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 the radius of the original drop be R and the radius of each smaller drop be r . Equating the initial and final volumes: 4 3 R^3 = 1000 4 3 r^3 R^3 = 1000 r^3 R = 10 r r = R 10 The initial surface energy is u_i = T 4 R^2 . The final total surface energy is u_f = 1000 T 4 r^2 . Substituting r = R 10 : u_f = 1000 T 4 ( R 10 )^2 = 10 T 4 R^2 = 10 u_i The ratio is u_f u_i = 10 . Given u_f u_i = 10 x , we get x = 1 . Answer: 1