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Question

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of the rotation is ω, then the difference in the heights of the liquid at the center of the vessel and the edge is

A
rω2g
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B
r2ω22g
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C
2grω
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D
ω22gr2
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Solution

The correct option is B r2ω22g

For forced vortex,
PAρg12gV2A+hA=PBρg12gV2B+hB

Here PA=PB, VA=0, hBhA=h, VB=rωV2B2g=hBhA=hh=ω2r22g

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