**Correct Option: A** ### Detailed Explanation To understand why option A is the correct answer, we need to delve into the concept of gravitational fields and how they behave around point masses. 1. **Definition of Gravitational Field**: A gravitational field is a region of space around a mass where another mass experiences a force due to gravity. The strength of this field is determined by the mass creating it and the distance from that mass. 2. **Gravitational Field Strength Formula**: The gravitational field strength (often denoted as \( g \)) at a distance \( r \) from a point mass \( M \) is given by the formula: \[ g = \frac{GM}{r^2} \] where: - \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)), - \( M \) is the mass creating the gravitational field, - \( r \) is the distance from the center of the mass to the point where the field strength is being measured. 3. **Analysis of Option A**: - **Directly Proportional to Mass**: The formula shows that the gravitational field strength \( g \) increases as the mass \( M \) increases. This means that if you have a larger mass, the gravitational field strength at a given distance will be stronger. - **Inversely Proportional to the Square of the Distance**: The \( r^2 \) in the denominator indicates that as you move further away from the mass (increasing \( r \)), the gravitational field strength decreases rapidly. Specifically, if you double the distance from the mass, the gravitational field strength becomes one-fourth of its original value. ### Why Other Options Are Incorrect **Option B**: "The gravitational field strength is constant regardless of distance from the mass." - This statement is incorrect because it contradicts the inverse square law described by the formula. As you move away from the mass, the gravitational field strength decreases, so it cannot be constant. **Option C**: "The gravitational field strength decreases linearly with distance from the mass." - This option is also incorrect. The gravitational field strength does not decrease linearly; it decreases with the square of the distance. For example, if you move from 1 meter to 2 meters away from a mass, the field strength does not halve; it actually becomes one-fourth of what it was at 1 meter. **Option D**: "The gravitational field strength only exists at the surface of the mass and not in the surrounding space." - This statement is false. The gravitational field exists in the space surrounding the mass, not just at its surface. In fact, the field strength can be measured at any point in space around the mass, and it is strongest at the surface and decreases with distance. ### Common Pitfalls - **Confusing Linear and Inverse Square Relationships**: Students often confuse linear relationships with inverse square relationships. Remember that gravitational force and field strength decrease with the square of the distance, not linearly. - **Ignoring the Concept of Field**: Some may think gravitational effects only occur at the mass itself. It's crucial to understand that gravitational fields extend into space around the mass. ### Revision Summary - The gravitational field strength \( g \) is given by \( g = \frac{GM}{r^2} \). - It is directly proportional to the mass \( M \) and inversely proportional to the square of the distance \( r \). - Gravitational field strength decreases rapidly as distance increases, not linearly. - Gravitational fields exist in the space surrounding a mass, not just at its surface.