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 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. $\frac{1}{2}M{\omega }^2{L}^2$
• B. $M{\omega }^{2}L$
• C. $\frac{1}{4}M{\omega }^{2}L$
• D. $\frac{1}{2}M{\omega }^{2}L$

Answer 1

Answer: (D)

$dm=\frac{M}{L}dx$
$dF=dm{\omega }^{2}x$
$F=\frac{M}{L}{\omega }^2\underset{0}{\overset{L}{\int }}xdx$
$=\frac{M}{L}{\omega }^2{\left|\frac{x^2}{2}\right|}_0^L$
$=\frac{1}{2}M{\omega }^{2}L$