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Ratio of gravitational force and electrostatic force between two electrons is:
1. 10-36
2. 10-39
3. 10-42
4. 10-47
5. None of these

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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.

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