A big drop is formed by coalescing 1000 small | vedclass

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(C) Let $r$ be the radius of each small droplet and $R$ be the radius of the big drop.Since the volume is conserved,the volume of $1000$ small droplet

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$1$

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(C) Let $r$ be the radius of each small droplet and $R$ be the radius of the big drop.Since the volume is conserved,the volume of $1000$ small droplets 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$The surface energy of a drop is given by $E = T 	imes A$,where $T$ is surface tension and $A$ is the surface area.Surface energy of $1000$ small droplets $(E_s)$ = $1000 	imes (4 \pi r^2 T) = 4000 \pi r^2 T$Surface energy of the big drop $(E_b)$ = $4 \pi R^2 T = 4 \pi (10r)^2 T = 400 \pi r^2 T$The ratio of surface energy of $1000$ droplets to that of the big drop is:$\frac{E_s}{E_b} = \frac{4000 \pi r^2 T}{400 \pi r^2 T} = 10$Given that the ratio is $\frac{10}{x}$,we have:$10 = \frac{10}{x}$Therefore,$x = 1$.

$A$ big drop is formed by coalescing $1000$ small droplets of water. The ratio of surface energy of $1000$ droplets to that of the energy of the big drop is $\frac{10}{x}$. The value of $x$ is . . . . . . .

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