Question

A liquid drop having surface energy \(E\) is sprayed into 512 droplets of same size. The final surface energy is

• A. 12 E
• B. 4 E
• C. 8 E
• D. 6 E

Hint:

Conserve volume to find the small radius, then compare total surface areas.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Surface energy is proportional to surface area. The total volume stays constant when the drop is sprayed.

Step 2: Radius of Droplets
\( \dfrac{4}{3}\pi R^3=512\cdot\dfrac{4}{3}\pi r^3 \)
\( R=8r \), so \( r=\dfrac{R}{8} \).

Step 3: Area Comparison
Initial area \( 4\pi R^2 \). Final area \( 512\times4\pi r^2=512\times4\pi\dfrac{R^2}{64}=8\times4\pi R^2 \).

Step 4: Final Energy
The final surface energy is \( 8E \), option (C).

Final Answer:
The final surface energy is 8 times the initial energy. \[ \boxed{\text{(C) }\text{8 E}} \]