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

Question

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 $(\frac{h_{1}}{h_{2}})$ of the heights of the liquid in the two arms is

TestHub · Accepted Answer

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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