The excess pressure inside a soap bubble is twice the excess pressurre inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is

Options

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

Answer

A

Explanation

We know that for soap bubble, `p=(4T)/(r )`
`"Given" p_(1)=3p_(1)`
`"Here" (4T)/(r_(1))=3((4T)/(r_(2))) Rightarrow r_(2)=3r_(1)....(i)`
`V_(1)=(4)/(3)=3pir_(1)^(3) and V_(2)=(4)/(3)pir_(2)^(3)=(4)/(3)pi(3r_(2)^(2))=(4)/(3)pi(27r_(1)^(3))`
`Rightarrow (V_(1))/(V_(2))=((4//3)pir_(1)^(3))/((4//3)pi27r^(3))=(1)/(27)`