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. `2piD^(2)T`
B. `4piD^(2)T`
C. `6piD^(2)T`
D. `8piD^(2)T`

Answer

C

Explanation

Work done `=` (increae in surface area) `xx` surface tension
`=2xx[4pi((2D)/(2))^2-4pi((D)/(2))^2]xxT`
[Since, for sap bubble, there are 2 free surfaces]
`=2xx(4piD^2-piD^2)T=6piD^2T`