Two bodies of masses 'm' and 2m are separated by a distance d'. The body of mass 'm' attracts another body of mass 2m with a force F, then the body of mass 2m attracts m with the force of______________

Options

A. F
B. 2F
C. ` (F)/(2)`
D. 3F

Answer

To solve the problem, we need to understand the concept of gravitational force between two masses. The gravitational force between two bodies is given by Newton's law of gravitation, which states:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two bodies,
- \( r \) is the distance between the centers of the two masses.

### Step-by-Step Solution:

1. **Identify the Masses and Distance**:
- We have two bodies: one with mass \( m \) and the other with mass \( 2m \).
- The distance between them is \( d \).

2. **Calculate the Force \( F \)**:
- According to the problem, the body of mass \( m \) attracts the body of mass \( 2m \) with a force \( F \).
- Using the formula for gravitational force, we can express this as:
\[ F = \frac{G \cdot m \cdot (2m)}{d^2} \]

3. **Calculate the Force on Mass \( m \) by Mass \( 2m \)**:
- Now, we need to find the force that the body of mass \( 2m \) exerts on the body of mass \( m \).
- Using the same formula for gravitational force, we have:
\[ F' = \frac{G \cdot (2m) \cdot m}{d^2} \]

4. **Compare the Two Forces**:
- Notice that:
\[ F' = \frac{G \cdot (2m) \cdot m}{d^2} = 2 \cdot \frac{G \cdot m \cdot (2m)}{d^2} = F \]
- Therefore, the force \( F' \) is equal to \( F \).

5. **Conclusion**:
- The body of mass \( 2m \) attracts the body of mass \( m \) with the same force \( F \).

### Final Answer:
The body of mass \( 2m \) attracts mass \( m \) with the force of **F**.