Q.
A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides (figure). If the radius of the vessel is 0.05 m and the sped of rotation is $2\ rad\ s^{- 1}$, find the difference in the height of the liquid at the centre of the vessel and its sides
A) 20 cm
B) 4 cm
C) 2 cm
D) 0.2 cm
Explanation
(c) According to Bernoulli’s Theorem; $p = \frac{1}{2}\rho\ v^{2}$ =constant. Near the ends, the velocity of liquid is higher so that pressure is lower as a result the liquid rises at the sides to compensate for this drop of pressure
$ie,\ \rho\ g\ h = \frac{1}{2}\rho\ v^{2} = \frac{1}{2}\rho r^{2}\omega^{2}$
Hence, $h = \frac{r^{2}\omega^{2}}{2g} = \frac{r^{2}(2\pi v)^{2}}{2g} = \frac{2\pi^{2}r^{2}v^{2}}{g}$
$= \frac{2 \times \pi^{2} \times (0.05)^{2} \times 2^{2}}{9.8}$
$= 0.02\ m = 2\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.