Question

A liquid is kept in a cylindrical jar, which is rotated about the cylindrical axis. The liquid rises at it sends. The radius of the jar is $r$ and speed of rotation is $\omega$. The difference in height at the centre and the sides of jar is.

• A. $\frac{r^2{\omega }^2}{g}$
• B. $\frac{r^2{\omega }^2}{2g}$
• C. $\frac{g}{r^2{\omega }^2}$
• D. $\frac{2g}{r^2{\omega }^2}$

Answer 1

The correct option is B $\frac{r^2{\omega }^2}{2g}$

Consider a particle at x distance from center. The forces acting on that point is $mr{\omega }^2$ and mg. Now $tan\theta =\frac{mr{\omega }^2}{mg}=\frac{dy}{dx}$. on integrating from 0 to y and 0 to r, we get $y=\frac{r^2{\omega }^2}{2g}$