Question

A liquid drop having surface energy $E$ is spread into 729 droplets of same size. The final surface energy of the droplets is

• A. 6 E
• B. 9 E
• C. E
• D. 3 E

Hint:

For splitting a drop into $n$ droplets, final energy is simply $n^{1/3} \times E$.

Answer 1

The Correct Option is B

Step 1: Concept
Surface energy is proportional to the surface area ($E \propto R^2$). When a drop splits into $n$ droplets, volume is conserved ($R^3 = n r^3$).

Step 2: Meaning
$r = \frac{R}{n^{1/3}}$. The total surface area of $n$ droplets is $A_{total} = n \times 4\pi r^2 = n \times 4\pi (R/n^{1/3})^2 = n^{1/3} \times A_{initial}$.

Step 3: Analysis
Given $n = 729$.
$n^{1/3} = (729)^{1/3} = 9$.
Final Energy $= 9 \times E_{initial} = 9E$.

Step 4: Conclusion
The final surface energy is $9 E$. Final Answer: (B)