Question

A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is ______.

T = surface tension of water

Options

• `8pi"R"^3T(1-r/R)`

• `8pi"R"^3T(1+r/R)`

• `4pi"R"^3T(1/r+1/R)`

• `4pi"R"^3T(1/r-1/R)`

Answer 1

A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is `underline(4pi"R"^3T(1/r-1/R))`.

Explanation:

`4/3piR^3rho=4/3pinr^2rho`

∴ R³ = nr³

W = ΔAT

`=4piT[nr^2-R^2]`

`=4piT[R^3/r^3*r^2-R^2]`

`=4piR^3T[R/r-1]`

`=4pi"R"^3T[1/r-1/R]`