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

Options

A. At all speeds, shape of the free surface is parabolloid.
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

A, B, C

Explanation

The equation of the free surface is
`y=(omega^(2)r^(2))/(2g)+y_(0)`

When the free surface touches the brim of the cyliner the lowest point of the paraboloid is at a height `H//3` above the base, as shown in figure. When the lowest point of the free surface touches the base of the cylinder, the height of water in the tank be `H//2`. It means that water musp spill out.