Question

The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance $5\times {10}^{-11}m$ , will be: (Charge on electron $=1.6\times {10}^{-19}C$ , mass of electron $=9.1\times {10}^{-31}kg$ , mass of proton $=1.6\times {10}^{-27}kg$ , $G=6.7\times {10}^{-11}N{m}^2/k{g}^2$ )

• A. $2.36\times {10}^{39}$
• B. $2.36\times {10}^{40}$
• C. $2.34\times {10}^{41}$
• D. $2.34\times {10}^{42}$

Answer 1

Answer: (A)

Gravitational force $F=\frac{G{M}_1{M}_2}{r^2}$
$F_G=\frac{6.7\times 10^{-11}\times 9.1\times 10^{-31}\times 1.6\times 10^{-27}}{{\left(5\times 10^{-11}\right)}^2}$
$=3.9\times 10^{-47}N$
Electrostatic force $F_E=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$
$F_e=\frac{9\times 10^9\times 1.6\times 10^{-19}\times 1.6\times 10^{-19}}{{\left(5\times 10^{-11}\right)}^2}$
$=9.22\times 10^{-8}N$
So, $\frac{\text{ Electrostatic force }}{\text{ Gravitational force }}=\frac{F_E}{F_G}$
$=\frac{9.22\times 10^{-8}}{3.9\times 10^{-47}}$
$=2.36\times 10^{39}$