The excess pressure due to surface tension inside a spherical drop is 6 . If 27 such drops coalesce, the excess pressure inside the new drop is

Options

A. ` 6 N//m^(2)`
B. ` 18 N//m^(2)`
C. `12 N//m^(2)`
D. `2 N//m^(2)`

Answer

D

Explanation

`P_(1)= 6 " N/m"^(2), v_(2) = 27 v_(1)`
` (4pi)/3 r_(2)^(3) = 27 xx (4pi)/3 r_(1)^(3)`
` r_(2) = 3 r_(1)`
`(P_(2))/(P_(1))=(r_(1))/(r_(2))`
` = (r_(1))/(3r_(1))= 1/3 `
` P_(2) = (P_(1))/3 = 6/3 = 2 " N/m"^(2)`