Question

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

• A. The force on the apple is greater than the force on the Earth because the Earth is more massive.
• B. The force on the apple is less than the force on the Earth because the tree is supporting the apple.
• C. The forces on the apple and Earth are equal.
• D. The force on the Earth is greater than the force on the apple because the Earth is more massive.

Answer 1

Answer: (C)

The forces on the apple and Earth are equal.

Answer 2

Core Concept: Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

Application: When the Earth exerts a gravitational force on the apple (pulling it downwards), the apple simultaneously exerts an equal and opposite gravitational force on the Earth (pulling the Earth upwards).

Magnitude of Forces: According to Newton's Law of Universal Gravitation, the force between two objects with masses $m_1$ and $m_2$ separated by a distance $r$ is given by:

$F = G \frac{m_1 m_2}{r^2}$

Here, $m_1$ is the mass of the apple and $m_2$ is the mass of the Earth. The formula shows that the force is symmetric; the force exerted by the Earth on the apple is exactly the same in magnitude as the force exerted by the apple on the Earth.

Effect of Mass: While the Earth is vastly more massive than the apple, which means the apple experiences a much greater acceleration ($a = F/m$) than the Earth due to this force, the magnitude of the force itself is equal for both.