When the distance between two objects with masses m and m is increased to 4d, the gravitational force between them becomes one-sixteenth as great. The correct option is:- O the force will be one-sixteenth as great.
The gravitational force between two objects depends on their masses and the distance between them. To determine how the force changes when the distance between the objects is increased to 4d, we can use the formula for gravitational force:
1. Calculate the initial gravitational force:
- The initial distance between the objects is d, and the masses of the objects are both m.
- The initial gravitational force is given by the formula: F = (G × m × m) / d^2, where G is the gravitational constant.
- Let's assume the initial gravitational force is F_initial.
2. Calculate the new gravitational force:
- When the distance between the objects is increased to 4d, the new distance is 4 times the initial distance.
- The new gravitational force is given by the formula: F_new = (G × m × m) / (4d)^2 = (G × m × m) / 16d^2.
3. Simplify the expression:
- F_new = (G × m × m) / 16d^2 = (1/16) × (G × m × m) / d^2.
From the simplification, we can see that the new gravitational force (F_new) is 1/16 times the initial gravitational force (F_initial).
So, the correct answer is: The force will be one-sixteenth as great.