A U-tube is partially filled with water and then an immiscible liquid is added to the right side.The top of the liquid is a distance h₁ above the level of interface between the liquid and water.On the left side of the tube the top of the water is a distance h₂ above the liquid-water interface on the right side.What is the density of the liquid in terms of the density of water
? Note that h₂ < h₁.

Question

A U-tube is partially filled with water and then an immiscible liquid is added to the right side.The top of the liquid is a distance h₁ above the level of interface between the liquid and water.On the left side of the tube the top of the water is a distance h₂ above the liquid-water interface on the right side.What is the density of the liquid in terms of the density of water

A U-tube is partially filled with water and then an immiscible liquid is added to the right side.The top of the liquid is a distance h<sub>1</sub> above the level of interface between the liquid and water.On the left side of the tube the top of the water is a distance h<sub>2</sub> above the liquid-water interface on the right side.What is the density of the liquid in terms of the density of water ? Note that h<sub>2</sub> < h<sub>1</sub>. A) B) C) D)

? Note that h₂ < h₁.

Quizplus · Accepted Answer

According to the U-tube principle, the pressure at points A and B should be equal. At point A: P = atmospheric pressure + ρ_water*g*h1 where ρ_water is the density of water, g is the acceleration due to gravity, and h1 is the height of water above point B. At point B: P = atmospheric pressure + ρ_liquid*g*h2 + ρ_water*g*(h1-h2) where ρ_liquid is the density of the immiscible liquid, and h2 is the height of the liquid above point B. Since the pressure at points A and B are equal: ρ_water*g*h1 = ρ_liquid*g*h2 + ρ_water*g*(h1-h2) ρ_liquid = ρwater * (h1-h2) / h2 Since h₂ < h₁, h2 is smaller than h1-h2, so ρ_liquid should be less than ρ_water. The only choice that satisfies this condition is B.

A U-Tube Is Partially Filled with Water and Then an Immiscible