A big drop is formed by coalescing 1000 small identical drops of water. If $\mathrm{E}_{1}$ be the total surface energy of 1000 small drops of water and $\mathrm{E}_{2}$ be the surface energy of single big drop of water, the $\mathrm{E}_{1}$ : $\mathrm{E}_{2}$ is $\mathrm{x}: 1$ where $\mathrm{x}=$ ______.

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Fluid Mechanics

A big drop is formed by coalescing 1000 small identical drops of water. If

E_{1}

be the total surface energy of 1000 small drops of water and

E_{2}

be the surface energy of single big drop of water, the

E_{1}

E_{2}

x : 1

where

x =

______.

Answer: 10

Solution

By conservation of volume, 1000 small drops of radius

r

coalesce into one big drop of radius

R

1000 \times \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} ⟹ R = 10 r

Surface energy of

n

drops of radius

a

and surface tension

S

n \times 4 π a^{2} S

. So:

E_{1} = 1000 \times 4 π r^{2} S

E_{2} = 4 π (10 r)^{2} S = 100 \times 4 π r^{2} S

\frac{E _{1}}{E _{2}} = \frac{1000}{100} = 10

x = 10

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Integer answer

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