A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height h , where the radius of its cross-section is b . If the surface tension of water is S , its density is ρ , and its contact angle with glass is θ , then value of h will be ( g is the acceleration due to gravity)

Question

A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height h , where the radius of its cross-section is b . If the surface tension of water is S , its density is ρ , and its contact angle with glass is θ , then value of h will be ( g is the acceleration due to gravity), 2 S b ρ g cos ⁡ ( θ - α ), 2 S b ρ g cos ⁡ θ + α, 2 S b ρ g cos ⁡ θ - α 2, 2 S b ρ g cos ⁡ θ + α 2

MARKS App · Accepted Answer

If R be the meniscus radius, ⇒ R cos ⁡ θ + α 2 = b Excess pressure on concave side of meniscus = 2 S R h ρ g = 2 S R = 2 S b cos ⁡ θ + α 2 ⇒ h = 2 S b ρ g cos ⁡ θ + α 2

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