Question

Eight identical drops of water falling through air with uniform velocity of 10 cm/s combine to form a single drop of big size, then terminal velocity of the big drop will be ______.

विकल्प

• 80 cm/s

• 10 cm/s

• 30 cm/s

• 40 cm/s

Answer 1

Eight identical drops of water falling through air with uniform velocity of 10 cm/s combine to form a single drop of big size, then terminal velocity of the big drop will be 40 cm/s.

Explanation:

Given, terminal velocity of each small drop

v₁ = 10 cm/s

When 8 small drops are combined to form bigger drop, then volume will be same.

If r, be radius of small drop and r₂ be radius of bigger drop, then v₂ = v₁ 

`4/3 pi"r"_2^3 = 8 xx 4/3 pi"r"_1^3`

⇒ r₂ = 2r₁

∴ Terminal velocity of the drop

v = `2/9 ("r"^2 (rho - sigma))/(9eta)`

i.e., `"v" prop "r"^2`

∴ `"v"_1/"v"_2 = "r"_1^2/"r"_2^2 = "r"_1^2/(2"r"_1)^2`

`=> "v"_1/"v"_2 = 1/4`

v₂ = 4v₁ = 4 × 10 = 40 cm/s