Question

What must the separation be between a 5.2 kgparticle and a 2.4 kgparticle for their gravitational attraction to have a magnitude of$\mathbf{2}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{12}}\mathbf{N}$?

Short answer

The separation between the two particles must be 19 m

Step-by-step solution

The given data

Mass of the first particle,${\mathrm{m}}_1=5.2\mathrm{kg}$

Mass of the second particle,$m_2=2.4\mathrm{kg}$;

The gravitational force of attraction between the particles,$F=2.3\times {10}^{-12}\mathrm{N}$

Understanding the concept of Newton’s law of gravitation

According to Newton’s law of gravitation, the force between two particles is directly proportional to the masses of two particles and inversely proportional to the square of the distance between them.

Formula:

Gravitational force of attraction, $F=\frac{GMm}{r^2}$ (i)

Calculating the distance between the two particles

Using equation (i), force between two particles is given by:

$F=\frac{G{m}_1{m}_2}{r^2}$

$2.3\times {10}^{-12}\mathrm{N}=\frac{6.67\times {10}^{-12}\mathrm{N}.{\mathrm{m}}^2/{\mathrm{kg}}^2\times 5.2\mathrm{kg}\times 2.4\mathrm{kg}}{{\mathrm{r}}^2}$

Now solving for the distance or separation between the particales,:

$$\begin{gathered} {\mathrm{r}}^2=\frac{6.67\times {10}^{-11}\times 5.2\times 2.4}{2.3\times {10}^{-12}} \\ \mathrm{r}=19\mathrm{m} \end{gathered}$$

Hence, the separation between the particles is 19 m .