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JEE Advanced2020PhysicsMechanical Properties of FluidsActual

An open-ended U-tube of uniform cross-sectional area contains water (density 10 3 kg m - 3 ). Initially the water level stands at 0 . 29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m - 3 is added to the left arm until its length is 0 . 1 m , as shown in the schematic figure below. The ratio h 1 h 2 of the heights of the liquid in the two arms is

Options

  1. A15 14
  2. B35 33
  3. C7 6
  4. D5 4

Correct answer

B. 35 33

Step-by-step solution

p 1 = p 2 ⇒ p 0 + 800 g × 0 . 1 + 1000 g ( 0 . 29 - x ) = 1000 g ( 0 . 29 + x ) + p 0 ⇒ 0 . 8 + 2 . 9 - 10 x = 2 . 9 + 10 x ⇒ x = 0 . 8 20 = 0 . 04 h 2 = 0 . 1 + 0 . 29 - x = 0 . 35 h 1 = 0 . 29 + x = 0 . 33 h 2 h 1 = 35 33 = 1 . 06

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