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

Answer

To solve the problem, we need to analyze the forces acting on the two bodies, A and B, and apply Newton's laws of motion. Let's break it down step by step.

### Step 1: Understand the scenario
We have two bodies:
- Body A with mass \( m_1 \)
- Body B with mass \( m_2 \)

Body A exerts a force on Body B, causing Body B to accelerate with an acceleration \( a_2 \).

### Step 2: Apply Newton's Third Law
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 Body A on Body B is equal in magnitude and opposite in direction to the force exerted by Body B on Body A.

### Step 3: Write the equations for forces
The force exerted by Body A on Body B can be expressed using Newton's second law:
\[ F_{AB} = m_2 \cdot a_2 \]
where \( F_{AB} \) is the force exerted by A on B.

By Newton's Third Law, the force exerted by Body B on Body A is:
\[ F_{BA} = m_1 \cdot a_1 \]
where \( a_1 \) is the acceleration of Body A.

### Step 4: Set the forces equal
Since \( F_{AB} = F_{BA} \), we can set the two expressions equal:
\[ m_2 \cdot a_2 = m_1 \cdot a_1 \]

### Step 5: Solve for the acceleration of Body A
To find the acceleration of Body A (\( a_1 \)), we can rearrange the equation:
\[ a_1 = \frac{m_2 \cdot a_2}{m_1} \]

### Conclusion
Thus, the magnitude of the acceleration of Body A is given by:
\[ a_1 = \frac{m_2 \cdot a_2}{m_1} \]

### Final Answer
The acceleration of Body A in magnitude is \( \frac{m_2 \cdot a_2}{m_1} \).

---