One thousand small water drops of equal radii | vedclass

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(C) Let $r$ be the radius of each small drop and $R$ be the radius of the big drop.Since the volume remains constant,the volume of $1000$ small drops

Vedclass · Accepted Answer

$1:10$

Vedclass · Answer

(C) Let $r$ be the radius of each small drop and $R$ be the radius of the big drop.Since the volume remains constant,the volume of $1000$ small drops equals the volume of the big drop: $1000 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$.This simplifies to $R^3 = 1000 r^3$,so $R = 10r$.The initial surface energy $U_i$ of $1000$ small drops is $U_i = 1000 	imes (4 \pi r^2 T)$,where $T$ is the surface tension.The final surface energy $U_f$ of the big drop is $U_f = 4 \pi R^2 T$.Substituting $R = 10r$,we get $U_f = 4 \pi (10r)^2 T = 400 \pi r^2 T$.The ratio of final surface energy to initial surface energy is $\frac{U_f}{U_i} = \frac{400 \pi r^2 T}{1000 	imes 4 \pi r^2 T} = \frac{400}{4000} = \frac{1}{10}$.

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is

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