Question

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

• A. \(1:1\)
• B. \(1:10\)
• C. \(1:100\)
• D. \(1:1000\)

Hint:

Volume stays the same, so the big drop radius is 10 times the small one.

Answer 1

The Correct Option is B

Step 1: Shortcut
For $n$ drops merging, area ratio $= n^{-1/3}$.

Step 2: Evaluate
$1000^{-1/3} = \frac1{10}$. Option (B).

Final Answer:
1:10. \[ \boxed{\text{(B)}\ 1:10} \]