A man pulls a block of mass equal to himself with a light string .The coefficient of friction between the man and the floor is greater than that between the block and the floor

Options

A. if the block does not move , then the man also does not move
B. the block can move even when the man is stationary
C. if both move then the acceleration of the block is greater than the acceleration of man
D. if both move then the acceleration of man is greater than the acceleration of block

Explanation

To solve the problem, we need to analyze the forces acting on both the man and the block, taking into account the coefficients of friction and the relationship between their masses.

### Step-by-Step Solution:

1. **Identify the Masses and Forces**:
- Let the mass of the man be \( m \).
- The mass of the block is also \( m \) (as stated in the problem).
- The gravitational force acting on both the man and the block is \( mg \).

2. **Friction Forces**:
- The coefficient of friction between the man and the floor is \( \mu_m \).
- The coefficient of friction between the block and the floor is \( \mu_b \).
- Given that \( \mu_m > \mu_b \), the maximum static friction force for the man is \( f_{f,m} = \mu_m mg \) and for the block is \( f_{f,b} = \mu_b mg \).

3. **Analyzing the Scenarios**:
- **If the block does not move**: The friction force acting on the block is equal to the tension \( T \) in the string. Since the block is stationary, \( T \leq f_{f,b} \). The man will also not move because the friction force acting on him is greater than or equal to the force he exerts to pull the block.
- **If the block can move**: The friction force acting on the block is less than the tension \( T \) in the string, allowing it to accelerate. The man can still remain stationary if the friction force acting on him is sufficient to counteract the tension.

4. **Acceleration Analysis**:
- If both the man and the block are moving, we can set up the equations of motion.
- For the man: \( T - f_{f,m} = m a_m \) (where \( a_m \) is the acceleration of the man).
- For the block: \( T - f_{f,b} = m a_b \) (where \( a_b \) is the acceleration of the block).
- Since \( f_{f,m} > f_{f,b} \), the acceleration of the block \( a_b \) will be greater than the acceleration of the man \( a_m \).

5. **Conclusion**:
- From our analysis, we can conclude:
- If the block does not move, the man also does not move.
- If the block can move, the man can remain stationary.
- If both move, the acceleration of the block is greater than that of the man.

### Final Answer:
- Options A, B, and C are correct.