A spherical drop of liquid splits into 1000 identical spherical drops. If u i is the surface energy of the original drop and u f is the total surface energy of the resulting drops, the (ignoring evaporation), u f u i = 10 x . Then value of x is ______:

Step-by-step solution

Let R be the radius of bigger drop and r be the radius of smaller drop. Here, volume will remain conserved, so V R = V r . ⇒ 4 3 π R 3 = 1000 × 4 3 π r 3 ⇒ R = 10 r As surface energy is stated as u = S A , here, S is surface tension and A is surface area. Thus, u i = S 4 π R 2 and u f = S 4 π r 2 × 1000 The ratio is u f u i = 1000 r 2 R 2 ⇒ u f u i = 10 1 Hence, the value of x = 1 .