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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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Solution

The correct option is B
From Bernoulli's theorem,
PA+12dv2A+dghA=PB+12dv2B+dghB
Here, hA=hB
PA+12dv2A=PB+12dv2B
PAPB=12d[v2Bv2A]
Now, vA=0,vB=rω and PAPB=hdg
hdg=12dr2ω2 or h=r2ω22g


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