Question

In a capillary tube having area cross-section 'A' water rises to a height 'h'. If cross-sectional area is reduced to `"A"/9`, the rise of water in the capillary tube is ______.

Options

• 4h

• 3h

• 2h

• h

Answer 1

In a capillary tube having area cross-section 'A' water rises to a height 'h'. If cross-sectional area is reduced to `"A"/9`, the rise of water in the capillary tube is 3h.

Explanation:

From Jurin's law, h ∝ `1/"r"` or, rh = constant

`"r"_1"h"_1="r"_2"h"_2`              A₁ = π`"r"_1^2`

`"r"_1/"r"_2="h"_2/"h"_1`                 A₂ = π`"r"_2^2`

3 = `"h"_2/"h"_1="h"_2/"h"_1`        `(pi"r"_1^2)/9=pi"r"_2^2`

h₂ = 3h₁ = 3h          `"r"_1^2/"r"_2^2` = 9 ⇒ `"r"_1/"r"_2` = 3h