A person is standing in an elevator. In which situation he finds his weight less ?

Options

A. when the elevator moves upward with constant acceleration
B. when the elevator moves downward with constant acceleration
C. when the elevator moves upward with uniform velocity
D. when the elevator moves downward with uniform velocity

Explanation

To determine in which situation a person standing in an elevator finds his weight less, we need to analyze the forces acting on the person in different scenarios. The weight of a person is the gravitational force acting on them, which can be represented as \( W = mg \), where \( m \) is the mass and \( g \) is the acceleration due to gravity.

Let's examine each option:

1. **Elevator moving upward with constant acceleration**:
- In this case, the person feels heavier because the elevator is accelerating upward. The effective weight \( W' \) can be calculated as:
\[ W' = m(g + a) \]
- Here, \( a \) is the upward acceleration of the elevator. Thus, the person feels an increase in weight.

2. **Elevator moving downward with constant acceleration**:
- In this scenario, the person feels lighter as the elevator accelerates downward. The effective weight can be calculated as:
\[ W' = m(g - a) \]
- Since \( a \) is the downward acceleration, the effective weight decreases, making the person feel lighter.

3. **Elevator moving upward with uniform velocity**:
- When the elevator moves with uniform velocity, there is no acceleration (\( a = 0 \)). The effective weight remains the same:
\[ W' = mg \]
- The person feels their normal weight.

4. **Elevator moving downward with uniform velocity**:
- Similar to the previous case, if the elevator is moving downward at a constant velocity, there is no acceleration (\( a = 0 \)). The effective weight remains:
\[ W' = mg \]
- The person also feels their normal weight.

From the analysis, the situation where the person feels their weight is less occurs when the elevator is moving downward with constant acceleration.

**Final Answer**: The person finds his weight less when the elevator is moving downward with constant acceleration.