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The problem shown in the image is about a system involving a small mass \( m \) sliding on a smooth circular path of radius \( R \) fixed to a larger block of mass \( M \). The question involves several parts, including finding the shift of the block \( M \) and the velocity of the block and the normal force acting on the mass \( m \) as it slides.

### Problem Breakdown:
1. **System Dynamics:**
   - Mass \( m \) is released from rest at the top of the circular path.
   - The larger block \( M \) is free to move horizontally on a smooth surface.
   - As mass \( m \) slides down the circular track, conservation of momentum and energy principles will likely be used to find the answers.

### Concepts Involved:
- **Conservation of Linear Momentum**: Since there are no external horizontal forces, the horizontal momentum of the system is conserved.
- **Conservation of Mechanical Energy**: As the small mass slides, its potential energy is converted into kinetic energy, which includes both the motion of \( m \) and the motion of the larger block \( M \).
  
### Part 1: Find the shift of \( M \) when \( m \) reaches positions 1 and 2.
- The system starts with no initial velocity.
- When \( m \) reaches position 1 or 2, its motion along the circular path has affected the horizontal displacement of \( M \). We would use the conservation of momentum and energy to derive the relationship between \( m \) and \( M \).

### Part 2: Find the velocity of \( M \) when \( m \) reaches point 1.
- Here, the kinetic energy of \( m \) and \( M \) is derived from the potential energy of \( m \) at the top of the curve. Using energy conservation, we can calculate the velocity.

### Part 3: Find the normal force \( N \) on the ball when at point 1.
- The normal force is a combination of gravitational force and the centripetal force acting on the mass \( m \), which depends on its velocity at that point.

Would you like me to go ahead with the detailed solution for each part of the problem? Additionally, here are some questions to expand on the concepts:

### Related Questions:
1. What is the principle of conservation of momentum, and how does it apply to this system?
2. How does the energy conservation law help in calculating the velocities of the objects in this system?
3. What is the relationship between kinetic energy and potential energy in systems involving gravity?
4. How does the normal force change as the ball moves along the circular path?
5. Can this type of system be solved using Lagrangian mechanics?

### Tip:
Always check for smooth surfaces and frictionless assumptions when applying energy conservation, as these significantly simplify the equations.

Find the shift of M when m reaches positions 1 and 2. Additionally, find the velocity of M when m reaches point 1, and the normal force on m at point 1.

Solve the problem involving a small mass sliding along a smooth circular path attached to a block of mass M. Learn how to apply the conservation of momentum and energy to find the shift of M, the velocity of the block, and the normal force on the small mass. This advanced physics problem covers core concepts in classical mechanics.

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