Question

The excess pressure inside the first soap bubble of radius 'R₁' is two times, that inside the second soap bubble of radius 'R₂'. The ratio of volumes of the first bubble to that of second bubble is ______.

Options

• 1 : 2

• 1 : 8

• 1 : 1

• 1 : 4

Answer 1

The excess pressure inside the first soap bubble of radius 'R₁' is two times, that inside the second soap bubble of radius 'R₂'. The ratio of volumes of the first bubble to that of second bubble is 1 : 8.

Explanation:

Excess pressure `"P"=(4T)/R`

`therefore"P"_1/"P"_2="R"_2/"R"_1`

`"P"_1/"P"_2=2`        `because"R"_2/"R"_1=2`

`"V"_1/"V"_2=(4/3piR_1^2)/(4/3piR_2^3)=R_1^2/R_2^3(1/2)^3=1/8`