An apple falls from a tree because of gravitational between the earth and apple. If `F_(1)` is the magnitude of force exerted by the earth on the apple and `F_(2)` is the magnitude of force exerted by apple on earth, then

Options

A. `F_(1)` is very much greater than `F_(2)`
B. `F_(2)` is very much greater than `F_(1)`
C. `F_(1)` is only a little greater than `F_(2)`
D. `F_(1)` and `F_(2)` are equal

Explanation

To solve the problem, we will analyze the forces acting between the Earth and the apple based on Newton's law of gravitation.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- When an apple falls from a tree, it experiences a gravitational force due to the Earth. This force can be denoted as \( F_1 \), which is the force exerted by the Earth on the apple.
- Simultaneously, the apple also exerts a gravitational force on the Earth, which we denote as \( F_2 \).

2. **Applying Newton's Third Law of Motion**:
- According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that the force exerted by the Earth on the apple (\( F_1 \)) is equal in magnitude and opposite in direction to the force exerted by the apple on the Earth (\( F_2 \)).
- Mathematically, this can be expressed as:
\[ F_1 = F_2 \]

3. **Conclusion**:
- Since both forces are equal in magnitude, we conclude that:
\[ F_1 \text{ (force by Earth on apple)} = F_2 \text{ (force by apple on Earth)} \]
- Therefore, the correct answer to the question is that \( F_1 \) and \( F_2 \) are equal.

### Final Answer:
- \( F_1 \) and \( F_2 \) are equal.