If a number of litle of droplets of water of surface tension S, all of the same radius r combine to from a single drop of radius R and the energy relased is converted into kinetic energy. Find the velocity acquired by the bigger drop. If the energy relased in converted inot heat, find the rise in temperature.

Answer

`sqrt(6S(R -r)/(r R))`

Explanation

Let there be n small drops combine to form a big drop. Then `n xx(4)/(3) pi r^3 = (4)/(3) pi R^3 = n = (R^3)/(r^3)`
Mass of bigger drop of water, `M = volume xx density o= (4)/(3) pi R^3xx1` [Density of water = 1g//c c] Energy relased = S.T. decrease in surface area `E = S xx 4 pi [nr^2 -R^2]`
`= Sxx4 pi [(R^3)/(r^3) r^2 - R^2] = 4pi S R^3 [(1)/(r ) - (1)/(R )]`
` = 3 xx(4)/(3)pi R^3 S [(R - r)/(R r)] = 3 MS((R - r)/(Rr))`
Kinetic energy produced = E `:. (1)/(2) M upsilon^2 = 2MS[(R - r)/(R r)] or upsilon = sqrt((6S(R -r))/(R r))`