https://file.aiquickdraw.com/mathbot/file/1729479019264jw2ybw0x.jpg

The problem in the image describes a system involving three blocks, \(A\), \(B\), and \(C\), of masses \(m_A\), \(m_B\), and \(m_C\), respectively. Here's the key information extracted:

- Blocks \(A\) and \(B\) are on a horizontal surface with negligible friction.
- Block \(A\) is attached to the table.
- Block \(C\), of mass \(m_C\), is suspended by a string that passes over a pulley and is connected to Block \(B\).
- The entire system is at rest.

The question asks: **Which of the following gives the magnitude of the force exerted by Block A on Block B?**

### Solution Approach:

1. **Force Analysis for Block B**: Block \(B\) is being pulled horizontally by the tension in the string, which is also connected to Block \(C\). Since the system is in equilibrium (at rest), the tension force \(T\) in the string will be equal to the weight of Block \(C\):
   \[
   T = m_C g
   \]
   where \(g\) is the acceleration due to gravity.

2. **Force exerted by Block A on Block B**: Since Block \(A\) is attached to the table, it must exert a reaction force to keep Block \(B\) stationary. This force is equal to the tension \(T\), which is the same as \(m_C g\).

### Final Answer:
The force exerted by Block \(A\) on Block \(B\) is the tension in the string, which is:
\[
\boxed{m_C g}
\]

Let me know if you'd like to explore the problem further or have any questions!

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Here are 5 related questions to deepen your understanding:
1. How would the force change if the surface had friction?
2. What happens if the mass of Block C increases?
3. How would the system behave if Block B were lighter than Block C?
4. What role does the pulley play in this system?
5. Can you calculate the tension if the blocks were accelerating?

**Tip**: In a static system like this, always start by analyzing the forces in equilibrium!

Blocks A and B, of masses mA and mB, respectively, are at rest on a horizontal surface with negligible friction. Block A is attached to the table. Block C, of mass mC, is suspended by a string that is tied to Block B and passes over a pulley as shown. The blocks all remain at rest. Which of the following gives the magnitude of the force exerted by Block A on Block B?

Understand how to analyze the forces in a system of blocks and pulley in equilibrium. This problem covers Newton's laws of motion, tension calculations, and forces at rest. Suitable for students in Grades 10-12.

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