Question

Six small raindrops each of radius 1.5 mm, come down with a terminal velocity of 6 cm s^(-1). They coalesce to form a bigger drop. What is the terminal velocity of the bigger drop?

Answer 1

Explanation:

Radius of each small drop r = 1.5 mm

= 0.15 cm

Terminal velocity for small drops vt=6cms−1vt=6cms-1

Let the density of water = ρρ

and the density of air =ρ'=ρ′

Then vt=2r29η(ρ−ρ')gvt=2r29η(ρ-ρ′)g

6 cm s−1=2×(0.15)29η(ρ−ρ')g ...(i)s-1=2×(0.15)29η(ρ-ρ′)g ...(i)

When the six drops combine, let the radius of the bigger drop be R.

Then volume of bigger drop = 6 ×× (volume of a small drop)

⇒43πR3=6×43πr3⇒43πR3=6×43πr3

⇒R3=6r3⇒R3=6r3

⇒R=(6)13r⇒R=(6)13r

= (6)1/3(0.15)(6)1/3(0.15)cm

Let the terminal velocity for this drop be 

Answer 2

Answer:vT = 19.81 m/s

Explanation: Let vT be terminal velocity of smaller raindrops.

And vT' be the terminal velocity of new raindrop formed by coalesce .

Relation between vT and vT' is

vT' = n^2/3vT

So from this relation

vT' = 6 ^2/3×6

vT'= 19.81 m/s