Question

Find the separation between two massive particles each of mass $5\text{mg}$ if they experience a gravitational force of $6.66\text{dyne}$.

Answer 1

Step 1:

Given: Mass of two massive particles

$$\begin{gathered} m_1=5\times {10}^{-3}\text{kg} \\ {m}_2=5\times {10}^{-3}\text{kg} \end{gathered}$$

Force $=6.66\text{dyne}$

Step 2:

According to Newton's Gravitational force

${\text{F}}_{}=\frac{{\text{Gm}}_1{\text{m}}_2}{{\text{r}}^2}\left(1\right)$

Step 3: We have to find the distance between two massive particles.

Step 4: Solution

put the values in the equation $\left(1\right)$ from the given data

$6.66\times {10}^{-5}=\frac{6.67\times {10}^{-11}\times 5\times {10}^{-3}\times 5\times {10}^{-3}}{{\text{r}}^2}$

$r^2=\frac{6.67\times {10}^{-11}\times 5\times {10}^{-3}\times 5\times {10}^{-3}}{6.66\times {10}^{-5}}$

By solving it, we get

$r^2=25\times {10}^{-12}m$

So, $r^{}=5\times {10}^{-6}m$

We can write it $\text{r}=5\text{μm}$

Hence, the separation between two massive particles is $5\text{μm}$