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

Let's assume that the immiscible liquid has density ρL and the height of the water column on the left side is hL. The height of the water column on the right side is then hL + h₂. Using Pascal's law, the pressure at the interface between the water and the immiscible liquid on both sides of the U-tube must be equal. Therefore, we have: ρLgh₁ + ρLgh₂ = ρghL where ρ is the density of water and g is the acceleration due to gravity. Rearranging this equation, we get: ρL/ρ = hL/(hL + h₂) Since we know that h₂ < h₁, we can see that ρL/ρ is less than 1, which means that the density of the immiscible liquid is less than the density of water. The only answer choice that reflects this relationship is B, which is the correct answer.

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