Properties Of Solids And Liquids Question 350
Question: One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is [MP PET 1997; KCET 1999]
Options:
A) 1000 : 1
B)1 : 1000
C) 10 : 1
D) 1 : 10
Show Answer
Answer:
Correct Answer: D
Solution:
As volume remain constant therefore $ R={{n}^{1/3}}r $
$ \frac{\text{surface energy of one big drop}}{\text{surface energy of }n\text{ drop}}=\frac{4\pi R^{2}T}{n\times 4\pi r^{2}T} $
$ \frac{R^{2}}{nr^{2}}=\frac{{{n}^{2/3}}r^{2}}{nr^{2}} $ = $ \frac{1}{{{n}^{1/3}}}=\frac{1}{{{(1000)}^{1/3}}}=\frac{1}{10} $
