Question

A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is ______.

विकल्प

• 1 : 2

• 2 : 1

• 1 : 4

• 1 : 1

Answer 1

A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is 1 : 1.

Explanation:

r₁ = r₂ = r

Surface tension of water (T_water)

Surface tension of soap solution

(T_soap) = `1/2` T_water

Excess pressure inside the drop

(P_drop) = `(2"T"_"water")/"r"`

Excess pressure in the soap bubble

`("P"_"bubble") = (4"T"_"soap")/"r"`

`("P"_"drop")/("P"_"bubble") = ((2"T"_"water")/"r")/((4"T"_"soap")/"r")` 

= `"T"_"water"/(2"T"_"soap")`

= `("P"_"drop")/("P"_"bubble") = 2/2 = 1;`

= `("P"_"drop")/("P"_"bubble")` = 1 : 1