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

# Galileo Book

## Objective

To verify that things fall together irrespective of their weight (mass).

## Introduction

Our common sense makes us believe that heavy objects fall quicker than lighter ones. Even our experience support this. We always see that papers, dried leaves etc.\ fall much slower than the stones. But is our common sense always true? Let us verify.

## Apparatus

a book and a paper sheet

## Procedure

Hold the book and the paper separately in two hands. Make surface of the paper and the book in horizontal plane. Drop them from the same height. The paper takes longer to fall.

Now, place the paper over the book. Take care that paper does not protrude out from the book. Drop them. Does paper still fall slower than the book?

## Discussion

Paper is much lighter than the book. So air drag is able to reduce its speed to a large extent. When paper is placed over the book, only the book encounters air drag. Hence they falls together.

Without going into the complexity of aerodynamics drag force, we can assume that drag forces ($$F$$) on the book and the paper are almost equal if they are falling with same speed. The Newton's second law gives downward acceleration of the book and the paper as,

\begin{align} &a_\text{book}=g-F/M, &a_\text{paper}=g-F/m, \nonumber \end{align}

Since $$m\ll M$$, we get \(a_\text{paper}