Question

Eight rain drops of radius 1 mm each falling downwards
with a terminal velocity of 5 cm/s coalesce to form a bigger
drop. Find the terminal velocity of bigger drop.​

Answer 1

NOTE:TERMINAL VELOCITY (V) DIRECTLY PROPORTIONAL TO r^2.

I HOPE IT WILL HELPS YOU.

Answer 2

Answer:

Let R and r be the radii of the big drop and each small drop respectively.

Volume of large drop = Volume of 8 small drop

We know :

Volume of drop = 4 / 3 π R³

= >  4 / 3 π R³ = 8 × 4 / 3 π r³

= > R³ = 8 r³

= > R = 2 r

We know Terminal velocity :

V = 2 / 9 ( ( r² ( ρ - r ) g ) / η

= > V ∝ r²

=  ( V₂ / V₁ ) = ( R² / r² )

= > V₂ = V₁ ( R / r )²

Putting values here we get :

V₂ = 5 ( 2 r / r )²

V₂ = ( 5 × 4 ) m / sec

V₂ = 20 m / sec

Therefore , terminal velocity of bigger drop is 20 / sec.