A closed tube in the form of an equilateral triangle of side $ℓ = 3 m$ contains equal volumes of three liquids which do not mix and is placed vertically with its lowest side horizontal. Find 'x' (in meter) in the figure if the densities of the liquids are in A.P.

Question

TestHub · Accepted Answer

Densities are in A.P.: ρ, ρ + d, ρ + 2d.

Equating pressure at the lowest corner from both arms:

$(ρ + 2 d) x sin 6 0^{\circ} + ρ (ℓ - x) sin 6 0^{\circ} = (ρ + d) (ℓ - x) sin 6 0^{\circ} + ρ x sin 6 0^{\circ}$

On solving, $3 d x = d ℓ \Rightarrow x = \frac{ℓ}{3} = \frac{3}{3} = 1 m$

Physics - Fluid Question with Solution | TestHub

Doubts & Discussion