Question

When a mercury drop of radius 'R', breaks into 'n' droplets of equal size, the radius 'r' of each droplet is ______.

Options

• `r=R/sqrt"n"`

• `r="R n"^(1/3)`

• `r="R"/"n"`

• `r="R"/"n"^(1/3)`

Answer 1

When a mercury drop of radius 'R', breaks into 'n' droplets of equal size, the radius 'r' of each droplet is `underline(r="R"/"n"^(1/3))`.

Explanation:

Volume remains constant

`therefore "n"xx4/3pir^3=4/3pi"R"^3`

∴ nr³ = R³

`therefore"n"^(1/3)r="R"`

`thereforer="R"/"n"^(1/3)`