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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:

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a

rω2g

b

r2ω22g

c

2grω

d

ω22gr2

answer is B.

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Detailed Solution

From Bernoulli’s theorem,PA+12dvA2+dghA =PB+12dvB2+dghBHere, hA=hB∴ PA+12dvA2=PB+12dvB2PA−PB=12d[vB2−vA2]Now, vA=0 , vB=rω and PA−PB=hdg∴ hdg=12dr2ω2 or h=r2ω22g

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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: