Eight equal drops of water are falling through air with a steady speed of 10 cm s - 1 . If the drops coalesce, the new velocity is:-

Step-by-step solution

The terminal velocity can be given by v T = 2 ( ρ - σ ) r 2 g 9 η . Clearly, v T ∝ r 2 Let the radius of the small drops be r 1 and the radius of the big drop be r 2 . So, 8 4 π 3 r 1 3 = 4 π 3 r 2 3 ⇒ r 1 = r 2 2 Hence, taking the ratio v T 1 v T 2 = r 1 r 2 2 ⇒ 10 v T 2 = 1 4 ⇒ v T 2 = 40   cm   s - 1