IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Why children fall down often?

## Objective

To verify that the height of the centre of mass plays an important role in falling.

## Introduction

Generally, small children fall often while walking. Their small height plays an important role in it.

## Apparatus

a meter scale, a one foot ruler

## Procedure

Hold both sticks vertically on a table. Tilt slightly and let them fall. Which stick hits the table first?

## Discussion

The centre of mass a body is a point where its entire mass can be assumed to be located for the purpose of studying its motion. It is a point where you can balance a body of your finger tip. The centre of mass of both the sticks is located at their mid point. Since the mid point (the centre of mass) of the smaller stick has to fall a lesser distance than the mid point of the larger stick, it hits the table top earlier (assume friction between the table and the stick to be negligibly small).

Perform the same experiment with two sticks of different lengths but of equal weights. Verify that the weight of the sticks does not play much role.

Children are shorter than adults, so their centre of mass is also lower. Thus, they get very little time to balance themselves when they starts falling. In addition to it, reaction time of the children is larger as compared to that of adults.

## Note

The time to fall is given by $$t=\sqrt{2h/g}$$, where $$h$$ is height of the centre of mass above the ground and $$g}$$ is the acceleration due to gravity.