Final answer:
The greatest gravitational force between two objects, according to Newton's Law of Universal Gravitation, will occur in Scenario C, where the combined mass is the largest (15 kg and 12 kg) and the distance between them is the smallest (0.5 m).
Step-by-step explanation:
To determine which scenario objects will have the greatest gravitational force between them, we must consider Newton's Law of Universal Gravitation. According to this law, the gravitational force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. The formula for gravitational force is given by:
Fgravity = G × (M1 × M2) / R2
Where Fgravity is the gravitational force, G is the gravitational constant, M1 and M2 are the masses of the objects, and R is the distance between the centers of the two objects.
Comparing the given scenarios, we find that:
- Scenario A has equal masses but a larger distance.
- Scenario B has larger combined mass but the same distance as A.
- Scenario C has the same combined mass as B but at a smaller distance.
- Scenario D has equal masses as A but at a smaller distance.
The inverse square law of gravitation tells us that when the distance is decreased by half (comparing 1.5 m to 0.5 m), the gravitational force increases by a factor of four (since (1.52) / (0.52) = 9/1 = 9). While doubling mass would double the force, reducing distance has a more significant effect. Therefore, the gravitational force will be greatest in Scenario C, where both masses are at their highest within the smallest distance.