First slide

Surface tension

Question

Energy needed in breaking a drop of radius R into n drops of radius r, is

Moderate

A

$(4 {πr}^{2} n - 4 {πR}^{2}) T$
B

$(\frac{4 π}{3} {nπr}^{2} - \frac{4}{3} {πR}^{2}) T$
C

$(4 {πR}^{2} - 4 {πr}^{2}) nT$
D

$(4 {πR}^{2} - n 4 {πr}^{2}) T$

Solution

Energy needed = work done In splitting, the volume remains unchanged
$∴ \frac{4}{3} π R^{3} = \frac{4}{3} π r^{3} \times n$
or $r = R / (n)^{1 / 3}$
Energy needed = W = surface tension x change in area
$= T [4 {πr}^{2} n - 4 {πR}^{2}]$

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