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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 rotation is ω, then the difference in the heights of the liquid at the centre of the vessel and the edge is

A
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C
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D
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Solution

## The correct option is B From Bernoulli's theorem, PA+12dv2A+dghA=PB+12dv2B+dghB Here, hA=hB ∴ PA+12dv2A=PB+12dv2B ⇒ PA−PB=12d[v2B−v2A] Now, vA=0,vB=rω and PA−PB=hdg ∴ hdg=12dr2ω2 or h=r2ω22g

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