Question

Two glass capillaries of radii r and 2r are kept vertical with their lower ends immersed in water
The heights to which water rises in them are in the ratio:​

Answer 1

Given :

Two glass capillaries of radii r and 2r are kept vertical with their lower ends immersed in water.

To Find :

Ratio of the heights to which water rises in them$.$

Solution :

❒ Expression of capillary rise or fall of a liquid is given by

• h = 2T cosθ / rρg

» h : height of liquid column

» T : surface tension of the liquid

» g : acc. due to gravity

» θ : angle of contact

» r : radius of the capillary bore

» ρ : density of the liquid

For pure liquid (like water), θ = 0°

Therefore, h = 2T / rρg

Here T, ρ and g are constants, so we can say that rise or fall in capillary is inversely proportional to the radius of capillary bore!

➙ h ∝ 1 / r

➙ h₁ / h₂ = r₂ / r₁

Given that, r₁ = r and r₂ = 2r

➙ h₁ / h₂ = 2r / r

➙ h₁ : h₂ = 2 : 1