JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Fluid Mechanics

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

(A)100 times
(B)10 times
(C) $\frac{1}{100}$ th
(D) $\frac{1}{10}$ th✓ Correct

Answer: (D)

Solution

Let each small droplet have radius r and the big drop have radius R. Volume is conserved when 1000 droplets coalesce:

\frac{4}{3} π R^{3} = 1000 \times \frac{4}{3} π r^{3}

, so

R = 10 r

. Surface energy is proportional to surface area. Before coalescing:

U_{i} = 1000 \times 4 π r^{2} S

. After coalescing:

U_{f} = 4 π R^{2} S = 4 π (10 r)^{2} S = 100 \times 4 π r^{2} S

. Comparing the two,

U_{f} = \frac{100}{1000} U_{i} = \frac{1}{10} U_{i}

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Single correct option

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