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Question

# A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid is rises at the sides. If the radius of the vessel is r and the speed of revolution is n rotations/second, find the difference in height of the liquid at the centre of vessel and its sides.

A
h=2π2n2r2g
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B
h=4π2n2r2g
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C
h=π2r2n2g
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D
None of these
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Solution

## The correct option is A h=2π2n2r2gFrom Berpoulli's theorem PA+12ρV2A+ρghA=PB+12PV2B+ρghBHere hA=hBPA−PB=12ρ(V2B−V2A)VA=0,VB=rωPA−PB=hρg⇒h=r2ω22gω=21mn→ rotation / second 1sec→n rotation1sec→21m angle h=4π2n2r22gh=2π2n2r2g

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