An apple hangs on a tree on the Earth. Which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

Newton's third law: for every force (action) there is an equal and opposite force (reaction). The gravitational attraction between two masses comes in an equal-and-opposite pair.

1) Relevant concepts
- Newton's law of universal gravitation: F = G m1 m2 / r^2.
- Newton's third law: the force on mass 1 due to mass 2 equals in magnitude and opposite in direction the force on mass 2 due to mass 1.
- Weight near Earth's surface: F ≈ m_apple g (g ≈ 9.8 m/s^2).

2) Step-by-step reasoning
- The Earth and apple attract each other gravitationally. The force on the apple from Earth (its weight) has the same magnitude as the force on the Earth from the apple, by Newton’s third law.
- Numerically: take a representative apple mass m_apple = 0.10 kg. Its weight F = m_apple g = 0.10 kg × 9.8 m/s^2 = 0.98 N. That is the magnitude of both forces in the pair: Earth on apple = 0.98 N downward; apple on Earth = 0.98 N upward.
- Why Earth doesn’t noticeably move: acceleration of Earth due to this force is a_E = F / M_Earth ≈ 0.98 N / (5.97×10^24 kg) ≈ 1.6×10^−25 m/s^2 — essentially zero for practical purposes, but nonzero in principle.

3) Why the correct answer is correct
- Option d states the forces on the apple and Earth are equal. This follows directly from Newton’s third law: the gravitational forces are equal in magnitude and opposite in direction.

4) Why the other options are incorrect
- a and c claim unequal forces because one body is more massive; mass does not change the equality of action–reaction forces (it only changes resulting accelerations).
- b confuses the support (tree) force on the apple with the gravitational reaction on the Earth; the tree provides an upward normal force on the apple, but it does not change the magnitude of the gravitational force pair between apple and Earth.
- e is wrong because gravity is a non-contact force; the forces are not zero.

Conclusion: The forces on the apple and Earth are equal (choice d), which matches the provided answer.

An apple hangs on a tree on the Earth. Which of the following statements is correct?单项选择题

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