Question

A circular cylinder of radius $R$ and height $H$ is filled with water to a height $\left(2/3\right)H$. It starts rotating about its axis with constantly increasing angular speed. Choose the correct alternatives:

• A. at all speeds, shape of the free surface is paraboloid
• B. the free surface touches first the brim of the cylinder and then the base of the cylinder
• C. the free surface cannot touch the base without spilling water
• D. the free surface touches the brim as well as the base at the same instant

Answer 1

Answer: (A), (B), (C)

The correct options are
A at all speeds, shape of the free surface is paraboloid
B the free surface touches first the brim of the cylinder and then the base of the cylinder
C the free surface cannot touch the base without spilling water

The equation of the free surface is $y=\frac{{\omega }^2{r}^2}{2g}+y_0$
When the free surface touches the brim of the cylinder, the lowest point of the paraboloid is at a height $H/3$ above the base, as shown in Fig (2nd). When the lowest point of the free surface touches the base of the cylinder, the height of water in the tank must be $H/2$. It means that water must spill out.