According to Newton's Third Law, an apple attracts the Earth with the same force that the Earth attracts the apple. The Earth does not appear to move…

Correct Option

The correct option is

The acceleration produced in the Earth is negligible due to its massive size.

Explanation

The interaction between the Earth and an apple is governed by Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. Consequently, the gravitational force exerted by the Earth on the apple is equal in magnitude to the force exerted by the apple on the Earth. The resulting motion is determined by Newton's Second Law of Motion ($F = ma$).

Detailed Analysis

• The force exerted by the apple is negligible compared to the Earth's force. is Incorrect: According to Newton's Third Law, the forces constitute an action-reaction pair. Therefore, the magnitude of the force exerted by the apple on the Earth is exactly equal to the force exerted by the Earth on the apple. It is not negligible.
• The acceleration produced in the Earth is negligible due to its massive size. is Correct: According to Newton's Second Law, acceleration is inversely proportional to mass for a given force ($a = \frac{F}{m}$).
  • The mass of the Earth is approximately $6 \times 10^{24}$ kg, which is astronomically larger than the mass of an apple.
  • Since the force $F$ is the same for both bodies, the acceleration produced in the Earth ($a_{Earth} = \frac{F}{M_{Earth}}$) is infinitesimally small and practically undetectable.
  • In contrast, the apple has a very small mass, resulting in a noticeable acceleration ($g \approx 9.8 \text{ m/s}^2$).
• The gravitational force is balanced by the atmosphere. is Incorrect: The atmosphere exerts pressure, but it does not balance the gravitational force between the Earth and the apple in a way that prevents the Earth's motion. The lack of perceptible motion is due to the Earth's immense inertia (mass).
• The Earth is an inertial frame of reference. is Incorrect: While the Earth is often approximated as an inertial frame of reference for terrestrial mechanics, this classification does not explain the dynamic response (acceleration) of the Earth to the gravitational force.

Key Takeaway: While action and reaction forces are always equal in magnitude, the accelerations they produce differ significantly if the masses of the interacting bodies are different ($a \propto \frac{1}{m}$).