# Rain Drops falling down in a uniform cloud

• Erfan
In summary, the conversation discusses a homework problem involving a uniform cloud of density ρ1 and a special rain drop that falls through the cloud. The rain drop maintains a spherical shape but its radius increases as it falls, and the water's density is ρ0. The problem asks to find a relation between the drop's velocity and the two densities, as well as the drop's acceleration. The differential equation for this problem is non-linear, and there is no air resistance force, but it may be possible to find a solution if linear air resistance is included.
Erfan

## Homework Statement

Consider a uniforms cloud of density ρ1 which consists of many little drops that are approximately still.Consider a special rain drop that is a little more bigger than the others so that it starts to fall down.Water drops stays spherical all the way.But the radius gets higher as it falls down.Also water's density is ρ0.
(a) Find a relation between $$\dot{r}$$, velocity of the drop, and the two densities.
(b) Find rain drop's acceleration.

## The Attempt at a Solution

The differential equation is non-linear.

We have no air resistance force.But it might be possible to find a solution when the air exerts linear resistance force.

## 1. What causes rain drops to fall in a uniform cloud?

Rain drops fall from clouds due to a process known as precipitation. This occurs when water droplets in the atmosphere become too heavy to remain suspended and fall to the ground.

## 2. How are rain drops formed in a uniform cloud?

Rain drops are formed when small water droplets in a cloud collide and merge with other droplets, eventually growing large enough to fall as precipitation.

## 3. Why do rain drops fall at different speeds in a uniform cloud?

The speed at which rain drops fall depends on their size, shape, and weight. Heavier and larger drops will fall faster than smaller and lighter drops.

## 4. How does the temperature of a cloud affect the formation of rain drops?

The temperature of a cloud plays a crucial role in the formation of rain drops. Warmer temperatures can lead to smaller droplets that take longer to form rain drops, while colder temperatures can result in larger droplets that fall faster.

## 5. Can rain drops fall in a uniform cloud without any wind?

Yes, rain drops can fall in a uniform cloud without wind. However, wind can affect the direction and intensity of the falling rain, as well as the shape and size of the rain drops.

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