The angular frequency is measured in rad `s^(-1)`. Its dimension in length are :

Options

A. (a)`-2`
B. (b)`-1`
C. (c)`0`
D. (d)`2`

Answer

To solve the problem of determining the dimensions of angular frequency in terms of length, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Frequency**:
Angular frequency (often denoted as ω) is defined as the rate of change of the phase of a sinusoidal waveform, or the rate of rotation in circular motion. It is measured in radians per second (rad/s).

2. **Identifying Units**:
The unit of angular frequency is given as radians per second. We can express this mathematically as:
\[ \text{Angular Frequency} = \frac{\text{radians}}{\text{seconds}} = \text{rad/s} \]

3. **Analyzing Radians**:
Radians are a measure of angle, and they are considered a dimensionless quantity. This means that when we express radians in terms of fundamental dimensions (mass, length, time), they do not contribute any dimensions. Therefore, we can state:
\[ \text{Dimension of radians} = 0 \text{ (dimensionless)} \]

4. **Analyzing Seconds**:
The second is a unit of time. In terms of fundamental dimensions, it is represented as:
\[ \text{Dimension of seconds} = [T]^{-1} \]

5. **Combining Dimensions**:
Since angular frequency is expressed as radians per second, and knowing that radians contribute no dimensions, we can write:
\[ \text{Dimension of Angular Frequency} = \frac{0}{[T]} = [T]^{-1} \]

6. **Determining Length Dimension**:
Since we are interested in the dimension of angular frequency in terms of length, we can conclude that:
\[ \text{Dimension of Length} = 0 \]

7. **Final Conclusion**:
Thus, the dimension of angular frequency in terms of length is:
\[ \text{Dimension in Length} = 0 \]

### Answer:
The dimension of angular frequency in terms of length is 0.