Question

A U shape tube contain fluid upto length $l$ in both limbs as shown in figure. What would be the minimum angular velocity with which tube should be rotated about any of the limbs so that length of fluid in that limb reduces to zero?

• A. $\sqrt{\frac{2g}{l}}$
• B. $2\sqrt{\frac{g}{l}}$
• C. $\sqrt{\frac{3g}{2l}}$
• D. $\sqrt{\frac{g}{2l}}$

Answer 1

The correct option is B $2\sqrt{\frac{g}{l}}$


By $\Delta P=2l\rho g$ .....(1)
& $\Delta P=\frac{\rho {\omega }^2{l}^2}{2}$ .....(2)

$2lpg=\frac{\rho {\omega }^2{l}^2}{2}\Rightarrow \omega =2\sqrt{\frac{g}{l}}$