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 $1.7\times {10}^{-27}kg$). Given : $e=1.6\times {10}^{-19}C$ and $G6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$.

• A. $5.5\times {10}^{-40}$
• B. $4.5\times {10}^{-40}$
• C. $4.5\times {10}^{-30}$
• D. $6.5\times {10}^{-40}$

Answer 1

Answer: (B)

$4.5\times {10}^{-40}$

The gravitational force : Electric force mass $=9.1\times {10}^{-31}kg$ (an electrons)

proton of mass $=1.7\times {10}^{-27}kg$

$e=1.6\times {10}^{-19}C$

$G=6.67\times {10}^{-11}{Nm}^2{Kg}^{-2}$

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

Let us assume electron and proton are placed with separation distance $r$ metre.

Gravitational force $F_G=$

$G.\frac{m_p\times m_c}{r^2}=\frac{6.67\times {10}^{-11}\times 1.7\times {10}^{-27}\times 9.1\times {10}^{-31}}{r^2}$

$=\frac{6.67\times 9.1\times 1.7}{r^2}\times {10}^{-69}⟶\left(1\right)$

Electrostatic force $F_E=\frac{9\times {10}^9\times 1.6\times 1.6}{r^2}\times {10}^{-38}⟶\left(2\right)$

hence,

$\frac{F_c}{F_e}=4.47\times {10}^{-40}$