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

The correct option is A $2.36\times {10}^{39}$


Gravitational force $F_G=\frac{G{m}_e{m}_p}{r^2}$
$F_G=\frac{6.7\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.6\times {10}^{-27}}{(5\times {10}^{-11}{)}^2}=3.9\times {10}^{-47}N$
Electrostatic force $F_e=\frac{1}{4\pi {ϵ}_0}\frac{e^2}{r^2}$
$F_e=\frac{9\times {10}^9\times 1.6\times {10}^{-19}\times 1.6\times {10}^{-19}}{(5\times {10}^{-11}{)}^2}=9.22\times {10}^{–8}N$
So, $\frac{F_e}{F_G}=\frac{9.22\times {10}^{-8}}{3.9\times {10}^{-47}}=2.36\times {10}^{39}$