Question

A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?

Answer 1

Let diameter of capillary tube = d mm

Let the radius of capillary tube r₁ = r mm

Capillary rise h₁ = 30 mm

Let the radius of another capillary tube r₂ = `2/3` r

Let the capillary rise of another capillary tube be h₂

We know that

T = `("hr"ρ"g")/2`

∴ `"h" ∝ 1/"r"`

`"h"_1/"h"_2 = "r"_2/"r"_1`

`30/"h"_2 = (2/3 "r")/"r"`

`30/"h"_2 = 2/3`

∴ h₂ = `(3 xx 30)/2` = 45 mm

Capillary rise in the new capillary tube = 45 mm