Chapter 5, Problem 31P

To determine

The individual masses of two objects.

Answer to Problem 31P

Solution:

Their individual masses are $3.94\text{kg}$ and $0.06\text{kg}$ .

Explanation of Solution

Given:

Two objects attract each other gravitationally with a force of $2.5\times {10}^{-}{}^{10}$ N when they are 0.25 apart.

Formula Used:

Gravitational force is given by:

  $F_g=G\frac{m_1{m}_2}{r^2}$

Where, G is the gravitational constant and r is the distance between the two masses.

  $F_g=2.5\times {10}^{-11}\text{N}$

  $\begin{array}{l}{m}_1{m}_2=\frac{F_g{r}^2}{G}\\ m_1{m}_2=\frac{2.5\times {10}^{-11}\times {(.25)}^2}{6.67\times {10}^{-11}}\end{array}$

Also, $m_1+m_2=4.0\text{kg}$

Now, ${(m_1-m_2)}^2={(m_1+m_2)}^2-4m_1{m}_2$

After solving the two equations:

  $\begin{array}{l}{m}_1=3.94\text{kg}\\ m_2=0.06\text{kg}\end{array}$

Conclusion:

Hence, their individual masses are $3.94\text{kg}$ and $0.06\text{kg}$ .