Two soap bubbles combine to form a single bubble. In this process, the change in volume and surface arca are respectively V and A. If p is the atmospheric pressure and T is the surface tension of the soap solution, the following relation is true.

Options

A. ` 4_pV+3TA=0`
B. `3_pV-4TA=0`
C. ` 4_pV-3TA=0`
D. ` 3_pV+4TA=0`

Answer

D

Explanation

`(P+ (4T)/r) 4/3 pi r^(3)`
`=(p+(4T)/r)4/3 pir_(1)^(3) +(p+(4T)/r_(2))4/3 pir_(2)^(3)`
`impliesP[4/3 pir^(3) -(4/3 pir_(1)^(3) + 4/3 pir_(2)^(3))] + 4/3[4pi r^(2) - (4pi r_(1)^(2) + 4pir_(2)^(2))]=0`
`therefore PV + 4/3 TA=0`
(or)
`therefore 3PV + 4/3 TA=0`