Question

Let 'R₁' and 'R₂' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is ______.

Options

• `"R"=("R"_1+"R"_2)/2`

• `"R"=sqrt("R"_1^2-"R"_2^2)`

• `"R"=sqrt("R"_1^2+"R"_2^2)`

• `"R"=("R"_1^3+"R"_2^3)^(1/3)`

Answer 1

Let 'R₁' and 'R₂' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is `underline("R"=("R"_1^3+"R"_2^3)^(1/3))`.

Explanation:

The Volume of the bigger drop is equal to the sum of the volumes of the smaller drops.

`4/3pi"R"^3=4/3pi"R"_1^3+4/3pi"R"_2^3`

`therefore"R"=root3("R"_1^3+"R"_2^3)`