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 forces acting on the man who is running on the ground, considering the coefficient of friction (μ) between him and the ground.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Man**:
- The weight of the man (W) acts downward and is equal to \( mg \), where \( m \) is the mass of the man and \( g \) is the acceleration due to gravity.
- The normal force (N) acts upward, balancing the weight of the man.
- Since the man is running, there is a frictional force (F_friction) acting on him. This frictional force is what allows him to run without slipping.

2. **Establish the Relationship Between Forces**:
- In the vertical direction, the forces must balance. Thus, we have:
\[ N = mg \]
- The maximum static frictional force can be expressed as:
\[ F_friction = \mu N = \mu mg \]
- This frictional force is what enables the man to accelerate forward.

3. **Determine the Direction of the Frictional Force**:
- The direction of the frictional force on the man is opposite to the direction of his motion. When he pushes backward against the ground, the ground pushes forward on him due to friction.

4. **Analyze the Maximum Acceleration**:
- The maximum acceleration (a_max) that the man can achieve without slipping can be calculated using Newton's second law:
\[ a_{max} = \frac{F_friction}{m} = \frac{\mu mg}{m} = \mu g \]
- Therefore, the maximum acceleration is not \( 2\mu g \) but simply \( \mu g \).

5. **Conclusion**:
- Based on the analysis, we can conclude that:
- The normal reaction force is equal to the weight of the man (correct).
- The direction of friction is opposite to the direction of motion (correct).
- The maximum acceleration is \( \mu g \) (not \( 2\mu g \)).

### Final Answer:
The correct statement is that the normal reaction force between the ground and the man is equal to the weight of the man (\( N = mg \)).