Question

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

• A. $\left(M{\omega }^{2}L\right)/2$
• B. $M{\omega }^{2}L$
• C. $\left(M{\omega }^{2}L\right)/4$
• D. $\left(M{\omega }^2{L}^3\right)/2$

Answer 1

The correct option is A $\left(M{\omega }^{2}L\right)/2$

Considering an elemental section dx. Mass of the elemental section =dm$=\frac{M}{L}dx$

As the tube is rotated with an angular velocity $\omega$

Centrifugal Force on the elemental section dx of mass dm will be dF=dmx${\omega }^2$

Now integrating the above eqaution with limits 0-L, we get,

$={\int }_0^L\frac{M}{L}{\omega }^{2}xdx=\frac{M}{2L}{\omega }^2{L}^2=\frac{ML{\omega }^2}{2}$