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.

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The free surface cannot touch the base without spilling water

The free surface touches first the brim of the cylinder and then the base of the cylinder

The free surface touches the brim as well as the base at the same instant.

At all speeds, shape of the free surface is parabolloid

answer is A, B, C.

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Detailed Solution

The equation of the free surface is $y = \frac{ω^{2} r^{2}}{2 g} + y_{0}$
Question Image
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 figure. 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.