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Question

If T is the surface tension of a liquid, then the energy needed to break the liquid drop of radius R into 64 identical drops is
  1. 6πR2T
  2. 2πR2T
  3. 12πR2T
  4. 8πR2T


Solution

The correct option is C 12πR2T
Given, 
Radius of larger drop =R
Surface Tension of liquid =T
Number of identical drops made from larger drop, n=64
Let us suppose, radius of smaller drop is r.
As volume of liquid will remain same.
Volume of larger drop =n× volume of smaller drop
43πR3=64×43πr3
r=R4  
We know that,
Work done = Surface Tension × change in surface area
W=T×ΔA 
=T(n×4πr24πR2) 
=T[64×4π(R4)24πR2] 
=12πR2T

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