Question

If a capillary tube is immersed vertically in water, rise of water in capillary is 'h₁'. When the whole arrangement is taken to a depth 'd' in a mine, the water level rises to 'h₂'. The ratio `"h"_1/"h"_2` is ______. (R = radius of earth)

Options

• `(1 - "d"/"R")`

• `(1 + "d"/"R")`

• `(1 + "d"^2/"R"^2)`

• `(1 - "d"^2/"R"^2)`

Answer 1

If a capillary tube is immersed vertically in water, rise of water in capillary is 'h₁'. When the whole arrangement is taken to a depth 'd' in a mine, the water level rises to 'h₂'. The ratio `"h"_1/"h"_2` is `underline((1 - "d"/"R"))`.

Explanation:

πr²h₁ ρg = 2πrT cos θ

`therefore "h"_1 prop 1/"g"`

`therefore "h"_1/"h"_2 = "g"_2/"g"_1 = ("g"(1 - "d"/"R"))/"g" = (1 - "d"/"R")`