Question

A given shaped glass tube having uniform area of cross-section is filled with water and is mounted on rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity $\omega$, then

• A. Water level in A will rise and fall in B.
• B. Water level in both A and B will rise.
• C. Water level in B will rise and fall in A.
• D. Water level in remains same in both A and B.

Answer 1

The correct option is B Water level in both A and B will rise.

Force acting on the liquid of length $dx$ as shown is:
$dF=Adx\rho {\omega }^{2}x$
Total force : $\int dF={\int }_0^{L}Adx\rho {\omega }^{2}x=\frac{A\rho {\omega }^2{L}^2}{2}$
Pressure at B will have an extra term due to this force.
Hence, water level will rise in in column B.
In the given problem, water level will rise in both A and B.