A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T , then the work done in the process will be :

Step-by-step solution

Let radius of the newly formed drops be r . As total volume will remain constant, therefore 4 3 π R 3 = 27 × 4 3 × π r 3 ⇒ R 3 = 27 r 3 ⇒ R = 3 r ⇒ r = R 3 ⇒ r 2 = R 2 9 Now, work done = T × Δ A = T 27 4 π r 2 - T 4 π R 2 = T 27 4 π R 2 9 - T 4 π R 2 = T π R 2 12 - 4 = 8 π R 2 T