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 $=1.6 \times 10^{-27} kg$ $\left.G=6.7 \times 10^{-11} Nm ^{2} / kg ^{2}\right)$

• 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 $F_{E}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}$
$F_{e} =\frac{9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{\left(5 \times 10^{-11}\right)^{2}}$
$=9.22 \times 10^{-8} N$
$\therefore \frac{\text { Electrostatic force }}{\text { Gravitational force }}=\frac{F_{E}}{F_{G}}$
$=\frac{9.22 \times 10^{-8}}{3.9 \times 10^{-47}}$
$=2.36 \times 10^{39}$