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A drop of radius 1 mm is sprayed into 1000 droplets of same size. If surface tension of the liquid is $40 d y n e c m^{- 1}$ , the amount of work done in the process is

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4.53 erg

4.53 J

$4.53 \times 10^{- 6} J$

$9.06 \times 10^{- 6} J$

answer is C.

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Detailed Solution

$W = 4 π T r^{2} [n^{\frac{1}{3}} - 1]$

$= 4 (3.14) (40) {(1 \times 10^{- 1})}^{2} [{(1000)}^{\frac{1}{3}} - 1]$

$= 4 (3.14) (4 \times 10^{- 1}) (10 - 1)$

$= 4.53 \times 10^{- 6} J$

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