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)=4R`
`r_(2) = 5R`
If the respective excess pressures are `AP_(1)` and `AP_(2)` then
`/_\ P_(1) = (4S)/r_(1)`
`/_\ P_(2) = (4S)/r_(2)`
`(/_\P_(1))/(/_\P_(2)) = r_(s)/r_(1) = 5/4`
Work done, in blowing the bubbles are
`W_(1) = S xx 2 xx4pir_(1)^(2)`
`W_(2) = S xx 2xx 4pir_(2)^(2)`
Thus`W_(1)/W_(2) = (r_(2)/r_(1))^(2) = (4/5)^(2)`
=`16/25`