Chapter 7, Problem 72A

a.

To determine

The gravitational force between the two spherical objects when the distance between them is $5.0\text{m}$ .

Answer to Problem 72A

  $1.70\times {10}^{-10}\text{N}$

Explanation of Solution

Given:

The mass of both the spherical objects is $m=8.0\text{kg}$ .

The distance between the spheres is $r=5.0\text{m}$ .

Formula used:

Gravitational force:

  $F=\frac{G{m}_1{m}_2}{r^2}$

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

Calculation:

The value of gravitational constant is

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Now, the gravitational force between the spheres is,

  $\begin{array}{c}F=\frac{G{m}_1{m}_2}{r^2}\\ =\frac{6.67\times {10}^{-11}\times 8\times 8}{{\left(5\right)}^2}\\ =1.70\times {10}^{-10}\text{N}\end{array}$

Conclusion:

Thus, the gravitational force between the spheres is $1.70\times {10}^{-10}\text{N}$ .

b.

To determine

The gravitational force between the two spherical objects when the distance between them is $5.0\times {10}^1\text{m}$ .

Answer to Problem 72A

  $1.70\times {10}^{-12}\text{N}$

Explanation of Solution

Given:

The mass of both the spherical objects is $m=8.0\text{kg}$ .

The distance between the spheres is $r=50\text{m}$ .

Formula used:

Gravitational force:

  $F=\frac{G{m}_1{m}_2}{r^2}$

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

Calculation:

The value of gravitational constant is

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Now, the gravitational force between the spheres is,

  $\begin{array}{c}F=\frac{G{m}_1{m}_2}{r^2}\\ =\frac{6.67\times {10}^{-11}\times 8\times 8}{{\left(50\right)}^2}\\ =1.70\times {10}^{-12}\text{N}\end{array}$

Conclusion:

Thus, the gravitational force between the spheres is $1.70\times {10}^{-12}\text{N}$ .