Chapter 13, Problem 30A

Irene says that Earth’s force of gravity is stronger on a piece of iron than on a piece of wood of the same mass. Do you agree? Defend your answer.

To determine

Whether one can agree that Earth’s force of gravity is stronger on a piece of iron than on a piece of wood of the same mass.

Explanation of Solution

Introduction:

The force of gravity is the attractive force between any two bodies that are having mass. This force is always attractive because it continuously attempts to pull the bodies together and never tries to push them away from each other. The force of gravity is one of the fundamental forces in nature which is responsible for the interactions among the objects in nature. This is the weakest among the four fundamental forces in nature − Strong nuclear force, Electromagnetic force, weak nuclear force, and gravitational force.

Law of universal gravitation states that gravitational force $\left(F\right)$ between the two objects varies directly with the masses of the two objects and inversely with the square of the distance between the two objects. Hence the gravitational force $\left(F\right)$ experienced by an object of mass $\left(m\right)$ falling towards the Earth can be written as,

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

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

  $M$ is mass of the Earth,

  $m$ is mass of an object,

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

It is given that mass of the iron piece and wooden piece are equal, then from the equation $\left(1\right)$ one can say that both iron and wooden piece will experience the same force due to Earth’s gravity. Because distance between both the objects and Earth would be the same.