Question

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is ______.

विकल्प

• 1 : 1000

• 1 : 10

• 1 : 100

• 1 : 1

Answer 1

One thousand small water drops of equal radii combine to form a big drop. The ratio of the final surface energy to the total initial surface energy is 1 : 10.

Explanation:

Let the initial radius be r₁.

The surface area of 1000 small water drops = `1000 × 4pir_1^2`

Volume of 1000 small drops = `1000 xx 4/3pir_1^3`

Let the final radius be r₂.

Since, initial volume = final volume

`1000 xx 4/3pir_1^3 = 4/3pir_2^3`

⇒ `1000r_1^3 = r_2^3 ⇒ r_2/r_1 = 10`

Let us assume surface tension remain constant, i.e. S.

Therefore, `(("Surface energy")_"final")/(("Surface energy")_"initial") = (S xx 4pir_2^2)/(S xx 4pir_1^2 xx 1000)`

= `(r_2/r_1)^2 xx 1/1000 = 1/10`