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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) $2\omega^2\over5g$

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

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


$\rho \mathrm{d}r\omega^2r= \rho gdh$

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



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