8000 identical water drops are combined to form a big. drop. Then, the ratio of final surface energy to the initial surface energy of all the drops together is

Options

A. `1:10`
B. `1:15`
C. `1:20`
D. `1:25`

Answer

C

Explanation

Volume of a big drop = Total volume of small drops
`4/3 pi R^(3) = 8000[4/3 pi r^(3)]`
R=20r
Initial surface energy, `U_(i) = n(4pir^(2)) sigma`
Where,
n - Number of drops
`sigma`- Surface Tension
Final surface eergy , `U_(f)=4piR^(2)sigma`
`U_(f)/U_(i) = (4piR^(2)sigma)/(n4pir^(2)sigma) = ((20r^(2)))/(8000r^(2))`
` therefore U_(f)/U_(i) = 1/20`