8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

Question

8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is (A) 1:10 (B) 1:15 (C) 1:20 (D) 1:25

Tardigrade Admin · Accepted Answer

As volume remains constant R3 = 8000 r3 ∴ R = 20 r ( textSurface energy of one big drop/ textSurface energy of 8000 small drop) = (4 π R2 T/8000 4 π r2 T) = (R2/8000 r2) = ((. 20 r .)2/8000 r2) = (1/20)

Q. $8000$ identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

$1 : 10$

$1 : 15$

$1 : 20$

$1 : 25$

As volume remains constant $R^{3} = 8000 r^{3}$ $∴ R = 20 r$
$\frac{Surface energy of one big drop}{Surface energy of 8000 small drop} = \frac{4 π R ^{2} T}{8000 4 π r ^{2} T}$
$= \frac{R ^{2}}{8000 r ^{2}} = \frac{( 20 r ) ^{2}}{8000 r ^{2}} = \frac{1}{20}$

Q. 8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

1:10

1:15

1:20

1:25