Statement A : When a person is on the floor of a lift which is at rest, the resultant force on him is equal to his weight
Statement B : When the lift is moving with uniform velocity, then the apparent weight of the man is zero

Options

A. A & B are correct
B. A & B are wrong
C. A is correct and B is wrong
D. A is wrong and B is correct

Answer

To analyze the statements provided in the question, we will break down each statement step by step.

### Step 1: Analyze Statement A
**Statement A**: "When a person is on the floor of a lift which is at rest, the resultant force on him is equal to his weight."

1. **Understanding Forces**: When a person is in a lift at rest, two forces act on him:
- The gravitational force (weight) acting downward, which is \( W = mg \) (where \( m \) is the mass of the person and \( g \) is the acceleration due to gravity).
- The normal force \( N \) exerted by the floor of the lift acting upward.

2. **Equilibrium Condition**: Since the lift is at rest, the person is also at rest. According to Newton's first law, if an object is at rest, the net force acting on it must be zero. Therefore, we have:
\[ N - mg = 0 \]
This implies:
\[ N = mg \]

3. **Resultant Force**: The resultant force on the person is the vector sum of all forces acting on him. Since the upward normal force equals the downward weight, the net force is:
\[ \text{Net Force} = N - mg = 0 \]
Thus, the resultant force is zero, not equal to his weight.

**Conclusion for Statement A**: The statement is incorrect.

### Step 2: Analyze Statement B
**Statement B**: "When the lift is moving with uniform velocity, then the apparent weight of the man is zero."

1. **Understanding Uniform Velocity**: When the lift moves with uniform velocity, it means that the lift is not accelerating. Hence, the acceleration \( a = 0 \).

2. **Forces Acting**: The same forces act on the person as in the first case:
- Weight \( W = mg \) acting downward.
- Normal force \( N \) acting upward.

3. **Equilibrium Condition**: Since there is no acceleration, the forces are balanced:
\[ N - mg = 0 \]
Therefore, we have:
\[ N = mg \]

4. **Apparent Weight**: The apparent weight of a person is defined as the normal force acting on them. Since \( N = mg \), the apparent weight is not zero; it is equal to his actual weight.

**Conclusion for Statement B**: The statement is incorrect.

### Final Conclusion
Both statements A and B are incorrect.

### Summary of the Solution
- Statement A is incorrect because the resultant force on a person in a stationary lift is zero, not equal to his weight.
- Statement B is incorrect because the apparent weight of a person in a lift moving with uniform velocity is equal to his actual weight, not zero.