A circular cylinder of radius R and height H is filled with
water to a height 2H/3. 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 parabolloid.
(B) The free surface touches first the brim of cylinder and then the base of the cylinder.
(C) The free surfaces cannot touch the base without spilling water.
(D) The free surfaces touches the brim as well as base at the same instant.

Question

Saurabh Koranglekar · Answer

The equation of the free surface isy=2g&omega;2r2​+y0​ Whenthe free surface touches the brim of the cylinder, the lowest point of the paraboloid is at a heightH/3above the base. When the lowest point of the free surface touches the base of the cylinder, the height of water in the tank must beH/2. It means that water must spill out.

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