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A big water drop is formed by the combin...

A big water drop is formed by the combination of 'n' small water drops of equal radii. The ratio of the surface energy of 'n' drops to the surface energy of big drop is

A

`n^(2):1`

B

`n:1`

C

`sqrt(n):1`

D

`root 3 (n):1`

Text Solution

Verified by Experts

The correct Answer is:
D
The mass and volume of the drop remain constant .
` :. 4/3 piR^(3) = n . (4/3 pir^(3)) `
` :. R^(3) = nr^(3) " " R = n^(1//3)" "`…(1)
` E_(1)` Surface energy of the big drop ` = 4piR^(2)T`
`E_(2)` = Surface energy of n drop ` = n xx 4pir^(2) xxT`
` :. (E_(2))/(E_(1)) = (nr^(2))/(R^(2)) = (nr^(2))/(n^(2//3))=n^(1//3)`
` :. E_(2) : E_(1) = 3sqrt(n):1`
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