Suppose the gravitational force between two spheres is 30 N. If the magnitude of each mass doubles, what is the force between the masses?

Question

BlackTom AI · Accepted Answer

Newton's law of universal gravitation: F = G m1 m2 / r^2, so the gravitational force is proportional to the product of the two masses.

1) Relevant knowledge points and concepts
- Newton's gravitational formula: F ∝ m1 m2 (with G and r fixed).
- If one mass doubles, the product doubles; if both masses double, the product increases by a factor of 2 × 2 = 4.
- The separation r and G remain unchanged in this scenario.

2) Complete reasoning process step by step
- Let original masses be m1 and m2 and original force F0 = G m1 m2 / r^2.
- New masses after doubling: m1' = 2 m1 and m2' = 2 m2.
- New force F' = G m1' m2' / r^2 = G (2 m1)(2 m2) / r^2.

3) Calculations with intermediate steps
- F' = G (2 m1)(2 m2) / r^2 = G (4 m1 m2) / r^2 = 4 [G m1 m2 / r^2].
- Therefore F' = 4 F0.
- Given F0 = 30 N, F' = 4 × 30 N = 120 N.

4) Why the correct answer is correct
- Doubling each mass multiplies their product by 4, so the gravitational force (which depends on that product) becomes four times larger. With the original 30 N, four times that value is 120 N.

5) Why the other options are incorrect
- a. 8 N: would be a reduction, not consistent with increasing both masses.
- b. 15 N: equals half the original force — corresponds to halving one or both masses, not doubling.
- c. 30 N: unchanged — would be correct only if masses or separation did not change.
- d. 60 N: twice the original — corresponds to doubling one mass while leaving the other unchanged, not doubling both.
- e. 120 N: four times the original, matching the correct factor-of-4 increase.

6) Conclusion confirming the final answer
- The new gravitational force is 120 N, which matches the provided correct answer e. 120 N.

Suppose the gravitational force between two spheres is 30 N. If the magnitude of each mass doubles, what is the force between the masses?单项选择题

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