Answer :
Let's compare the constants used to calculate the electrical and gravitational forces to determine their relative magnitudes and understand which force is larger.
### Step-by-Step Comparison:
1. Identify the constants:
- The constant for the electrical force is \( 8.99 \times 10^9 \).
- The constant for the gravitational force is \( 6.67 \times 10^{-11} \).
2. Compare the numerical values before the exponent:
- The numerical part for the electrical force is 8.99.
- The numerical part for the gravitational force is 6.67.
- 8.99 is greater than 6.67, but this comparison doesn't complete the picture because we also need to take into account the exponents in the constants.
3. Compare the order of magnitudes (exponents):
- The exponent for the electrical force is \( 10^9 \), which is a very large number.
- The exponent for the gravitational force is \( 10^{-11} \), which is a very small number.
- \( 10^9 \) is vastly greater than \( 10^{-11} \).
4. Analyze the impact on the forces:
- Since \( 10^9 \) is much greater than \( 10^{-11} \), the electrical force constant (which is \( 8.99 \times 10^9 \)) is much larger than the gravitational force constant (which is \( 6.67 \times 10^{-11} \)).
- This significant difference in the order of magnitude between the constants means that the electrical force is much larger than the gravitational force.
Therefore, the correct explanation is:
The electrical force is much larger than the gravitational force because [tex]\(10^9\)[/tex] is much greater than [tex]\(10^{-11}\)[/tex].
### Step-by-Step Comparison:
1. Identify the constants:
- The constant for the electrical force is \( 8.99 \times 10^9 \).
- The constant for the gravitational force is \( 6.67 \times 10^{-11} \).
2. Compare the numerical values before the exponent:
- The numerical part for the electrical force is 8.99.
- The numerical part for the gravitational force is 6.67.
- 8.99 is greater than 6.67, but this comparison doesn't complete the picture because we also need to take into account the exponents in the constants.
3. Compare the order of magnitudes (exponents):
- The exponent for the electrical force is \( 10^9 \), which is a very large number.
- The exponent for the gravitational force is \( 10^{-11} \), which is a very small number.
- \( 10^9 \) is vastly greater than \( 10^{-11} \).
4. Analyze the impact on the forces:
- Since \( 10^9 \) is much greater than \( 10^{-11} \), the electrical force constant (which is \( 8.99 \times 10^9 \)) is much larger than the gravitational force constant (which is \( 6.67 \times 10^{-11} \)).
- This significant difference in the order of magnitude between the constants means that the electrical force is much larger than the gravitational force.
Therefore, the correct explanation is:
The electrical force is much larger than the gravitational force because [tex]\(10^9\)[/tex] is much greater than [tex]\(10^{-11}\)[/tex].
