Consider an elevator moving downwards with an acceleration a, the force exerted by a passenger of mass m on the floor of the elevator is `:`

Options

A. ma
B. ma-mg
C. mg-ma
D. mg`|`ma

Answer

To solve the problem of finding the force exerted by a passenger of mass \( m \) on the floor of an elevator that is moving downwards with an acceleration \( a \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Passenger**:
- The weight of the passenger acting downwards, which is given by \( mg \) (where \( g \) is the acceleration due to gravity).
- The normal force \( N \) acting upwards from the floor of the elevator.

2. **Draw the Free Body Diagram**:
- Represent the passenger and indicate the forces: \( mg \) acting downwards and \( N \) acting upwards.

3. **Set Up the Equation of Motion**:
- Since the elevator is accelerating downwards with an acceleration \( a \), we can apply Newton's second law.
- The net force acting on the passenger can be expressed as:
\[ F_{\text{net}} = mg - N \]
- According to Newton's second law, this net force is also equal to the mass times the acceleration of the passenger:
\[ F_{\text{net}} = ma \]

4. **Combine the Equations**:
- Setting the two expressions for net force equal gives:
\[ mg - N = ma \]

5. **Solve for the Normal Force \( N \)**:
- Rearranging the equation to isolate \( N \):
\[ N = mg - ma \]

6. **Interpret the Result**:
- The normal force \( N \) represents the force exerted by the passenger on the floor of the elevator. Thus, the force exerted by the passenger on the elevator is:
\[ N = m(g - a) \]

### Final Answer:
The force exerted by a passenger of mass \( m \) on the floor of the elevator is:
\[ N = m(g - a) \]