The correct option is **D. Both electrostatic and gravitational forces follow an inverse square law with respect to distance.** ### Detailed Explanation 1. **Understanding the Forces**: - **Electrostatic Forces**: These are the forces between charged particles. They can be either attractive (between opposite charges) or repulsive (between like charges). - **Gravitational Forces**: These are the forces of attraction between masses. They are always attractive, as gravity pulls objects toward each other. 2. **Inverse Square Law**: - Both electrostatic and gravitational forces follow the inverse square law, which states that the force between two point charges (or masses) is inversely proportional to the square of the distance between them. This can be mathematically expressed as: - **Electrostatic Force (Coulomb's Law)**: \[ F_e = k \frac{|q_1 q_2|}{r^2} \] where \( F_e \) is the electrostatic force, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges. - **Gravitational Force (Newton's Law of Gravitation)**: \[ F_g = G \frac{m_1 m_2}{r^2} \] where \( F_g \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between the centers of the two masses. 3. **Why Option D is Correct**: - Both forces decrease in strength as the distance increases, specifically following the inverse square relationship. This means that if you double the distance between the two charges or masses, the force becomes one-fourth as strong. ### Analysis of Other Options - **Option A**: "Electrostatic forces are always attractive, while gravitational forces can be both attractive and repulsive." - **Why it's wrong**: This statement is incorrect because while electrostatic forces can be both attractive and repulsive depending on the nature of the charges, gravitational forces are always attractive. Therefore, this option misrepresents the nature of gravitational forces. - **Option B**: "Gravitational forces are generally much stronger than electrostatic forces at the atomic scale." - **Why it's wrong**: This statement is misleading. At the atomic scale, electrostatic forces are significantly stronger than gravitational forces. For example, the electrostatic force between two electrons is about \( 10^{42} \) times stronger than the gravitational force between them. Thus, this option incorrectly compares the relative strengths of the two forces. - **Option C**: "Electrostatic forces operate over much larger distances than gravitational forces." - **Why it's wrong**: This statement is also incorrect. Both forces can act over large distances, but the strength of electrostatic forces diminishes rapidly with distance due to the inverse square law. Gravitational forces, while weaker, can also act over vast distances, such as between celestial bodies. However, electrostatic forces are generally more significant at smaller distances (like atomic scales) compared to gravitational forces. ### Summary for Revision - Both electrostatic and gravitational forces follow the inverse square law, meaning their strength decreases with the square of the distance. - Electrostatic forces can be attractive or repulsive, while gravitational forces are always attractive. - At the atomic scale, electrostatic forces are much stronger than gravitational forces. - Understanding the nature and behavior of these forces is crucial for solving problems in physics related to charge and mass interactions.