A big drop is formed by coalescing 1000 small | vedclass

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(D) Let the radius of each small droplet be $r$ and the radius of the big drop be $R$.Since the volume remains conserved,the volume of the big drop eq

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$\frac{1}{10}$ th

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(D) Let the radius of each small droplet be $r$ and the radius of the big drop be $R$.Since the volume remains conserved,the volume of the big drop equals the sum of the volumes of $1000$ small droplets:$\frac{4}{3} \pi R^3 = 1000 	imes \frac{4}{3} \pi r^3$$R^3 = 1000 r^3$$R = 10r$The initial surface energy $U_i$ of $1000$ small droplets is:$U_i = 1000 	imes (4 \pi r^2 S)$,where $S$ is the surface tension.The final surface energy $U_f$ of the big drop is:$U_f = 4 \pi R^2 S$Substituting $R = 10r$:$U_f = 4 \pi (10r)^2 S = 100 	imes (4 \pi r^2 S)$Comparing $U_f$ and $U_i$:$U_f = \frac{100 	imes (4 \pi r^2 S)}{1000 	imes (4 \pi r^2 S)} U_i$$U_f = \frac{1}{10} U_i$Thus,the surface energy becomes $\frac{1}{10}$ th of the initial value.

$A$ big drop is formed by coalescing $1000$ small droplets of water. The surface energy will become :

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