Single Choice

The ratio of electric force to the gravitational force between two protons separated by a finite distance is of the order of:

A$$10^{-19}$$
B$$10^{+19}$$
C$$10^{-36}$$
D$$10^{+36}$$
Correct Answer

Solution

$$Gravitational\ force\ = \dfrac{G(m_p)^2}{r^2}$$
$$Electric\ force\ = \dfrac{K(e)(e)}{r^2}$$
$$Ratio\ = \dfrac{K(1.6\times 10^{-19})^2}{r^2}\times \dfrac{r^2}{G\times (1.6\ 7\times 10^{-27})^2}$$
$$= \dfrac{(9\times 10^9)\times (1.6\times 10^{-19})^2}{(6.6\ 7\times 10^{-11})(1.6\ 7\times 10^{-27})^2}$$
$$=1.23\times 10^{20}\times 10^{16}$$
$$= 10^{36}$$(order of magnitude)

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