Question

The work done in splitting a spherical liquid drop of radius \( a \) into eight liquid droplets of the same size (surface tension of the liquid = \( S \)) is

• A. \( 8\pi Sa^2 \)
• B. \( \pi Sa^2 \)
• C. \( 2\pi Sa^2 \)
• D. \( 4\pi Sa^2 \)
• E. \( 16\pi Sa^2 \)

Hint:

Always conserve volume when a drop splits.

Answer 1

The Correct Option is D

Concept: Work done = increase in surface energy: \[ W = S \Delta A \]

Step 1: Volume conservation.
\[ \frac{4}{3}\pi a^3 = 8 \cdot \frac{4}{3}\pi r^3 \Rightarrow r = \frac{a}{2} \]

Step 2: Surface areas.
Initial: \[ 4\pi a^2 \] Final: \[ 8 \cdot 4\pi r^2 = 8 \cdot 4\pi \frac{a^2}{4} = 8\pi a^2 \]

Step 3: Increase.
\[ \Delta A = 8\pi a^2 - 4\pi a^2 = 4\pi a^2 \] \[ W = 4\pi Sa^2 \]