A body A mass `m_(1)` exerts a force on another body B of mass `m_(2)` . If the acceleration of B be `a_(2)` , then the acceleration (in magnitude) of A is

Options

A. `(m_(2))/(m_(1))a_(2)`
B. `m_(1)m_(2)a_(2)`
C. `(m_(1))/(m_(2))a_(2)`
D. `(m_(1)+m_(2))a_(2)`

Explanation

To solve the problem, we will apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Let's break down the steps to find the acceleration of body A when body B is accelerating.

### Step-by-step Solution:

1. **Identify the Forces**:
- Body A (mass \( m_1 \)) exerts a force on body B (mass \( m_2 \)).
- According to Newton's third law, body B exerts an equal and opposite force on body A.

2. **Write the Force Equation for Body B**:
- The force exerted by body A on body B can be expressed using Newton's second law:
\[ F_{AB} = m_2 \cdot a_2 \]
- Here, \( F_{AB} \) is the force exerted by A on B, \( m_2 \) is the mass of body B, and \( a_2 \) is the acceleration of body B.

3. **Write the Force Equation for Body A**:
- The force exerted by body B on body A is equal in magnitude and opposite in direction to the force exerted by A on B:
\[ F_{BA} = m_1 \cdot a_1 \]
- Here, \( F_{BA} \) is the force exerted by B on A, \( m_1 \) is the mass of body A, and \( a_1 \) is the acceleration of body A.

4. **Set the Forces Equal**:
- According to Newton's third law:
\[ F_{AB} = F_{BA} \]
- Therefore, we can equate the two expressions:
\[ m_2 \cdot a_2 = m_1 \cdot a_1 \]

5. **Solve for the Acceleration of Body A**:
- Rearranging the equation to find \( a_1 \):
\[ a_1 = \frac{m_2 \cdot a_2}{m_1} \]

### Final Answer:
The magnitude of the acceleration of body A is given by:
\[ a_1 = \frac{m_2 \cdot a_2}{m_1} \]