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9.2 , surface tension — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics9.2 , surface tension1 Mark
MCQ
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
  • A
    $1000:1$
  • B
    $1 : 1000$
  • C
    $10:1$
  • ✓
    $1:10$
✓

Answer

Correct option: D.
$1:10$
d
(d) As volume remain constant therefore $R = {n^{1/3}}r$

$\frac{{{\rm{surface\, energy\, of\, one \,big \,drop}}}}{{{\rm{surface \,energy \,of \,}}n{\rm{ drop}}}} = \frac{{4\pi {R^2}T}}{{n \times 4\pi {r^2}T}}$

$\frac{{{R^2}}}{{n{r^2}}} = \frac{{{n^{2/3}}{r^2}}}{{n{r^2}}}$ = $\frac{1}{{{n^{1/3}}}} = \frac{1}{{{{(1000)}^{1/3}}}} = \frac{1}{{10}}$

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