A drop of water of radius 1 mm is broken into 1000 droplets of equal size. The ratio of total surface area after : before equals:
A1 : 10
B10 : 1
C1 : 1000
D1000 : 1
Answer & Solution
Correct answer: B. 10 : 1
Volume conservation: $\frac{4}{3}\pi R^3 = 1000 \cdot \frac{4}{3}\pi r^3$ ⇒ $r = R/10$. Surface area before: $4\pi R^2$. After: $1000 \times 4\pi r^2 = 1000 \times 4\pi R^2/100 = 10 \times 4\pi R^2$. Ratio = 10:1 — surface area grows 10×, requiring 9× work against surface tension.
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