Question

A liquid is kept in a cylindrical vessel, which is rotated along its axis. The liquid rises at the side. If the radius of the vessel is 5 cm and the frequency of rotation is 4 rev/s, then the difference in the height of the liquid at the centre of the vessel and its sides is:

• A. 8 cm
• B. 2 cm
• C. 40 cm
• D. 4 cm

Answer 1

The correct option is A 8 cm

Given $R=5cm,\omega =2\pi \left(4\right)$ rad/s
We apply the Bernoulli's equation between the center point and the point at the circumference in the water we get:
$p_1-p_2=\frac{1}{2}\rho v^2$
$h\rho g=\frac{1}{2}\rho (r\omega {)}^2$
$h=\frac{w^2{r}^2}{2g}=\frac{4\times {\pi }^2\times 4^2\times {0.05}^2}{2g}=0.08m=8cm$