Two bodies of masses `m_(1) and m_(2)` are separated by certain distance. If `vecF_(12)` is the force on `m_(1)` due to `m_(2)` and `vecF_(21)` is the force on `m_(2)` due to `m_(1)`, then

Options

A. `F_(12)=F_(21)`
B. `vecF_(12)=vecF_(21)`
C. `vecF_(12)=-vecF_(21)`
D. none

Answer

To solve the question regarding the forces acting between two bodies of masses \( m_1 \) and \( m_2 \), we will analyze the gravitational forces acting on each mass due to the other.

### Step-by-Step Solution:

**Step 1: Understand the Gravitational Force Formula**
The gravitational force between two masses is given by Newton's law of gravitation:
\[ F = \frac{G m_1 m_2}{r^2} \]
where \( F \) is the magnitude of the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between the centers of the two masses.

**Step 2: Identify the Forces Acting on Each Mass**
- The force on mass \( m_1 \) due to mass \( m_2 \) is denoted as \( \vec{F}_{12} \).
- The force on mass \( m_2 \) due to mass \( m_1 \) is denoted as \( \vec{F}_{21} \).

**Step 3: Magnitudes of the Forces**
According to Newton's law of gravitation, the magnitudes of the forces are equal:
\[ |\vec{F}_{12}| = |\vec{F}_{21}| = \frac{G m_1 m_2}{r^2} \]

**Step 4: Direction of the Forces**
- The direction of \( \vec{F}_{12} \) is attractive, pointing towards \( m_2 \).
- The direction of \( \vec{F}_{21} \) is also attractive, pointing towards \( m_1 \).
- Therefore, the forces are equal in magnitude but opposite in direction.

**Step 5: Relationship Between the Forces**
This can be expressed mathematically as:
\[ \vec{F}_{21} = -\vec{F}_{12} \]
This indicates that the force on \( m_2 \) due to \( m_1 \) is equal in magnitude but opposite in direction to the force on \( m_1 \) due to \( m_2 \).

### Conclusion:
Thus, we conclude:
- The magnitudes of the forces \( \vec{F}_{12} \) and \( \vec{F}_{21} \) are equal.
- The directions of the forces are opposite.