A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure.
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 $5 \mathrm{~cm}$ and the angular speed of rotation is $\omega \mathrm{rad} \mathrm{s}^{-1}$. The difference in the height, $h$ (in $\mathrm{cm}$ ) of liquid at the centre of vessel and at the side will be :
Correct Option: , 3
(3) Here, $\rho d r \omega^{2} r=\rho g d h$
$\Rightarrow \omega^{2} \int_{0}^{R} r d r=g \int_{0}^{h} d h$
$\Rightarrow \frac{\omega^{2} R^{2}}{2}=g h$\ $($ Given $R=5 \mathrm{~cm})$
$\therefore h=\frac{\omega^{2} R^{2}}{2 g}=\frac{25 \omega^{2}}{2 g}$
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