Air is pushed into a soap bubble of radius r to double 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`=`(increase in surface)`xx`Surface tension
`=2xx[4pi((2D)/2)^(2)-4pi(D/2)^(2)]xxT`
(since for sap bubble, there are two free surfaces)
`=2xx(4piD^(2)=piD^(2))T=6piD^(2)T`