Chapter 13, Problem 1P

To determine

To determine: The gravitational force between the spheres.

Answer to Problem 1P

Answer: The gravitational force between the spheres is $7.41\times {10}^{-10}\text{N}$.

Explanation of Solution

Explanation:

Given information:

Two lead spheres masses of $1.50\text{kg}$ and $15.0\text{g}$ whose centers of separated by about $4.50\text{cm}$.

Formula to calculate the gravitational force between the two person is,

$F=G\frac{m_1{m}_2}{r^2}$

$F$ is the gravitational force.

$G$ is the gravitational constant.

$m_1$ is the mass of the first sphere.

$m_2$ is the mass of second sphere.

$r$ is the distance between centers of the spheres.

Substitute $1.50\text{kg}$ for $m_1$, $15\text{g}$ for $m_2$, $4.50\text{cm}$ for $r$ and $6.67\times {10}^{11}{\text{Nm}}^{\text{2}}/{\text{kg}}^{\text{2}}$ for $G$ to find $F$.

$\begin{array}{c}F=6.67\times {10}^{-11}{\text{Nm}}^{\text{2}}/{\text{kg}}^{\text{2}}\times \frac{\left(1.50\text{kg}\times 15\text{g}\times \frac{1\text{kg}}{1000\text{g}}\right)}{{\left(4.50\text{cm}\times \frac{1\text{m}}{100\text{cm}}\right)}^2}\\ =7.41\times {10}^{-10}\text{N}\end{array}$

Conclusion:

Therefore, the gravitational force between the spheres is $7.41\times {10}^{-10}\text{N}$.