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(A) Let $R$ be the radius of the original drop and $r$ be the radius of each of the $1000$ smaller drops.Since the volume remains constant: $1000 	im

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$1$

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(A) Let $R$ be the radius of the original drop and $r$ be the radius of each of the $1000$ smaller drops.Since the volume remains constant: $1000 	imes (4/3 \pi r^3) = 4/3 \pi R^3$.This simplifies to $1000r^3 = R^3$, which gives $R = 10r$ or $r = R/10$.The initial surface energy is $u_i = T 	imes 4\pi R^2$, where $T$ is the surface tension.The final total surface energy is $u_f = 1000 	imes (T 	imes 4\pi r^2)$.Substituting $r = R/10$: $u_f = 1000 	imes T 	imes 4\pi (R/10)^2 = 1000 	imes T 	imes 4\pi (R^2/100) = 10 	imes (T 	imes 4\pi R^2) = 10 u_i$.Thus, $u_f/u_i = 10$.Given $u_f/u_i = 10/x$, we have $10 = 10/x$, which implies $x = 1$.

$A$ spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops (ignoring evaporation), and $u_f/u_i = (10/x)$, then the value of $x$ is:

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