω2rdr

Also, this pressure will be equal to the gauge pressure due to the height of the fluid column.

dP=ρgdh

ρω2rdr=ρgdh

ω2R0rdr=gh0dh

ω2R22=gh

Given that,R=5 cm

h=ω2R22g=25ω22g

Hence, option (C) is correct.

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