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

Step-by-step solution

Given, terminal velocity of each small drop v 1 = 10 c m s When 8 small drops are combined to form bigger If r 1 be radius of small drop and r 2 be radius of bigger drop, then v 2 = v 1 4 3 π r 2 3 = 8 × 4 3 π r 1 3 ⇒ r 2 = 2 r 1 ∴ Terminal velocity of the drop v = 2 r 2 9 p - σ 9 η i.e., v ∝ 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 v 2 = 4 v 2 = 4 × 10 = 40