A liquid rises to a height of 9 cm in a glass capillary tube of radius

1.	A liquid rises to a height of 9 cm in a glass capillary tube of radius 0.02 cm. What will be the height of the liquid column in a glass capillary tube of radius 0.03 cm ?
Answer» Data : h₁ = 9 cm, r₁ = 0.02 cm, r₂ = 0.03 cm For the first capillary, T = \(\frac{r_1h_1pg}{2\,cos\,\theta}\) For the second capillary, T = \(\frac{r_2h_2pg}{2\,cos\,\theta}\) ∴ \(\frac{r_1h_1pg}{2\,cos\,\theta}\) - \(\frac{r_2h_2pg}{2\,cos\,\theta}\) ∴ r₁h₁= r₂h₂ The height of the liquid column in the second capillary, h₂ = \(\frac{r_1h_1}{r_2}\) = \(\frac{0.02\times9}{0.03}\) = 6 cm

A liquid rises to a height of 9 cm in a glass capillary tube of radius 0.02 cm. What will be the height of the liquid column in a glass capillary tube of radius 0.03 cm ?

Answer»

Data : h₁ = 9 cm, r₁ = 0.02 cm, r₂ = 0.03 cm

For the first capillary, T = \(\frac{r_1h_1pg}{2\,cos\,\theta}\)

For the second capillary, T = \(\frac{r_2h_2pg}{2\,cos\,\theta}\)

∴ \(\frac{r_1h_1pg}{2\,cos\,\theta}\) - \(\frac{r_2h_2pg}{2\,cos\,\theta}\)

∴ r₁h₁= r₂h₂

The height of the liquid column in the second capillary,

h₂ = \(\frac{r_1h_1}{r_2}\) = \(\frac{0.02\times9}{0.03}\) = 6 cm