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 ends with a uniform angular velocity $\omega$ . The force exerted by the liquid at the other end is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$dM=\left(\frac{M}{L}\right)dx$

force on ${}^{\prime }d{M}^{\prime }$ mass is

$dF=\left(dM\right){\omega }^{2}x$

By integration we can get the force exerted by whole liquid

$\Rightarrow F=\underset{0}{\overset{L}{\int }}\frac{M}{L}{\omega }^{2}xdx=\frac{1}{2}M{\omega }^{2}L$