A mercury drop of radius `R` is sprayed into `n` droplets of equal size. Calculate the energy expended if surface tension of mercury is `T`.

Options

A. `4piR^2T(N^((1)/(3))-1)`
B. `2R^2T(N^((1)/(3))-1)`
C. `4piR^2T(N^((2)/(3))-1)`
D. none of these

Answer

A

Explanation

`triangleU=N(4pir_1^2)T-4piR^2T`
`=4piT(Nr_1^2-R^2)` .(i)
By mass conservation
`N((2)/(3)pir_1^3rho)=(4)/(3)piR^3rho`
`r_1=(R )/((N)^((1)/(3)))`. (ii)
Substitude `r_1` from equation (ii) in equation (i).
`triangleU=4piR^2T(N^((1)/(3))-1)`