# A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides

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A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $\omega$ rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the will be :

(1) $5\omega^2\over2g$

(2) $2\omega^2\over25g$

(3) $25\omega^2\over2g$

(4) $2\omega^2\over5g$

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Properties of solids and liquids, applications and limitations of Bernoulli's law

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done_all

Ans. (3) $25\omega^2\over2g$

Sol.

$\rho \mathrm{d}r\omega^2r= \rho gdh$

$\omega^2\int\limits_0^R r\mathrm{d}r=g\int\limits_0^h dh$

${\omega^2R^2\over2}=gh$

$h={\omega^2R^2\over2g}={25\omega^2\over2g}$

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Sir, Can you please again explain this solution??
I don't got it