Question

The surface energy of a liquid drop is ' $V$ '. It is sprayed into 1000 equal droplets. The surface energy of all the droplets is

• A. V
• B. 10 V
• C. 100 V
• D. 1000 V

Hint:

If a drop is split into $n$ droplets, the surface area (and energy) increases by a factor of $n^{1/3}$. Here $1000^{1/3} = 10$.

Answer 1

The Correct Option is B

Step 1: Concept
Surface energy ($E$) is proportional to surface area ($A$): $E = T \times A$. Area of a sphere is $4\pi R^2$.

Step 2: Meaning
Volume remains constant: $\frac{4}{3}\pi R^3 = 1000 \times \frac{4}{3}\pi r^3 \implies R = 10r$ or $r = R/10$.

Step 3: Analysis
Initial Energy $V = T(4\pi R^2)$.
Final Energy $E_f = 1000 \times T(4\pi r^2) = 1000 \times T \times 4\pi (R/10)^2$.
$E_f = 1000 \times \frac{T(4\pi R^2)}{100} = 10 \times V$.

Step 4: Conclusion
The final surface energy is $10 V$. Final Answer: (B)