Question

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of the vessel is $5\text{cm}$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, $\text{in cm}$, will be:

• A. $2.0$
• B. $1.2$
• C. $0.1$
• D. $0.4$

Answer 1

The correct option is A $2.0$


$\text{Using,}{v}^2=u^2+2gy$

$\Rightarrow v^2=2gy[\because \text{u=0 at (0,0)}]$

$\because v=\omega r$

$\Rightarrow y=\frac{{\omega }^2{x}^2}{2g}$

$\Rightarrow y=\frac{(2\times 2\pi {)}^2\times (0.05{)}^2}{20}$

$\Rightarrow y=2\times {10}^{-2}\text{m}=2\text{cm}$

Hence, option $\left(A\right)$ is correct.