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1000 water droplets having a radius of 0...

1000 water droplets having a radius of 0.01 cm each coalesce to form a single big drop. What will be the decrease in energy ? The surface tension of water = 72 dyn. `cm^-1`.

Text Solution

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Let the radius of the single big drop be R.
`therefore" " (4)/(3)piR^3=(4)/(3)pi(0.01)^3xx1000 or, R=0.1 cm`
Surface area of the big drop`=4pi(0.1)^2 cm^2`
Total surface area of 1000 droplets
`=4pi(0.01)^2xx1000cm^2`
`therefore` Decrease in area
`=4pi(0.01)^2xx1000-4pi(0.1)^2`
`=4pi(0.1-0.01)=4pixx0.09 cm^2`
`therefore ` Decrease in energy
`=4pixx0.09xx72=81.43 erg.`
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