Question

Eight spherical rain drops of same mass and radius are falling down with a terminal velocity of 6 cm/s. If they coalesce to form on big drop. what will be its terminal speed? Neglect the buoyancy due to air? a)1.5cm/s b)6cm/s c)24cm/s d)32cm/s

Answer 1

24 cm/s

Explanation:

Two forces act on a falling raindrop of mass `m` and radius `a`:
- its weight `mg`
- the viscous drag `-6 pi eta a v`

So the net force is

`F = mg-6 pi eta a v`

The terminal velocity is reached when the drag force becomes large enough to cancel the weight

`0=mg-6 pi eta a v_t implies v_t propto m/a`

When 8 raindrops coalesce, the mass increases by a factor of 8. So does the volume. This means that the radius doubles. So, the terminal velocity increases by a factor of 4.