Final answer:
Object A with a mass of 10 grams exerts a greater gravitational force than Object B with a mass of 5 grams, although two asteroids with different masses will experience the same force but different accelerations due to the mass difference.
Step-by-step explanation:
If Object A has a mass of 10 grams and Object B has a mass of 5 grams, and we ignore all other factors like the distance between them and their positions, Object A would have a greater gravitational force. This is based on the universal law of gravitation formulated by Sir Isaac Newton, which states that the gravitational force is directly proportional to the product of the masses involved and inversely proportional to the square of the distance between their centers.
For two asteroids attracting each other gravitationally, if one asteroid has twice the mass of the other, they will experience the same gravitational force due to Newton's third law, which states that for every action, there is an equal and opposite reaction. However, the one with the lesser mass will experience greater acceleration because force also equals mass times acceleration (F=ma), so the same force on a smaller mass produces a larger acceleration.