Question

Compute the ratio of the gravitational force and electrostatic force between an electron (mass $9.1\times {10}^{31}kg$) and a proton (mass $1.7\times {10}^{-27}kg$)

Answer 1

Mass of electron$=9.1\times {10}^{-31}$ (value given in the question is wrong)

Let us assume that electron and proton placed with separation distance r meters.

Gravitational Force $F_G=\frac{G\times m_p\times m_e}{r^2}=\frac{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.7\times {10}^{-27}}{r^2}=\frac{6.67\times 9.1\times 1.7\times {10}^{-69}}{r^2}.....................\left(i\right)$

Electrostatic Force $F_E=\frac{1}{4\pi {\epsilon }_0}\frac{e^2}{r^2}=\frac{9\times {10}^9\times 1.6\times 1.6\times {10}^{-38}}{r^2}.................................................\left(ii\right)$

Hence,

$\frac{F_G}{F_E}=4.47\times {10}^{-40}$