Question

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. ${10}^{+36}$

Answer 1

The correct option is D ${10}^{+36}$

$Gravitationalforce=\frac{G(m_p{)}^2}{r^2}$
$Electricforce=\frac{K\left(e\right)\left(e\right)}{r^2}$
$Ratio=\frac{K(1.6\times {10}^{-19}{)}^2}{r^2}\times \frac{r^2}{G\times (1.67\times {10}^{-27}{)}^2}$
$=\frac{(9\times {10}^9)\times (1.6\times {10}^{-19}{)}^2}{(6.67\times {10}^{-11})(1.67\times {10}^{-27}{)}^2}$
$=1.23\times {10}^{20}\times {10}^{16}$
$={10}^{36}$(order of magnitude)