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: Find the radius
\(\frac43\pi R^3 = 1000\cdot\frac43\pi r^3\), so \(R = 10r\).

Step 2: Surface areas
Final area \(= 4\pi R^2 = 400\pi r^2\). Initial area \(= 1000\cdot4\pi r^2 = 4000\pi r^2\).

Step 3: Ratio
Surface energy is surface tension times area, so the ratio is \(\frac{400}{4000} = \frac1{10}\), i.e. \(1:10\). Option (B).

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