A person is standing in an elevator. In which situation he finds his weight less than actual when:

Options

A. The elevator moves upward with constant acceleration
B. The elevator moves downward with constant acceleration
C. The elevator moves upwards with uniform velocity
D. The elevetor moves downwards with uniform velocity.

Explanation

To determine in which situation a person standing in an elevator feels their weight to be less than their actual weight, we need to analyze the forces acting on the person in different scenarios.

### Step-by-Step Solution:

1. **Understanding Weight**:
- The actual weight of a person is given by the formula \( W = mg \), where \( m \) is the mass of the person and \( g \) is the acceleration due to gravity.

2. **Elevator Scenarios**:
- We need to consider different scenarios of the elevator's motion:
- (a) Elevator moving upward with acceleration
- (b) Elevator moving downward with acceleration
- (c) Elevator moving upward with uniform velocity
- (d) Elevator moving downward with uniform velocity

3. **Case Analysis**:
- **(a) Elevator moving upward with acceleration**:
- In this case, the effective weight felt by the person is \( W' = mg + ma \) (where \( a \) is the upward acceleration). The person feels heavier.

- **(b) Elevator moving downward with acceleration**:
- Here, the effective weight felt by the person is \( W' = mg - ma \). If the downward acceleration \( a \) is significant enough, the person will feel lighter than their actual weight. This is the scenario where the person feels their weight is less than actual.

- **(c) Elevator moving upward with uniform velocity**:
- When the elevator moves with uniform velocity, the acceleration is zero, so the effective weight remains \( W' = mg \). The person feels the same weight as their actual weight.

- **(d) Elevator moving downward with uniform velocity**:
- Similar to the previous case, the acceleration is zero, and the effective weight remains \( W' = mg \). The person feels the same weight as their actual weight.

4. **Conclusion**:
- The only scenario where the person feels their weight is less than their actual weight is when the elevator is moving downward with acceleration.

### Final Answer:
The person finds their weight less than actual when the elevator is moving downward with acceleration.