Chapter 13, Problem 4A

What is the gravitational force between two 1-kilogram bodies that are 1 meter apart?

To determine

The gravitational force between two bodies for the given specifications.

Answer to Problem 4A

  $F=6.674\times {10}^{-11}\text{ N}$

Explanation of Solution

Given:

Mass of two objects is $m_1=m_2=1\text{ kg}$

Distance between the two objects is $d\text{ = 1 m}$

Formula used:

The expression for the gravitational force between two objects of masses $m_1$ and $m_2$ separated by a distance $d$ is given by,

  $F\text{ = G}\frac{m_1{m}_2}{d^2}$$\left(1\right)$

Where $\text{ G}$ is gravitational constant, $\text{ G}=6.674\times {10}^{-11}\text{ N}\cdot {\text{m}}^2/{\text{kg}}^2$

Calculation:

Substituting the numerical values in equation $\left(1\right)$ ,

  $\begin{array}{c}F=\frac{\left(6.674\times {10}^{-11}\text{ N}\cdot {\text{m}}^2/{\text{kg}}^2\right)\left(1\text{ kg}\right)\left(1\text{ kg}\right)}{{\left(\text{1 m}\right)}^2}\\ =6.674\times {10}^{-11}\text{N}\end{array}$

Conclusion:

The gravitational force between two $1-\text{kilogram}$ bodies that are $\text{1 m}$ apart is $6.674\times {10}^{-11}\text{ N}$ .