The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio between the volume of the first and the second bubble?

Options

A. `9:1`
B. `1:3`
C. `1:9`
D. `3:1`

Answer

C

Explanation

Pressure , `P=(4S)/(r)` or `P prop (1)/(r)`
`therefore (P_(1))/(P_(2))=(r_(2))/(r_(1))=(3)/(1)" "…(i)`
or `r_(2)=3r_(1)`
Also `(A_(1))/(A_(2))=(4pir_(1)^(2))/(4pir_(2)^(2))=((r_(1))/(r_(2)))^(2)=((r_(1))/(3r_(1)))^(2)" "`(Using (i))
`=(1)/(9)`