JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Fluid Mechanics

A spherical drop of liquid splits into 1000 identical spherical drops. If

u_{i}

is the surface energy of the original drop and

u_{f}

is the total surface energy of the resulting drops, the (ignoring evaporation).

\frac{u _{f}}{u _{i}} = (\frac{10}{x})

. Then value of

x

is ____:

Answer: 1

Solution

Conserving volume,

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

, so

R = 10 r

. Surface energy scales with surface area, giving

u_{i} = T 4 π R^{2}

for the parent drop and

u_{f} = 1000 T 4 π r^{2}

for the fragments. Their ratio is

\frac{u _{f}}{u _{i}} = \frac{1000 r ^{2}}{R ^{2}} = \frac{1000 r ^{2}}{100 r ^{2}} = 10

. Set against

\frac{10}{x}

, this fixes

x = 1

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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