Question

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

• A. $\frac{r\omega }{2g}$
• B. $\frac{r^2{\omega }^2}{2g}$
• C. $\sqrt{2gr\omega }$
• D. $\frac{{\omega }^2}{2g{r}^2}$

Answer 1

The correct option is B $\frac{r^2{\omega }^2}{2g}$


For forced vortex,
$\frac{P_A}{\rho g}-\frac{1}{2g}{V}_A^2+h_A=\frac{P_B}{\rho g}-\frac{1}{2g}{V}_B^2+h_B$

$Here{P}_A=P_B,V_A=0,h_B-h_A=h,V_B=r\omega \Rightarrow \frac{V_B^2}{2g}=h_B-h_A=h\Rightarrow h=\frac{{\omega }^2{r}^2}{2g}$