Question

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) $2\omega^2\over5g$

Comments

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

Answer 1

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

Sol. 

$\rho \mathrm{d}r\omega^2r= \rho gdh$

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

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

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

Comments

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