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 $F_{E}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}$
$F_{e} =\frac{9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{\left(5 \times 10^{-11}\right)^{2}}$
$=9.22 \times 10^{-8} N$
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} $