A spherical liquid drop splits in to 729 identical spherical drops. If E is the surface energy of the original drop and U is the total surface energy of resulting drops, then E U = 1 x . The value of x is

Step-by-step solution

The volume of liquid remains constant when the spherical drop splits into 729 identical smaller drops. The radius R of the original drop and radius r of each small drop satisfy R^3 = 729r^3 , so R = 9r . The surface energy of the original drop is E = 4 R^2 , where is the surface tension. The total surface energy of the 729 smaller drops is U = 729 4 r^2 . The ratio becomes E U = R^2 729r^2 Substituting R = 9r gives E U = (9r)^2 729r^2 = 81 729 = 1 9 Since E U = 1 x , we conclude that x = 9 .