If a body of moment of inertia `2kgm^2` revolves about its own axis making 2 rotations per second, then its angular momentum (in J s) is

Options

A. `2pi`
B. `4pi`
C. `6 pi`
D. `8 pi`

Answer

To find the angular momentum of a body revolving about its own axis, we can use the formula:

\[ L = I \cdot \omega \]

where:
- \( L \) is the angular momentum,
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity in radians per second.

### Step 1: Identify the given values
- Moment of inertia \( I = 2 \, \text{kg m}^2 \)
- The body makes 2 rotations per second.

### Step 2: Convert rotations per second to radians per second
Since one complete rotation corresponds to \( 2\pi \) radians, we can calculate the angular velocity \( \omega \):

\[ \text{Number of rotations per second} = 2 \, \text{rotations/second} \]

\[ \text{Angular displacement for 2 rotations} = 2 \times 2\pi = 4\pi \, \text{radians} \]

Since this occurs in 1 second, we have:

\[ \omega = \frac{\text{Angular displacement}}{\text{Time}} = \frac{4\pi \, \text{radians}}{1 \, \text{second}} = 4\pi \, \text{radians/second} \]

### Step 3: Substitute the values into the angular momentum formula
Now we can substitute the values of \( I \) and \( \omega \) into the angular momentum formula:

\[ L = I \cdot \omega = 2 \, \text{kg m}^2 \cdot 4\pi \, \text{radians/second} \]

Calculating this gives:

\[ L = 8\pi \, \text{kg m}^2/\text{s} = 8\pi \, \text{J s} \]

### Final Answer
Thus, the angular momentum \( L \) is:

\[ L = 8\pi \, \text{J s} \]