A very massive object A and a less massive object B move toward each other under the influence of mutual gravitation. Which force, if either, is greater?

Question

BlackTom AI · Accepted Answer

Newton’s law of universal gravitation gives the magnitude of the force between two masses: F = G m_A m_B / r^2. Newton’s third law states that forces between two interacting bodies are equal in magnitude and opposite in direction. These two principles are the relevant knowledge points.

1) Relevant concepts
- Law of gravitation: F = G m_A m_B / r^2 (G is the gravitational constant, r the separation).
- Newton’s third law: for every action there is an equal and opposite reaction; the force on A by B equals in magnitude the force on B by A.

2) Step-by-step reasoning
- Compute the gravitational force magnitude using the formula above. The formula is symmetric in m_A and m_B, so it yields the same scalar value whether you view it as the force on A due to B or on B due to A.
- Apply Newton’s third law: the two forces form an action–reaction pair and must have equal magnitudes and opposite directions.

3) Example calculation (intermediate steps shown)
- Choose m_A = 100 kg, m_B = 10 kg, r = 1 m, G = 6.67×10^−11 N·m^2/kg^2.
- F = G m_A m_B / r^2 = (6.67×10^−11)(100)(10) / 1^2 = 6.67×10^−8 N.
- This 6.67×10^−8 N is the magnitude of the force on A due to B and also the magnitude of the force on B due to A.
- Note accelerations differ: a_A = F/m_A = 6.67×10^−8 /100 = 6.67×10^−10 m/s^2, a_B = F/m_B = 6.67×10^−8 /10 = 6.67×10^−9 m/s^2. Different accelerations do not imply unequal forces.

4) Why the correct answer is correct
- The gravitational force formula is symmetric and Newton’s third law enforces equal-and-opposite forces. Therefore neither object feels a greater gravitational force; the magnitudes are identical.

5) Why the other options are incorrect
- (a) “The force on B” greater: incorrect because symmetry and Newton’s third law prohibit unequal magnitudes.
- (b) “The force on A” greater: incorrect for the same reason.
- Different masses only change accelerations, not the magnitudes of the mutual forces.

6) Conclusion
- Both forces are the same in magnitude. This confirms the correct answer: c. Both forces are the same.

A very massive object A and a less massive object B move toward each other under the influence of mutual gravitation. Which force, if either, is greater?单项选择题

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