If T is the surface tension of a liquid, the energy needed to break a liquid drop of radius R into 64 drops is :-

Options

A. `6piR^(2)T`
B. `piR^(2)T`
C. `12piR^(2)T`
D. `8 piR^(2)T`

Answer

C

Explanation

Total volume of 64 drops = volume of big drop
` 64 xx 4/3 pir^(3) = 4/3 piR^(3)`
` Rightarrow = 64r^(3) or R = 4r or r= R/4`
Energy of bigdrop `(E_(1))= T.4piR^(2)`
Energy of 64 drops `(E_(2))`
`= 64(T xx 4pir^(2))`
` = 64 [ T xx 4pi (R/4)^(2)]`
` 16 piTR^(2)` Energy needed to break the drop into 64 droplets.
` DeltaW = E_(2)-E_(1) = 12piR^(2)T`