An upright $U-$tube manometer with its limbs $0.6 m$ high and spaced $0.3 m$ apart contains a liquid to a height of $0.4 m$ in each limb. If the $U-$tube is rotated at $10 radians/second$ about a vertical axis at $0.1 m$ from one limb. Choose the correct options

Let $z_{min}$ be the minimum reference level of the dotted parabola and $z_1$ and $z_2$ the liquid levels above the base.

$$\begin{gathered} z_1=\frac{r_1^2{\omega }^2}{2g}+z_{min}=\frac{0.1^2+{10}^2}{2\times 9.81}+z_{min}, \\ {z}_2=\frac{r_2^2{\omega }^2}{2g}+z_{min}=\frac{0.2^2+{10}^2}{2\times 9.81}+z_{min} \end{gathered}$$

But $z_1+z_2=2\times 0.4=0.8 m$

Hence $0.8=\frac{0.2^2\times {10}^2+0.1\times {10}^2}{2\times 9.81}+2z_{min}$

Hence, $z_{min}=0.273 m$

Consequently,

$$\begin{gathered} z_1=0.273+\frac{0.1^2\times {10}^2}{2\times 9.81}=0.324 m \\ {z}_2=0.273+\frac{0.2^2\times {10}^2}{2\times 9.81}=0.477 m \end{gathered}$$