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 ' h₁ ' and ' h₂ ' respectively. If the surface tensions of liquids are in the ratio 6: 5, the ratio of heights ((h₁)/(h₂)) is (Assume that their angles of contact are same) (a) 0.4 (b) 0.5 (c) 0.8 (d) 0.9

Answer: (d). h = (2Tcos θ)/(rρ g) ⇒ h ∝ T/ρ (same r, θ). (h₁)/(h₂) = (T₁)/(T₂) × (ρ₂)/(ρ₁) = 6/5 × 3/4 = 18/20 So the answer is (d) 0.9.

Two capillary tubes of the same diameter are kept vertically in two… | MHT CET 2023 (11 May, Shift 1)

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Angle of Contact & Capillarity

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 ' $h_2$ ' respectively. If the surface tensions of liquids are in the ratio $6 : 5$ , the ratio of heights $\left(\frac{h_1}{h_2}\right)$ is

(Assume that their angles of contact are same)

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Answer: (d)

$h = \frac{2T\cos\theta}{r\rho g} \Rightarrow h \propto \frac{T}{\rho}$ (same $r$ , $\theta$ ).
$\frac{h_1}{h_2} = \frac{T_1}{T_2} \times \frac{\rho_2}{\rho_1} = \frac{6}{5} \times \frac{3}{4} = \frac{18}{20}$
So the answer is (d) $0.9$ .

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