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)

$ d m =\frac{M}{L} d x$
$d F =d m \omega^{2} x$
$F =\frac{M}{L} \omega^{2} \int\limits_{0}^{L} x d x$
$=\frac{M}{L} \omega^{2}\left|\frac{x^{2}}{2}\right|_{0}^{L} $
$=\frac{1}{2} M \omega^{2} L $