Eight mercury drops, each of radius , coalesce to form a bigger drop. The surface energy released in this process is

Question

Eight mercury drops, each of radius $r$ , coalesce to form a bigger drop. The surface energy released in this process is ______. (S is the surface tension of mercury). [2026]

Smart Achievers · Accepted Answer

(2)

$Conservation volume,$

$(8) [\frac{4}{3} π r^{3}] = \frac{4}{3} π R^{3} \Rightarrow R = 2 r$

$U_{i} = (8) (4 π r^{2}) (S); S = surface tension$

$U_{i} = 32 π r^{2} S$

$U_{f} = (4 π R^{2}) (S) = 4 π {(2 r)}^{2} (S) = 16 π r^{2} S$

$Energy released Δ U = U_{i} - U_{f} = 16 π r^{2} S$

Solution

Q.
Eight mercury drops, each of radius $r$ , coalesce to form a bigger drop. The surface energy released in this process is ______. (S is the surface tension of mercury). [2026]

1 $8 π r^{2} S$

2 $16 π r^{2} S$

3 $64 π r^{2} S$

4 $4 π r^{2} S$

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Solution

Q. Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is ______. (S is the surface tension of mercury). [2026]

1 8πr2S

2 16πr2S

3 64πr2S

4 4πr2S