**Correct Option: A. 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 (denoted as \( g \)) at a distance \( r \) from a point mass \( M \) is defined by the formula: \[ g = \frac{GM}{r^2} \] where \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)). 2. **Inverse Square Law**: - The formula shows that gravitational field strength is inversely proportional to the square of the distance from the mass. This means that as you move away from the mass, the strength of the gravitational field decreases rapidly. - For example, if you double the distance from the mass (i.e., \( r \) becomes \( 2r \)), the gravitational field strength becomes: \[ g' = \frac{GM}{(2r)^2} = \frac{GM}{4r^2} = \frac{1}{4}g \] This illustrates that the gravitational field strength is reduced to a quarter of its original value when the distance is doubled. 3. **Why Option A is Correct**: - Option A accurately reflects the relationship described by the formula. As distance increases, the gravitational field strength decreases with the square of that distance, confirming the inverse square law. ### Analysis of Other Options: - **Option B: The gravitational field strength remains constant regardless of distance from the mass.** - This statement is incorrect because it contradicts the inverse square law. If the gravitational field strength were constant, it would imply that the force of gravity does not change with distance, which is not true. The gravitational force diminishes as you move away from the mass. - **Option C: The gravitational field is strongest at a distance equal to the mass's radius.** - This statement is misleading. While it may be true that the gravitational field strength is significant at the surface of a mass (like a planet), it does not mean that it is the strongest at that distance. The strength of the gravitational field continues to decrease as you move away from the mass, and it is not necessarily strongest at the radius of the mass. - **Option D: The gravitational field strength increases linearly with distance from the mass.** - This option is incorrect because it suggests a direct proportionality between gravitational field strength and distance, which is the opposite of what the inverse square law states. As distance increases, the gravitational field strength decreases, not increases. ### Common Pitfalls: - Students often confuse the concepts of gravitational force and gravitational field strength. Remember that gravitational field strength is a measure of the force per unit mass experienced by an object in the field. - It’s important to visualize how gravitational fields behave. Drawing diagrams can help illustrate how the strength of the field diminishes with distance. ### Revision Summary: - The gravitational field strength decreases with the square of the distance from a point mass (Option A). - The formula for gravitational field strength is \( g = \frac{GM}{r^2} \). - The inverse square law is fundamental in understanding gravitational interactions. - Always differentiate between gravitational field strength and gravitational force; they are related but distinct concepts.