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 rotation is $\omega$, then the difference in the heights of the liquid at the centre of the vessel and the edge is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

From Bernoulli's theorem,
$P_A+\frac{1}{2}d{v}_A^2+dg{h}_A=P_B+\frac{1}{2}d{v}_B^2+dg{h}_B$
Here, $h_A=h_B$
$\therefore$ $P_A+\frac{1}{2}d{v}_A^2=P_B+\frac{1}{2}d{v}_B^2$
$\Rightarrow$ $P_A-P_B=\frac{1}{2}d[v_B^2-v_A^2]$
Now, $v_A=0,v_B=r\omega$ and $P_A-P_B=hdg$
$\therefore$ $hdg=\frac{1}{2}d{r}^2{\omega }^2$ or $h=\frac{r^2{\omega }^2}{2g}$