Tension in the cable supporting an elevator, is equal to the weight of the elevator. From this, we can conclude that the elevator is going up or down with a

Options

A. uniform velocity
B. uniform acceleration
C. variable acceleration
D. either ( 2) and ( 3)

Answer

To solve the problem regarding the tension in the cable supporting an elevator, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Elevator**:
- The tension (T) in the cable acts upward.
- The weight (W) of the elevator acts downward. The weight can be expressed as \( W = mg \), where \( m \) is the mass of the elevator and \( g \) is the acceleration due to gravity.

2. **Set Up the Equation for Net Force**:
- According to Newton's second law, the net force (F_net) acting on the elevator can be expressed as:
\[ F_{net} = T - W \]

3. **Given Condition**:
- It is given that the tension in the cable is equal to the weight of the elevator:
\[ T = W \]

4. **Substitute the Given Condition into the Net Force Equation**:
- By substituting \( T = W \) into the net force equation, we have:
\[ F_{net} = T - W = W - W = 0 \]

5. **Interpret the Result**:
- Since the net force is zero, we can apply Newton's second law:
\[ F_{net} = ma \]
- Here, \( a \) is the acceleration of the elevator. Since \( F_{net} = 0 \), it follows that:
\[ ma = 0 \]
- Given that the mass \( m \) cannot be zero, we conclude that the acceleration \( a \) must also be zero:
\[ a = 0 \]

6. **Conclusion**:
- When the acceleration of the elevator is zero, it means that the elevator is moving with a constant velocity. This could either be at rest or moving at a uniform speed. Therefore, we conclude that the elevator is moving with uniform velocity.

### Final Answer:
The elevator is going up or down with a uniform velocity.

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