The correct option is **D. Both forces obey the inverse square law, but electrostatic forces are significantly stronger than gravitational forces.** ### Detailed Explanation: 1. **Understanding the Forces**: - **Gravitational Force**: This is the force of attraction between two masses. It is always attractive and is described by Newton's law of universal gravitation, which states that the force \( F_g \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by: \[ F_g = G \frac{m_1 m_2}{r^2} \] where \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)). - **Electrostatic Force**: This is the force between two charged objects. It can be either attractive or repulsive, depending on the nature of the charges (like charges repel, unlike charges attract). The electrostatic force \( F_e \) is described by Coulomb's law: \[ F_e = k \frac{|q_1 q_2|}{r^2} \] where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), and \( q_1 \) and \( q_2 \) are the magnitudes of the charges. 2. **Inverse Square Law**: - Both gravitational and electrostatic forces follow the inverse square law, which means that the force decreases with the square of the distance between the two objects. This is evident in both formulas, where the force is inversely proportional to \( r^2 \). 3. **Strength Comparison**: - The strength of electrostatic forces is significantly greater than that of gravitational forces. For example, the electrostatic force between two protons is about \( 10^{36} \) times stronger than the gravitational force between them. This immense difference in strength is crucial in understanding why electrostatic forces dominate at the atomic and molecular levels, while gravitational forces are more significant on a cosmic scale. ### Why Other Options Are Incorrect: - **Option A**: "Electrostatic forces are always attractive, while gravitational forces can be both attractive and repulsive." - This statement is incorrect because while gravitational forces are indeed always attractive, electrostatic forces can be both attractive and repulsive depending on the charges involved. Therefore, this option misrepresents the nature of electrostatic forces. - **Option B**: "Gravitational forces depend on mass, while electrostatic forces depend on charge." - While this statement is true, it does not capture the relationship between the two forces in the context of the question. The question specifically asks about the relationship between the two forces, and this option does not address their comparative strengths or the inverse square law. - **Option C**: "Electrostatic forces are much weaker than gravitational forces at all distances." - This statement is false. As previously mentioned, electrostatic forces are much stronger than gravitational forces, especially at small distances (like those found in atomic interactions). This option contradicts the fundamental understanding of these forces. ### Summary for Revision: - Both gravitational and electrostatic forces obey the inverse square law, meaning their strength decreases with the square of the distance between the objects. - Gravitational forces are always attractive, while electrostatic forces can be either attractive or repulsive. - Electrostatic forces are significantly stronger than gravitational forces, especially at small distances. - Understanding the nature and strength of these forces is crucial for applications in physics, from atomic interactions to celestial mechanics.