A U-tube of base length 'l' filled with the same volume of two liquids of densities ρ and 2ρ is moving with an acceleration 'a' on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by

For the given situation, liquid of density 2ρ should be behind that of ρ. From the right limb, PA=Patm+ρgh PB=PA+ρa12=Pmin+ρgh+ρa12 PC=PB+(2ρ)a12=Pmin+ρgh+32ρal        (i) But from the left limb,PC=Patm+(2ρ)gh      (ii) From Eqs. (i) and (ii), Patm+ρgh+32ρal=Patm+2ρgh ⇒h=3al2g