The correct option is **C. The gravitational field strength decreases with the square of the distance from the mass.** ### Detailed Explanation: 1. **Understanding Gravitational Field Strength**: - The gravitational field strength (often denoted as \( g \)) at a distance \( r \) from a point mass \( M \) is defined as the force \( F \) experienced by a unit mass \( m \) placed at that distance. Mathematically, it is expressed as: \[ g = \frac{F}{m} \] - According to Newton's law of universal gravitation, the force \( F \) between two masses \( M \) (the point mass) and \( m \) (the test mass) is given by: \[ F = \frac{G \cdot M \cdot m}{r^2} \] where \( G \) is the gravitational constant. 2. **Deriving Gravitational Field Strength**: - Substituting the expression for \( F \) into the equation for \( g \): \[ g = \frac{F}{m} = \frac{G \cdot M \cdot m}{r^2 \cdot m} = \frac{G \cdot M}{r^2} \] - This shows that the gravitational field strength \( g \) is inversely proportional to the square of the distance \( r \) from the mass \( M \). Therefore, as you move further away from the mass, the gravitational field strength decreases with the square of the distance. 3. **Why Option C is Correct**: - Option C accurately reflects the derived relationship: as the distance \( r \) increases, \( g \) decreases according to the formula \( g = \frac{G \cdot M}{r^2} \). This means that if you double the distance from the mass, the gravitational field strength becomes one-fourth of its original value. ### Analysis of Other Options: - **Option A: The gravitational field strength decreases linearly with distance.** - This statement is incorrect because the relationship between gravitational field strength and distance is not linear. A linear decrease would imply that if you double the distance, the gravitational field strength would halve, which is not the case. Instead, it decreases with the square of the distance. - **Option B: The gravitational field is constant regardless of distance from the mass.** - This option is also incorrect. The gravitational field strength is not constant; it varies with distance. As derived, it decreases as you move away from the mass, which contradicts the idea of a constant field. - **Option D: The gravitational field strength increases with distance from the mass.** - This statement is fundamentally wrong. The gravitational field strength does not increase with distance; it decreases. An increase in distance leads to a weaker gravitational pull, not a stronger one. ### Common Pitfalls: - Students often confuse the concepts of gravitational force and gravitational field strength. Remember that gravitational field strength is the force per unit mass, while gravitational force is the interaction between two masses. - It’s important to visualize the concept: imagine a point mass like a planet. As you move away from it, the gravitational pull you feel becomes weaker, which is a direct consequence of the \( \frac{1}{r^2} \) relationship. ### Revision Summary: - The gravitational field strength \( g \) decreases with the square of the distance from a point mass, as given by \( g = \frac{G \cdot M}{r^2} \). - Option C is correct; the other options misrepresent the relationship between gravitational field strength and distance. - Remember that gravitational field strength is not constant and does not decrease linearly with distance. - Visualize the concept to better understand how gravitational forces work in relation to distance.