A big drop is formed by coalescing 1000 small | vedclass

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(A) Let $r$ be the radius of each small drop and $R$ be the radius of the big drop.Since the volume remains conserved during the coalescence of $1000$

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$10$

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(A) Let $r$ be the radius of each small drop and $R$ be the radius of the big drop.Since the volume remains conserved during the coalescence of $1000$ small drops into one big drop:$1000 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$R^3 = 1000 r^3 \implies R = 10r$.Surface energy $E$ is given by $E = S 	imes A$,where $S$ is surface tension and $A$ is the surface area.Total surface energy of $1000$ small drops: $E_1 = 1000 	imes (4 \pi r^2 	imes S) = 4000 \pi r^2 S$.Surface energy of the big drop: $E_2 = 4 \pi R^2 S = 4 \pi (10r)^2 S = 400 \pi r^2 S$.The ratio $E_1 : E_2 = \frac{4000 \pi r^2 S}{400 \pi r^2 S} = \frac{10}{1}$.Therefore,$x = 10$.

$A$ 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 the single big drop of water,then the ratio $E_1 : E_2$ is $x : 1$,where $x = . . . . . . $.

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