The radii of two air bubbles are in the ratio 4 : 5. Find the ratio of excess pressure inside them. Also compare the works done in blowing these bubbles.

Explanation

Let the radii of two air bubbles be
`r_(1) = 4 R`
`r_(2) = 5 R`
If the respective excess pressures are `Delta P_(1) and Delta P_(2)`
Then
`Delta P_(1) = (4S)/(r_(1))`
`Delta P_(2) =(4S)/(r_(2))`
`(Delta P_(1))/(Delta P_(2))=(r_(2))/(r_(1))=(5)/(4)`
Work done in blowing the bubbles are
`W_(1) = S xx 2 xx 4 pi r_(1)^(2)`
`W_(2) = S xx 2 xx 4 pi r_(2)^(2)`
Thus `(W_(1))/(W_(2))=((r_(1))/(r_(2)))^(2)=((4)/(5))^(2)`
`=(16)/(25)`