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Question

A. liquid drop of radius ‘R’ breaks into 64 tiny droplets each of radius ‘r’. If the surface tension of the liquid is ‘T’ then gain in energy is:

A
48πR2T
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B
12πr2T
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C
96πr2T
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D
192πr2T
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Solution

The correct option is C 192πr2T
Let the density of the liquid be ρ.
Mass of the liquid drops must be equal to the total mass of the droplets.
ρ×4π3R3=64×ρ×4π3r3 R=4r

Change in surface area ΔA=64×4πr24πR2
ΔA=64×4π×r24π(4r)2=192πr2
Gain in energy E=TΔA=192πr2T

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