A man of mass 80kg pushes box of mass 20kg horizontaly. The man moves the box with a constant acceleration of `2 m//s^(2)` but his foot does not slip on the ground. There is no friction between the box and the ground. There is no friction between the box and the ground. whereas there is sufficient friction between the man's foot and the ground to prevent him from slipping.
Assertion:- The force applied by the man on the box is equal and opposite to the force applied by the force applid by the box on the man.
Reason:- Friction force applied by the ground on the man is 200N.

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Answer

To solve the problem, we need to analyze the forces acting on both the man and the box, and then apply Newton's laws of motion.

### Step 1: Identify the forces acting on the box
The box has a mass of 20 kg and is being pushed by the man with a constant acceleration of \(2 \, \text{m/s}^2\). According to Newton's second law, the net force acting on the box can be calculated using the formula:
\[ F = m \cdot a \]
where:
- \(m\) is the mass of the box (20 kg)
- \(a\) is the acceleration (2 m/s²)

Calculating the force:
\[ F = 20 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 40 \, \text{N} \]

### Step 2: Apply Newton's Third Law
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the force applied by the man on the box is equal in magnitude and opposite in direction to the force applied by the box on the man.

Thus, if the man exerts a force of \(F = 40 \, \text{N}\) on the box, the box exerts an equal and opposite force of \(40 \, \text{N}\) on the man.

### Step 3: Analyze the forces acting on the man
The man has a mass of 80 kg. The frictional force that prevents him from slipping is what allows him to push the box. The frictional force must be equal to the force exerted by the box on the man, which we calculated to be \(40 \, \text{N}\).

### Step 4: Calculate the frictional force
The frictional force can be calculated as:
\[ F_{\text{friction}} = m_{\text{man}} \cdot a_{\text{man}} \]
However, since the man is not accelerating, we can conclude that the frictional force must balance the force exerted by the box on him. Therefore:
\[ F_{\text{friction}} = 40 \, \text{N} \]

### Step 5: Evaluate the assertion and reason
- **Assertion**: The force applied by the man on the box is equal and opposite to the force applied by the box on the man. This is true based on Newton's third law.
- **Reason**: The friction force applied by the ground on the man is 200 N. This is false because we calculated the frictional force to be 40 N.

### Conclusion
The assertion is true, but the reason is false. Therefore, the correct answer is that the assertion is true and the reason is false.