Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio 4 : 3 . The rise of liquid in two capillaries is ' h 1 ' and ' h

Question

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio 4 : 3 . The rise of liquid in two capillaries is ' h 1 ​ ' and ' h h 2 ​ ' respectively. If the surface tensions of liquids are in the ratio 6 : 5 , the ratio of heights ( h 2 ​ h 1 ​ ​ ) is (Assume that their angles of contact are same)

TestHub · Accepted Answer

Given: Density ratio: ρ 2 ​ ρ 1 ​ ​ = 3 4 ​ and surface tension ratio: T 2 ​ T 1 ​ ​ = 5 6 ​ ∴ Rise of liquid in a capillary: h = r ρ g 2 T cos θ ​ For constant θ , r and g , h ∴ ​ ∝ ρ T ​ h 2 ​ h 1 ​ ​ = T 2 ​ ρ 1 ​ T 1 ​ ρ 2 ​ ​ = 5 × 4 6 × 3 ​ = 0.9 ​

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