One thousand small water drops of equal radii | vedclass

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(D) Let the radius of the big drop be $R$ and the radius of each small drop be $r$.Given the number of small drops,$n = 1000$.Since the volume remains

Vedclass · Accepted Answer

$1: 10$

Vedclass · Answer

(D) Let the radius of the big drop be $R$ and the radius of each small drop be $r$.Given the number of small drops,$n = 1000$.Since the volume remains constant during the process,we have:$V_{	ext{final}} = V_{	ext{initial}}$$\frac{4}{3} \pi R^3 = n \left( \frac{4}{3} \pi r^3 ight)$$R^3 = 1000 r^3 \Rightarrow R = 10r$ ...$(i)$Initial surface energy,$SE_i = n 	imes (T 	imes 4 \pi r^2)$,where $T$ is the surface tension.Final surface energy,$SE_f = T 	imes 4 \pi R^2$.The ratio of final surface energy to total initial surface energy is:$\frac{SE_f}{SE_i} = \frac{T 	imes 4 \pi R^2}{n 	imes T 	imes 4 \pi r^2} = \frac{R^2}{n r^2}$Substituting $R = 10r$ and $n = 1000$:$\frac{SE_f}{SE_i} = \frac{(10r)^2}{1000 r^2} = \frac{100 r^2}{1000 r^2} = \frac{1}{10}$.Thus,the ratio is $1: 10$.

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

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