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Q.

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 5cm and the angular speed of rotation is ω  rad s−1. The difference in the height, h(in cm) of liquid at the center of vessel and at the side will be:

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a

25ω22g

b

2ω25g

c

5ω22g

d

2ω225g

answer is A.

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Detailed Solution

Select an element of width dx , which is rotating in circle of radius x.​We can equate vertical pressure with horizontal pressure.ρgh= 0rρω2xdx=ρω2r22​⇒h=ω2r22g=25ω22gin CGS
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