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

Options

A. `1:3`
B. `1:9`
C. `1:27`
D. `9:1`

Answer

C

Explanation

Excess pressure inside a soap bubble,
`p = (4S)/(R) rArr (p_(1))/(p_(2)) = (R_(2))/(R_(1))`
Given, `p_(1) = 3p_(2)`
`:. (3p_(2))/(p_(2)) = (R_(2))/(R_(1)) rArr (R_(1))/(R_(2)) = (1)/(3)`
Therefore, ratio of volumes of bubbles,
`(V_(1))/(V_(2)) = ((4)/(3)pi R_(1)^(3))/((4)/(3) pi R_(2)^(3))`
`= (R_(1)^(3))/(R_(2)^(3)) = ((1)/(3))^(3) = (1)/(27)`
`rArr V_(1) : V_(2) = 1 : 27`