Question

A liquid drop having surface energy 'E' is spread into 216 droplets of same size. The final surface energy of the droplets is ____________.

Options

• 2E

• 4E

• 8E

• 6E

Answer 1

A liquid drop having surface energy 'E' is spread into 216 droplets of same size. The final surface energy of the droplets is 6E.

Explanation:

`"Surface area of drop,"  "A"_1 = 4pi "R"^2`

`"Surface area of 216 droplets,"  "A"_2 = 216 (4pi "r"^2)`

`because "volume of drop" = "n" xx ("volume of droplet")`

`therefore 4/3 pi"R"^3 = 216 xx 4/3 pi"r"^3`

`therefore "R" = 6r`

`therefore  "A"_2 = 216 ((4pi"R"^2))/36`

`therefore "A"_2 = 6 (4pi"R"^2)`

`"Surface energy" prop "Area"`

`therefore "E"_2/"E"_1= "A"_2/"A"_1 = (6 (4pi "R"^2))/(4pi"R"^2)`

`"E"_2 = 6"E"_1 = 6"E"`    ......`{because "E"_1 = "E"}`