Answer to Question #83941 in Mechanics | Relativity for SHOURYA

Question

64 equal rain drops are falling in air with constant velocity 5 cm/s.if the drops coalesce then the constant velocity of the new drop will be

Answer 1

Since the drops move with constant velocity, the force of gravity is balanced by the force of air resistance.

Constant velocity for free falling bodies depends on their area.

For one drop (assume it has spherical shape) with radius

$$r$$

the volume, the area, and the velocity are correspondingly:

where

$$k$$

- a coefficient.

For one spherical drop with radius

$$R$$

made of

$$n$$

drops coalesced:

Thus the final terminal velocity depends on the quantity of drops only.