A liquid drop of diameter D splits into 3375 | vedclass

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(A) Let the radius of the large drop be $R = D/2$. Let the radius of each small drop be $r$.Since the volume remains constant,the volume of the large

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$14 \pi D^2 S$

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(A) Let the radius of the large drop be $R = D/2$. Let the radius of each small drop be $r$.Since the volume remains constant,the volume of the large drop equals the sum of the volumes of $n = 3375$ small drops:$\frac{4}{3} \pi R^3 = n 	imes \frac{4}{3} \pi r^3$$R^3 = 3375 r^3$Taking the cube root on both sides: $R = 3375^{1/3} r = 15r$,so $r = R/15$.The initial surface area is $A_i = 4 \pi R^2$.The final surface area is $A_f = n 	imes 4 \pi r^2 = 3375 	imes 4 \pi (R/15)^2 = 3375 	imes 4 \pi (R^2 / 225) = 15 	imes 4 \pi R^2 = 60 \pi R^2$.The change in surface area is $\Delta A = A_f - A_i = 60 \pi R^2 - 4 \pi R^2 = 56 \pi R^2$.The change in surface energy is $\Delta U = S 	imes \Delta A = S 	imes 56 \pi R^2$.Substituting $R = D/2$,we get $\Delta U = S 	imes 56 \pi (D/2)^2 = S 	imes 56 \pi (D^2 / 4) = 14 \pi D^2 S$.

$A$ liquid drop of diameter $D$ splits into $3375$ small identical drops. If $S$ is the surface tension of the liquid,then the change in the surface energy in the process is

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