A big drop is formed by coalescing 1000 small identical drops of water. If E 1 be the total surface energy of 1000 small drops of water and E 2 be the surface energy of single big drop of water, the E 1 : E 2 is x : 1 , where x = ________.

Step-by-step solution

Let radius of the small drop be r and the radius of the big drop be R . Then, total volume will remain constant, therefore 1000 × ρ 4 3 π r 3 = 4 3 π R 3 ρ ⇒ R = 10 r Initial total surface energy, E 1 = 1000 × 4 π r 2 × S and E 2 = 4 π ( 10 r ) 2 S ⇒ E 1 E 2 = 10 1 Hence , x = 10 .