A water drop of diameter 2 mm is split up into 10^9 identical water drops. Calculate the work done in this process.

Q: A water drop of diameter 2 mm is split up into 109 identical water drops. Calculate the work done in this process.
(The surface tension of water is 7.3 × 10-2 N/m)

Sol: Let a water drop of radius R be split up into 10^9 identical water drops each of radius r.

R = D/2 = 2/2 = 1 mm= 1 × 10-3 m

No. droplets n = 109 ; T = 7.3 × 10-2 N/m

W = 4 π R2 T [n1/3 -1]

= 4π (10-3 )2  × 7.3 × 10-2 [(109 )1/3 -1]

=9.17 × 10-4 J