Chapter 7, Problem 48A

To determine

The mass of each sphere.

Answer to Problem 48A

  $0.373\text{kg}$ and $0.746\text{kg}$

Explanation of Solution

Given:

The mass of one sphere is twice the mass of the other sphere. And, the distance between the centers of the sphere is $2.6\text{ m}$ .

The gravitational force between them is $2.75\times {10}^{-12}\text{N}$ .

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:

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

Let the mass of the first sphere is “ m ”, then the mass of the second sphere as given will be,

  $m_2=2m$

Then using the given values of gravitational force and the distance between the spheres, the mass of the first sphere will be,

  $\begin{array}{c}F=\frac{G{m}_1{m}_2}{r^2}\\ 2.75\times {10}^{-12}=\frac{6.67\times {10}^{-11}\times m\text{}\times 2m}{{\left(2.6\right)}^2}\\ =0.373\text{kg}\end{array}$

And, the mass of the second sphere will be,

  $\begin{array}{c}{m}_2=2m\\ =2\left(0.373\text{kg}\right)\\ =0.746\text{kg}\end{array}$

Conclusion:

Thus, the mass of the first and second sphere is $0.373\text{kg}$ and $0.746\text{kg}$ , respectively.