JEE Main 2025 · Physics · Fluid Mechanics, Elasticity and Surface Tension · medium

One thousand identical spherical water droplets, each of radius 1 mm, coalesce into a single large drop. The surface tension of water is 0.07 N m^-1.…

Numerical answer

One thousand identical spherical water droplets, each of radius

1\ \mathrm{mm}

, coalesce into a single large drop. The surface tension of water is

0.07\ \mathrm{N\,m^{-1}}

. The surface energy released is

N\pi\times10^{-6}\ \mathrm{J}

, where

N

is ______.

Show answer and solution

Answer: 252

Volume conservation:

\tfrac43\pi R^3 = 1000\cdot\tfrac43\pi r^3

gives

R=10r=10\ \mathrm{mm}

. Initial surface area

=1000\times4\pi r^2 = 4000\pi\ \mathrm{mm^2}

; final area

=4\pi R^2 = 400\pi\ \mathrm{mm^2}

. Decrease in area

=3600\pi\ \mathrm{mm^2} = 3600\pi\times10^{-6}\ \mathrm{m^2}

. Energy released

=T\,\Delta A = 0.07\times3600\pi\times10^{-6} = 252\pi\times10^{-6}\ \mathrm{J}

. Hence

N=252

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