Question

If T is the surface tension of a liquid, the energy needed to break a liquid drop of radius R into 64 drops is
A. `6 pi R^(2)T`
B. `pi R^(2)T`
C. `12 pi R^(2)T`
D. `8 pi R^(2)T`

Answer 1

Correct Answer - C
Total volume of 64 drops = Volume of big drop
`64xx(4)/(3) pi r^(3)=(4)/(3)pi R^(3) implies R^(3)=64r^(3)`
`implies R= 4r " " implies r=(R )/(4)`
Energy of big drop `=T. 4pi R^(2)`
Energy of 64 drops `=64(Txx4pi r^(2))=64[Txx4pi((R )/(4))^(2)]`
`=16 pi TR^(2)`
`therefore` Energy needed to break the drop into 64 droplets.
`Delta W=E_(2)-E_(1)=12 pi R^(2)T`