Air is pushed inot a soap bubble of radius r to duble its radius. If the surface tension of the soap solution is S, the work done in the process is

Options

A. `8pi r^(2)S`
B. `12pi r^(2)S`
C. `16pi r^(2)S`
D. `24pi r^(2)S`

Answer

D

Explanation

A soap bubble has two surfaces, hence its surface potential energy is
`U_(0) = 2(4pi r^(2))S= 8pi r^(2)S`
If the radius of the soap bubble is doubled, then its surface potential energy.
`U_(f) = 2(4pi (2r)^(2))S= 32pi r^(2).S`
The work done in this process is `Delta U= U_(f) - U_(a)= 24pi r^(2).S`
`rArr` d is correct