A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become

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Solution

Q.
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become [2024]

1 100 times

2 10 times

3 $\frac{1}{100}$ th

4 $\frac{1}{10}$ th

Ans.
(4)

Lets say radius of small droplets is $r$ and that of big drop is R,

By conservation of volume:

$\frac{4}{3} {πR}^{3} = 1000 \frac{4}{3} {πr}^{3} \Rightarrow R = 10 r$

$∴$ Surface energy of 1000 droplets

$U_{i} = 1000 (4 {πr}^{2} S)$

$U_{f} = 4 π R^{2} = 100 (4 {πr}^{2} S)$

$U_{f} = \frac{1}{10} U_{i}$

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