The radius of a soap bubble is r. the surface tension of soap solution is T, keeping temperature constant, the radius of the soap bubble is doubled the energy necessary for this will be-

Options

A. `32 pi R^(2)T`
B. `24 piR^(2)T`
C. `16 piR^(2)T`
D. `8piR^(2)T`

Explanation

Given :
Initial radius of soap bubble =R
surface tension of soap solution =T
Final radius of soap bubble =2R
The initial energy needed to blow the soap bubble is `E_(1)=2xx4piR^(2)xxT=8piR^(2)T`
and final energy needed to blow the soap bubble is
`E_(2)=2xx4pi(4R)^(2) =32 pi R^(2)T`
Hence extra energy is needed is given by
`E_(2)-E_(1)=32 pi R^(2)T -8 pi R^(2)T=24 pi R^(2)T`