What change in surface energy will be noticed when a drop of radius R splits up into 1000 droplets of radius r, surface tension T ?

Question

What change in surface energy will be noticed when a drop of radius R splits up into 1000 droplets of radius r, surface tension T ? (A) 4 π R2 T (B) 7 π R2 T (C) 16 π R2 T (D) 36 π R2 T

Tardigrade Admin · Accepted Answer

Increase in surface energy = surface tension × increase in surface area =S(1000 × 4 π r2-4 π R2) (100 × (4/3) π r3=(4/3) R2 or r=(R/10)) =S × 4 π(1000 × (R2/100)-R2)=36 π R2 S

Q. What change in surface energy will be noticed when a drop of radius $R$ splits up into $1000$ droplets of radius $r$ , surface tension $T ?$

$4 π R^{2} T$

$7 π R^{2} T$

$16 π R^{2} T$

$36 π R^{2} T$

Increase in surface energy $=$ surface tension $\times$ increase in surface area
$= S (1000 \times 4 π r^{2} - 4 π R^{2})$
$(100 \times \frac{4}{3} π r^{3} = \frac{4}{3} R^{2}$ or $r = \frac{R}{10})$
$= S \times 4 π (1000 \times \frac{R ^{2}}{100} - R^{2}) = 36 π R^{2} S$

Q. What change in surface energy will be noticed when a drop of radius R splits up into 1000 droplets of radius r, surface tension T?

4πR2T

7πR2T

16πR2T

36πR2T