Question

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10^-5 m. This tube is immersed vertically into a liquid of surface tension 5.06 × 10^-2 N/m. When the length x × 10^-2 m of the tube is immersed in liquid then the liquid level inside and outside the capillary tube becomes the same, then the value of x is ______ m. (Assume atmospheric pressure is 1.01 × 105 `"N"/"m"^2`) 

Options

• 0.01

• 0.02

• 0.03

• 0.04

Answer 1

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10^-5 m. This tube is immersed vertically into a liquid of surface tension 5.06 × 10^-2 N/m. When the length x × 10^-2 m of the tube is immersed in liquid then the liquid level inside and outside the capillary tube becomes the same, then the value of x is 0.01 m. (Assume atmospheric pressure is 1.01 × 105 `"N"/"m"^2`) 

Explanation:

If final pressure of gas in tube is P₂ then

P₂ - `"2T"/"r"` = P₀

(as levels inside and outside are same)

i.e. P₂ = P₀ + `"2T"/"r"`

but as temperature remains constant

∴ P₁V₁ = P₂V₂

P₀AL = `("P"_0+"2T"/"r")`A(L - h)

On solving, h = 0.01 m