Question

The excess of pressure inside the first soap bubble is three times that inside the second bubble. The ratio of volume of the first to second bubble is ______.

Options

• 1 : 3

• 1 : 9

• 1 : 27

• 3 : 1

Answer 1

The excess of pressure inside the first soap bubble is three times that inside the second bubble. The ratio of volume of the first to second bubble is 1 : 27.

Explanation:

Excess pressure in first soap bubble,

p₁ = `(4"T")/"r"_1`

∴ excess pressure inside second bubble, 

p₂ = `(4"T")/"r"_2`

On dividing these, we get

`"p"_1/"p"_2="r"_2/"r"_1`

but ⇒ `("r"_1/"r"_2)^3=1/27`

So, ratio of their volumes is,

`(4/3pi"r"_1^3)/(4/3pi"r"_2^3)="v"_1/"v"_2`

⇒ `"v"_1/"v"_2=1/27`