Chapter 7, Problem 32A

To determine

The change in the gravitational force between the masses when the distance between them is doubled.

Answer to Problem 32A

Decreases by a factor of 4.

Explanation of Solution

Given:

The distance between the two masses is doubled.

Formula used:

Universal law of Gravitation:

  $F=\frac{G{m}_1{m}_2}{r^2}$

Where, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between the masses.

Calculation:

Let the initial gravitational force between the masses $m_1$ and $m_2$ having the distance $r$ between them be $F$ , then

  $F=\frac{G{m}_1{m}_2}{r^2}$

Now, if the distance between the masses is doubled, then the new gravitational force between the masses will be,

  $\begin{array}{l}F\text{'}=\frac{G{m}_1{m}_2}{{\left(2r\right)}^2}\\ F\text{'}=\frac{G{m}_1{m}_2}{4r^2}\\ F\text{'}=\frac{F}{4}\end{array}$

Conclusion:

Thus, the new gravitational force between the masses will be decreased by the factor of 4.