Two soap bubbles in vacuum of radius `3cm` and` 4cm` coalesce to form a single bubble, in same temperature. What will be the radius of the new bubble?

Options

A. `7cm`
B. `(12)/(7) cm`
C. `12cm`
D. `5cm`

Answer

D

Explanation

`n=n_(1)+n_(2)`
` (pV)/(RT)=(p_(1)V_(1))/(RT)+(p_(2)V_(2))/(RT)`
or, `pV=p_(1)v_(1)+p_(2)v_(2)`
`:. ((4t)/(r ))(4/3 pir^(3))=((4t)/(r_(1) ))(4/3 pir_(1)^(3))`
`+((4t)/(r_(2)))(4/3 pir_(2)^(3))`
`:. r=sqrt(r_(1)^(2)+r_(2)^2)`
`=5cm`.