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The problem in the image is asking for the force exerted by block A on block B, given that blocks A and B are accelerated along a smooth horizontal surface by a force \( F \) applied to block A. The masses of blocks A and B are \( m \) and \( 4m \), respectively.

### Solution Breakdown:

1. **Total Mass of the System**: 
   The total mass of the system (both blocks) is:
   \[
   m_{\text{total}} = m + 4m = 5m
   \]

2. **Acceleration of the System**: 
   Since the force \( F \) is applied to both blocks together, the acceleration \( a \) of the system can be calculated using Newton’s second law:
   \[
   F = m_{\text{total}} \cdot a \quad \Rightarrow \quad a = \frac{F}{5m}
   \]

3. **Force Exerted by A on B**:
   To find the force that block A exerts on block B, we focus on block B. The only force acting on block B in the horizontal direction is the force from block A, which we will call \( F_{\text{A on B}} \). Using Newton's second law for block B:
   \[
   F_{\text{A on B}} = m_B \cdot a = 4m \cdot \frac{F}{5m} = \frac{4F}{5}
   \]

Thus, the magnitude of the force exerted on block B by block A is \( \frac{4F}{5} \), which corresponds to option C in the provided answers.

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Do you have any further questions, or would you like additional details? Here are 5 related questions that build on this concept:

1. What would be the force on block A due to block B?
2. How would the forces change if the masses of A and B were equal?
3. What is the net force acting on block A alone?
4. How would the situation change if the surface was not smooth (friction included)?
5. What if the applied force \( F \) was instead applied to block B?

**Tip**: In problems involving multiple objects, always analyze the entire system's motion first, then isolate each object to find internal forces!

Diagram 3 shows block A and B, with masses m and 4m respectively, are accelerated along a smooth horizontal surface by a force F applied to block A. What is the magnitude of the force exerted on block B by block A during this acceleration?

Learn how to calculate the force exerted by block A on block B, where block A (mass m) and block B (mass 4m) are accelerated by a force F along a smooth surface. This solution involves applying Newton's second law and dynamics principles, suitable for students in Grades 11-12.

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