The dimension of angular momentum is

Options

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

Explanation

To find the dimension of angular momentum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Angular Momentum**:
Angular momentum (J) is defined as the product of the moment of inertia (I) and the angular velocity (ω).
\[ J = I \cdot \omega \]

2. **Identify the Moment of Inertia**:
The moment of inertia (I) for a point mass is given by the formula:
\[ I = m \cdot r^2 \]
where \( m \) is the mass and \( r \) is the distance from the axis of rotation.

3. **Determine the Dimensions of Moment of Inertia**:
The dimension of mass (m) is \( [M] \) and the dimension of distance (r) is \( [L] \). Therefore, the dimension of moment of inertia (I) is:
\[ [I] = [M][L^2] = M L^2 \]

4. **Identify the Dimension of Angular Velocity**:
Angular velocity (ω) is defined as the rate of change of angular displacement with respect to time. Its dimension is:
\[ [\omega] = T^{-1} \]

5. **Combine the Dimensions**:
Now, substituting the dimensions of moment of inertia and angular velocity into the equation for angular momentum:
\[ [J] = [I] \cdot [\omega] = (M L^2) \cdot (T^{-1}) = M L^2 T^{-1} \]

6. **Final Result**:
Therefore, the dimension of angular momentum (J) is:
\[ [J] = M L^2 T^{-1} \]

### Answer:
The dimension of angular momentum is \( M L^2 T^{-1} \).

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