Question

Calculate the ratio of the electrostatic force and the gravitational force exerted by
two protons on each other.

Answer 1

The gravitational force can calculate by the formula Gm1m2/ r2 and the electrostatic force can be calculated by the formula q1q2/ r2 .

Answer 2

Answer:

The ratio of electrostatic force to gravitational force is $\bold{F_{e} / F_{g}=1.24 \times 10^{36}}$

Explanation:

The ratio of electrostatic force and gravitational force is given as follows –

As we know that charge on proton =  $\bold{=1.6 \times 10^{-19} \mathrm{C}}$

Mass of proton = $\bold{1.67 \times 10^{-27} \mathrm{kg}}$

$\begin{aligned} \mathrm{F}_{\mathrm{e}}=& \mathrm{kq}^{2} / \mathrm{r}^{2} \\ & \Rightarrow \mathrm{F}=9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19} / \mathrm{r}^{2} \end{aligned}$

$\begin{array}{l}{\Rightarrow \mathrm{F}=23.04 \times 10^{-29} / \mathrm{r}^{2}} \\ {\mathrm{F}_{\mathrm{g}}=\mathrm{G} \mathrm{m}^{2} / \mathrm{r}^{2}} \\ {\Rightarrow \mathrm{F}=6.67 \times 10^{-11} \times 1.67 \times 10^{-27} \times 1.67 \times 10^{-27} / \mathrm{r}^{2}} \\ {\Rightarrow \mathrm{F}=18.66 \times 10^{-11} / \mathrm{r}^{2}}\end{array}$

Ratio of electrostatic force and gravitational force –

$\begin{array}{c}{\mathrm{F}_{\mathrm{e}} / \mathrm{F}_{\mathrm{g}}=\left(23.04 \times 10^{-29} / \mathrm{r}^{2}\right) /\left(18.66 \times 10^{-65} / \mathrm{r}^{2}\right)} \\ {\Rightarrow \bold{F_{e} / F_{g}=1.24 \times 10^{36}}}\end{array}$