The dimensional formula of angular velocity is

Options

A. `[M^(0)L^(0)T^(-1)]`
B. `[MLT^(-1)]`
C. `[M^(0)L^(0)T^(1)]`
D. `[ML^(0)T^(-2)]`

Explanation

To find the dimensional formula of angular velocity, we can follow these steps:

### Step 1: Understand the definition of angular velocity
Angular velocity (ω) is defined as the rate of change of angular displacement with respect to time. It is usually expressed in radians per second (rad/s).

### Step 2: Relate angular velocity to frequency
Angular velocity can also be expressed in terms of frequency (f). The relationship is given by:
\[ \omega = 2\pi f \]
where \( f \) is the frequency in hertz (Hz), which is the number of cycles per second.

### Step 3: Express frequency in terms of time
Frequency is the reciprocal of the time period (T):
\[ f = \frac{1}{T} \]
Substituting this into the equation for angular velocity gives:
\[ \omega = 2\pi \left(\frac{1}{T}\right) \]

### Step 4: Identify the dimensional formula of the components
- The term \( 2\pi \) is dimensionless.
- The time period \( T \) has the dimensional formula of time, which is represented as \( [T] \).

### Step 5: Write the dimensional formula of angular velocity
From the equation:
\[ \omega = \frac{2\pi}{T} \]
We can see that the dimensional formula of angular velocity will be:
\[ [\omega] = \frac{1}{[T]} \]
This can be expressed as:
\[ [\omega] = [M^0 L^0 T^{-1}] \]

### Conclusion
Thus, the dimensional formula of angular velocity is:
\[ [\omega] = [M^0 L^0 T^{-1}] \]