The work done to get n smaller equal size spherical drops from a bigger size spherical drop of water is proportional to

Options

A. `(1/n^(2//3) -1)`
B. `(1 - 1/n^(1//3))`
C. `(n^(2//3) -1)`
D. `(n^(4/3)-1)`

Answer

B

Explanation

`nxx4/3 pir^(3) = 4/3 piR^(3)`
`therefore R=n^(1//3)r`
`Delta A=A_(2) - A_(1) = n4pir^(2) - 4piR^(2)`
`= n4pir^(2) [ 1- 1/n^(1//3)]`
`therefore DeltaA propto [1- 1/n^(1//3)]`
`therefore W propto [1 - 1/n^(1//3)]` `[because Wpropto DeltaA]`