The rotational kinetic energy of a body is E and its moment of inertia is l. The angular momentum is

Options

A. EI
B. `2sqrt(EI)`
C. `sqrt(2EI)`
D. `E//I`

Explanation

To find the angular momentum of a body given its rotational kinetic energy \( E \) and its moment of inertia \( I \), we can follow these steps:

### Step-by-Step Solution:

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

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

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

4. **Substitute \( \omega \) into the Angular Momentum Formula**:
Now, substitute the expression for \( \omega \) into the angular momentum formula:
\[ L = I \left(\sqrt{\frac{2E}{I}}\right) \]

5. **Simplify the Expression**:
This can be simplified as follows:
\[ L = I \cdot \sqrt{\frac{2E}{I}} = \sqrt{I^2 \cdot \frac{2E}{I}} = \sqrt{2EI} \]

6. **Final Result**:
Therefore, the angular momentum \( L \) in terms of the rotational kinetic energy \( E \) and the moment of inertia \( I \) is:
\[ L = \sqrt{2EI} \]

### Conclusion:
The angular momentum of the body is given by:
\[ L = \sqrt{2EI} \]