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

• A. 1000 : 1
• B. 1 : 1000
• C. 10 : 1
• D. 1 : 10

Answer 1

Answer: (D)

1 : 10

Answer 2

As volume remain constant therefore

$R = n ^ { 1 / 3 } r$

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

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