### Correct Option: A. g = GM/r² #### Detailed Explanation: 1. **Understanding Gravitational Field Strength**: - Gravitational field strength (g) is defined as the force per unit mass experienced by a small test mass placed in the field of a larger mass. It indicates how strong the gravitational pull is at a certain distance from a mass. 2. **Newton's Law of Universal Gravitation**: - According to Newton's law, the gravitational force (F) between two masses (M and m) separated by a distance (r) is given by the formula: \[ F = \frac{GMm}{r^2} \] - Here, G is the gravitational constant, M is the mass creating the gravitational field, m is the test mass, and r is the distance between the centers of the two masses. 3. **Deriving Gravitational Field Strength**: - To find the gravitational field strength (g), we need to express the force per unit mass. The gravitational force acting on the test mass (m) can be expressed as: \[ F = mg \] - Setting the two expressions for force equal gives: \[ mg = \frac{GMm}{r^2} \] - We can cancel the test mass (m) from both sides (assuming m ≠ 0): \[ g = \frac{GM}{r^2} \] - This shows that the gravitational field strength (g) at a distance (r) from a point mass (M) is indeed given by the formula: \[ g = \frac{GM}{r^2} \] 4. **Why Other Options Are Incorrect**: - **Option B: g = M/r²**: - This option is incorrect because it omits the gravitational constant (G). The gravitational field strength depends on both the mass creating the field and the gravitational constant, which is essential for the correct calculation of gravitational forces. - **Option C: g = G/r²**: - This option is also incorrect as it suggests that gravitational field strength is directly proportional to G and inversely proportional to the square of the distance without considering the mass (M) that creates the gravitational field. The mass is a crucial factor in determining the strength of the gravitational field. - **Option D: g = 2GM/r³**: - This option is incorrect because it introduces an unnecessary factor of 2 and changes the exponent of r. The correct relationship is derived from Newton's law and does not include such modifications. The exponent should be -2, not -3, as per the inverse square law of gravitation. #### Summary of Key Points: - Gravitational field strength (g) is the force per unit mass due to gravity. - It is mathematically represented as \( g = \frac{GM}{r^2} \). - The formula derives from Newton's law of universal gravitation. - The other options fail to include necessary constants or misrepresent the relationship between mass, distance, and gravitational strength. ### Revision Summary: - Gravitational field strength (g) is defined as \( g = \frac{GM}{r^2} \). - It describes the gravitational force experienced by a unit mass at a distance r from mass M. - The gravitational constant (G) is essential in the formula. - Understanding the derivation from Newton's law helps clarify why other options are incorrect.