Chapter 13, Problem 29A

Gravitational force acts on all objects in proportion to their masses. Why, then, doesn’t a heavy object fall faster than a lighter one? (Is the answer something you learned much earlier?)

To determine

To Explain: A heavy object doesn’t fall faster than a lighter one.

Explanation of Solution

Introduction:

The force of gravity is one of the fundamental forces in nature, which is responsible for the attractive force between any two objects that are having mass. This is the weakest among the four fundamental forces in nature − Strong nuclear force, Electromagnetic force, gravitational force, and weak nuclear force.

The gravitational force $\left(F\right)$ experienced by an object of mass $\left(m\right)$ falling towards the Earth can be written as,

  $F=\frac{GMm}{d^2}=mg$ $\left(1\right)$

  $\Rightarrow g=\frac{GM}{d^2}$ $\left(2\right)$

Where $\text{ G}$ is gravitational constant, $\text{ G}=6.673\times {10}^{-11}\text{ N}{\text{.m}}^2/{\text{kg}}^2$

  $g$ is acceleration due to gravity, $g=9.8{\text{ m/s}}^2$

  $M$ is mass of the Earth,

  $m$ is mass of an object,

  $d$ is distance between the Earth and an object.

From the expressions $\left(1\right)$ and $\left(2\right)$ , it is clear that gravitational force $\left(F\right)$ directly depends on the mass of an object $\left(m\right)$ whereas the acceleration due to gravity $\left(g\right)$ is independent of mass of an object $\left(m\right)$ . Hence, in the absence of air resistance both the lighter and heavier objects fall with the equal acceleration.