Question

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be ______.

Options

• 2v

• `sqrt2"v"`

• 2^2/3v

• `"v"/sqrt2`

Answer 1

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be 2^2/3v.

Explanation:

According to question,

v_t ∝ r²

`4/3pi"R"^3=2xx4/3pi"r"^3`

⇒ R = 2^1/3r

∴ `"v"_2/"v"_1=("r"_2/"r"_1)^2`

= `("R"/"r")^2` = 2^2/3

⇒ v₂ = 2^2/3v