A man is running on the ground .It is known that the coefficient of friction between the man and the ground is `mu` . Then which of the following statements is correct

Options

A. Normal reaction between man and ground is equal to weight of man
B. The direction of friction on man is in the direction of normal reaction on the man
C. Direction of friction on man is opposite to the direction of motion of man
D. Maximum acceleration of man can be `2mug`

Answer

To solve the problem, we need to analyze the situation of a man running on the ground with a coefficient of friction `mu` between him and the ground. We will evaluate the statements provided and determine which one is correct.

### Step-by-Step Solution:

1. **Identify Forces Acting on the Man**:
- The gravitational force acting on the man is given by \( F_g = mg \), where \( m \) is the mass of the man and \( g \) is the acceleration due to gravity.
- The normal force \( N \) acting on the man by the ground is equal to the gravitational force when the man is on a flat surface, so \( N = mg \).

**Hint**: Remember that the normal force balances the weight of the man when he is on a flat surface.

2. **Static Friction Force**:
- The static friction force \( F_s \) is responsible for the man's ability to run. The maximum static friction force can be expressed as:
\[ F_s^{max} = \mu N = \mu (mg) \]
- This means the maximum static friction force that can act on the man is proportional to the normal force and the coefficient of friction.

**Hint**: The static friction force prevents slipping and allows the man to accelerate forward.

3. **Acceleration of the Man**:
- The maximum acceleration \( a_{max} \) that the man can achieve while running is given by:
\[ a_{max} = \frac{F_s^{max}}{m} = \frac{\mu mg}{m} = \mu g \]
- Thus, the maximum acceleration of the man is \( \mu g \).

**Hint**: The acceleration is directly related to the coefficient of friction and gravitational acceleration.

4. **Evaluating the Statements**:
- **Statement A**: "The normal reaction between the man and the ground is equal to the weight of the man."
- This statement is correct because \( N = mg \).
- **Statement B**: "The direction of friction on the man is in the direction of the normal reaction on the man."
- This statement is incorrect because friction acts tangentially to the surface.
- **Statement C**: "The direction of friction on the man is opposite to the direction of the motion of the man."
- This statement is incorrect because static friction acts in the direction of motion to prevent slipping.
- **Statement D**: "The maximum acceleration of the man can be \( 2\mu g \)."
- This statement is incorrect because we found that the maximum acceleration is \( \mu g \).

5. **Conclusion**:
- The only correct statement is **Statement A**: "The normal reaction between the man and the ground is equal to the weight of the man."

### Final Answer:
The correct statement is **A**: The normal reaction between the man and the ground is equal to the weight of the man.