If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be -
(a) going up with increasing speed
( b) going down with increasing speed
( c) going up with uniform speed
( d) going down with uniform speed

Options

A. going up with increasing speed
B. going down with incresing speed
C. going up with uniform speed
D. going down with uniform speed

Answer

To solve the question, we need to analyze the situation where the tension in the cable supporting an elevator is equal to the weight of the elevator.

### Step-by-Step Solution:

1. **Understanding Forces Acting on the Elevator**:
- The forces acting on the elevator are:
- The tension (T) in the cable acting upwards.
- The weight (W) of the elevator acting downwards, which is given by W = mg (where m is the mass of the elevator and g is the acceleration due to gravity).

2. **Setting Up the Equation**:
- According to the problem, the tension in the cable is equal to the weight of the elevator:
\[ T = W = mg \]

3. **Calculating the Net Force**:
- The net force (F_net) acting on the elevator can be calculated using Newton's second law:
\[ F_{\text{net}} = T - W \]
- Substituting the values, we get:
\[ F_{\text{net}} = mg - mg = 0 \]

4. **Determining the Acceleration**:
- Since the net force is zero, according to Newton's second law (F = ma), the acceleration (a) of the elevator is:
\[ F_{\text{net}} = ma \implies 0 = ma \implies a = 0 \]

5. **Interpreting the Result**:
- An acceleration of zero means that the elevator is either at rest or moving with a constant velocity (uniform speed). This means the elevator can either be:
- Moving upwards with uniform speed.
- Moving downwards with uniform speed.

6. **Evaluating the Options**:
- (a) Going up with increasing speed: **Incorrect** (there would be a net force upwards).
- (b) Going down with increasing speed: **Incorrect** (there would be a net force downwards).
- (c) Going up with uniform speed: **Correct**.
- (d) Going down with uniform speed: **Correct**.

### Conclusion:
The correct answers are (c) going up with uniform speed and (d) going down with uniform speed.