Chapter 18, Problem 40A

Which fall faster, large or small raindrops?

To determine

To Explain: The one which will fall faster-large, or small raindrop.

Explanation of Solution

Introduction:

The velocity of an object which is falling through the atmosphere does not depend upon the mass.

When an object falls from some height then only two types of force acts on the object. The first force is gravitational force and its direction is towards the center of the earth. Its magnitude is approximately constant.

The second force is the drag force or air resistance force. Its direction is opposite to the gravitational force. It depends upon the instantaneous velocity of the falling object and surface area of the falling object.

When large and small raindrops fall from the same height, then its velocity at any instant does not depend upon the mass. The magnitude of the acceleration due to gravity on both the raindrops will be the same.

So, it can be concluded that the instantaneous velocity will only depend upon the magnitude of the air resistance force.

The cross-section area of a large raindrop is large as compared to a small raindrop. The air resistance is force directly proportional to the cross-sectional area of the raindrops.

The air resistance force acting on the large raindrop is more as compared to the small rain raindrop. The direction of the air resistance force is opposite to the velocity of raindrops.

Therefore, small raindrops will experience small air resistance and fall with greater speed as compared to large raindrops.