Question

A tube of length $L$ is filled completely with an incompressible liquid mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is:

• A. $\frac{ML{\omega }^2}{2}$
• B. $\frac{M{L}^2{\omega }^2}{}$
• C. $ML{\omega }^2$
• D. $\frac{M{L}^2{\omega }^2}{2}$

Answer 1

The correct option is A $\frac{ML{\omega }^2}{2}$

Centrifugal force $={\int }_0^{l}dm{\omega }^{2}x={\int }_0^l\frac{M}{L}dx{\omega }^{2}x=\frac{M}{L}{\omega }^2{\int }_0^{l}xdxF=\frac{M{\omega }^{2}L}{2}$