A big drop of water is sprayed into 1000 small droplets. Find the ratio of surface potential energy of drop to single droplet? from Physics Mechanical Properties of Fluids Class 11 Manipur Board
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Physics Part II

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A big drop of water is sprayed into 1000 small droplets. Find the ratio of surface potential energy of drop to single droplet?

Let, 

Radius of small droplet be 'r', 

Radius of big drop be 'R'. 

Volume of water will remain constant on splitting the drop into droplets. 

Therefore, 

R= nr3

Here n = 1000, 

Therefpre, R = 10 r

Now, the surface of the potential energy of drop is, 

straight E subscript 1 space equals space 4 πR squared straight T

and space the space surface space potential space energy space of space droplet space is comma space

straight E subscript 2 space equals space 4 πr squared straight T

Therefore comma space the space ratio space of space the space surface
space potential space energy space of space drop space to space single space drop space is comma space

straight E subscript 1 over straight E subscript 2 space equals space straight R squared over straight r squared space equals space fraction numerator left parenthesis 10 space straight r right parenthesis squared over denominator straight r squared end fraction space equals space 100 over 1

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