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.

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!