Kinetic energy of a body is 4j and its moment of inertia is `2kg m^(2)`, then angular momentum is

Options

A. `2kg m^(2)//s`
B. `6kg m^(2)//s`
C. `8kg m^(2)//s`
D. `4kg m^(2)//s`

Explanation

To find the angular momentum \( L \) of a body given its kinetic energy \( E \) and moment of inertia \( I \), we can use the relationship between these quantities.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Kinetic Energy, \( E = 4 \, \text{J} \)
- Moment of Inertia, \( I = 2 \, \text{kg m}^2 \)

2. **Use the Formula for Kinetic Energy in Rotational Motion:**
The kinetic energy \( E \) of a rotating body is given by the formula:
\[ E = \frac{1}{2} I \omega^2 \]
where \( \omega \) is the angular velocity.

3. **Rearrange the Formula to Find Angular Velocity \( \omega \):**
From the kinetic energy formula, we can express \( \omega^2 \) as:
\[ \omega^2 = \frac{2E}{I} \]

4. **Substitute the Known Values:**
Plugging in the values of \( E \) and \( I \):
\[ \omega^2 = \frac{2 \times 4 \, \text{J}}{2 \, \text{kg m}^2} = \frac{8}{2} = 4 \, \text{rad}^2/\text{s}^2 \]

5. **Calculate Angular Velocity \( \omega \):**
Taking the square root to find \( \omega \):
\[ \omega = \sqrt{4} = 2 \, \text{rad/s} \]

6. **Use the Formula for Angular Momentum:**
The angular momentum \( L \) is given by:
\[ L = I \omega \]

7. **Substitute the Values of \( I \) and \( \omega \):**
Now substituting the values:
\[ L = 2 \, \text{kg m}^2 \times 2 \, \text{rad/s} = 4 \, \text{kg m}^2/\text{s} \]

8. **Final Result:**
Therefore, the angular momentum \( L \) is:
\[ L = 4 \, \text{kg m}^2/\text{s} \]

### Conclusion:
The angular momentum of the body is \( 4 \, \text{kg m}^2/\text{s} \).

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