Statement A : If the lift is falling freely then the man on its floor experiences no reaction from the floor.
Statement B : If the lift moves down with an acceleration `a gt g`, then the normal reaction becomes negative and the man feels floating up in the lift.

Options

A. A and B are correct
B. A and B are false
C. A is true and B is false
D. A is false and B is true

Answer

To analyze the statements provided in the question, let's break down the reasoning step by step.

### Step 1: Analyze Statement A
**Statement A**: If the lift is falling freely, then the man on its floor experiences no reaction from the floor.

1. When the lift is in free fall, it accelerates downward with an acceleration equal to the acceleration due to gravity (g).
2. The man inside the lift also experiences the same gravitational acceleration (g).
3. The forces acting on the man are:
- Weight (mg) acting downward.
- Normal force (N) acting upward from the floor of the lift.
4. Since both the man and the lift are accelerating downward at the same rate, the normal force (N) must balance the weight (mg) in such a way that:
\[ N + mg = mg \]
Simplifying this gives:
\[ N = 0 \]
5. Therefore, the man experiences no normal reaction force from the floor of the lift.

**Conclusion for Statement A**: This statement is true.

### Step 2: Analyze Statement B
**Statement B**: If the lift moves down with an acceleration `a > g`, then the normal reaction becomes negative and the man feels floating up in the lift.

1. In this case, the lift is moving downward with an acceleration greater than g (a > g).
2. The forces acting on the man are:
- Weight (mg) acting downward.
- Normal force (N) acting upward from the floor of the lift.
3. The equation of motion for the man in the lift can be expressed as:
\[ N + ma = mg \]
Rearranging gives:
\[ N = mg - ma \]
4. Since a > g, it follows that:
\[ N = mg - ma < 0 \]
5. A negative normal force indicates that the man is not in contact with the floor of the lift, leading to the sensation of floating.

**Conclusion for Statement B**: This statement is also true.

### Final Conclusion
Both statements A and B are true. Therefore, the correct answer is that both statements are correct.

### Summary of the Solution
- **Statement A**: True (the man experiences no reaction force when the lift is in free fall).
- **Statement B**: True (the man feels floating when the lift accelerates downward faster than g).