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  • A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the center of the circular base. If the radius of the vessel is r and angular velocity of rotation

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the center of the circular base. If the radius of the vessel is r and angular velocity of rotation is \mathrm{\omega}, then the difference in the heights of the liquid at the center of the vessel and the edge is:

Option: 1

\mathrm{\frac{\mathrm{r} \omega}{2 \mathrm{~g}}}


Option: 2

\mathrm{\frac{r^2 \omega^2}{2 g}}


Option: 3

\mathrm{\sqrt{2 \mathrm{gr} \omega}}


Option: 4

\mathrm{\frac{\omega^2}{2 g r^2}}


Answers (1)

best_answer

\mathrm{\begin{aligned} &\left(P-P_0\right) A \int d m r \omega^2 \\ &=\omega^2 \int \rho \cdot A r d r \\ &=\rho A \omega^2 \frac{r^2}{2} \\ & \rho g h A=\rho A \frac{\omega^2 r^2}{2} \quad\left(\because P-P_0=\rho g h\right) \\ & \therefore h=\frac{r^2 \omega^2}{2 g} \end{aligned}}

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HARSH KANKARIA

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