Question

A large number of liquid drops each of radius 'a' are merged to form a single spherical drop of radius 'b'. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is [p = density of liquid, T = surface tension of liquid] ____________.

Options

• `[(6"T")/"p"(1/"a"-1/"b")]^(1//2)`

• `[(6"T")/"p"(1/"b"-1/"a")]^(1//2)`

• `["p"/("6T")(1/"a"-1/"b")]^(1//2)`

• `["p"/("6T")(1/"b"-1/"a")]^(1//2)`

Answer 1

A large number of liquid drops each of radius 'a' are merged to form a single spherical drop of radius 'b'. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is [p = density of liquid, T = surface tension of liquid] `[(6"T")/"p"(1/"a"-1/"b")]^(1//2)`.

Explanation:

`"As," 4/3 pi"b"^3 = N xx 4/3pi"a"^3`

`therefore "b"^3 = "Na"^3`

Energy released,

`Delta "U" = "T" xx 4pi"a"^2 xx "N" - "T" xx 4pi"b"^2`

`= "T" xx 4pi"b"^3/"a" - "T" xx 4pi"b"^2`

This energy is converted into K.E.

`therefore 1/2 "mv"^2 = "T" xx 4pi"b"^3 [1/"a"-1/"b"]`

`Rightarrow 1/2 "p" xx 4/3 pi"b"^3 xx "v"^2 = "T" xx 4pi"b"^3 (1/"a"-1/"b")`

`"v" = [(6"T")/"p"(1/"a"-1/"b")]^(1//2)`