A sphere liquid drop of radius R is divided into eight equal droplets. If surface tension is S, then the work done in this process will be

Options

A. `2pi R^(2)S`
B. `3pi R^(2)S`
C. `4pi R^(2)S`
D. `2pi RS^(2)`

Answer

C

Explanation

Volume of big drop = Volume of 8 small droplets
`(4)/(3)pi R^(3) = 8 xx (4)/(3)pi R^(3) rArr r = R//2`
Work done `= S xx (4pi r^(2) xx 8 - 4pi R^(2))`
`= S xx 4pi ((R^(2))/(4) xx 8 - R^(2)) = 4pi R^(2)S`