One thousand small water drops of equal radii | vedclass

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

Vedclass · Accepted Answer

$1$:$10$

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(A) Let the radius of each small drop be $r$ and the radius of the big drop be $R$.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$$1000 r^3 = R^3$$R = 10r$Initial surface energy $(E_i)$ = $1000 	imes (4 \pi r^2 T)$, where $T$ is the surface tension.Final surface energy $(E_f)$ = $4 \pi R^2 T = 4 \pi (10r)^2 T = 400 \pi r^2 T$.The ratio of final surface energy to initial surface energy is:$\frac{E_f}{E_i} = \frac{400 \pi r^2 T}{1000 	imes 4 \pi r^2 T} = \frac{400}{4000} = \frac{1}{10}$.

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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