A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ 1 and ρ 2 ( ρ 1 ρ 2 ) , fill half the circle. The angle θ

Question

A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ 1 and ρ 2 ( ρ 1 > ρ 2 ) , fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is:

TestHub · Accepted Answer

Pressure at the point A is the same on both sides of the tube, ρ 1 g r ( cos θ − sin θ ) = ρ 2 g r ( sin θ + cos θ ) ⇒ ρ 1 ρ 2 = sin θ + cos θ cos θ - sin θ = tan θ + 1 1 - tan θ ⇒ ρ 1 - ρ 1 tan θ = ρ 2 + ρ 2 tan θ ⇒ ρ 1 + ρ 2 tan θ = ρ 1 - ρ 2 θ = tan - 1 ⁡ ρ 1 - ρ 2 ρ 1 + ρ 2

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