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JEE Main20202 Sep 2020Morning ShiftPhysicsRotational MotionActual

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s - 1 . The difference in the height, h in cm of liquid at the Centre of vessel and at the sides of the vessel will be :

Options

  1. A2 ω 2 25 g
  2. B5 ω 2 2 g
  3. C25 ω 2 2 g
  4. D2 ω 2 5 g

Correct answer

C. 25 ω 2 2 g

Step-by-step solution

ρ d r ω 2 r = ρ g d h ω 2 ∫ 0 R r   d r = g ∫ 0 h d h ω 2 R 2 2 = g h h = ω 2 R 2 2 g = 25 ω 2 2 g   cm .

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