Correct Answer - Option 3 : 10

^{-42}
__CONCEPT__

**The universal law of gravitation: **

- According to this law, the magnitude of the
**gravitational force** between two bodies is **directly proportional to the product of their masses and inversely proportional to the square of the distance between them**.
- The gravitational force will always be of attraction type.

\(⇒ F=G\frac{m_{1}m_{2}}{r^{2}}\)

Where G = 6.67×10^{-11} N-m2/kg2, m1 and m2 = masses and r = distance between the masses

Coulomb's law:

- According to this law, the magnitude of the
**electric force** between two point charges is **directly proportional to the product of the magnitude of the two charges and inversely proportional to the square of the distance between them**.
- It acts along the line joining the two charges.

\(⇒ F=k\frac{q_{1}q_{2}}{r^{2}}\)

Where k = 9×109 N-m2/C2, q1 and q2 = charges and r = distance between the charges

__CALCULATION:__

Given m = 9.1×10^{-31} kg and q = 1.6×10^{-19} C

- The gravitational force between two electrons,

\(\Rightarrow F_{1}=6.67\times10^{-11}\frac{(9.1\times10^{-31})^{2}}{r^{2}}\) -----(1)

- The electrostatic force between two electrons,

\(\Rightarrow F_{2}=9\times10^{9}\frac{(1.6\times10^{-19})^{2}}{r^{2}}\) -----(2)

by dividing equation 1 and equation 2,

\(\Rightarrow \frac{F_{1}}{F_{2}}=23.9\times10^{-44}=2.3\times10^{-43}\)

- Hence, option 3 is correct.