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

Options

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

Explanation

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

### Step 1: Write the formula for rotational kinetic energy
The rotational kinetic energy \( E \) of a body is given by the formula:
\[ E = \frac{1}{2} I \omega^2 \]
where \( \omega \) is the angular velocity.

### Step 2: Rearrange the equation to solve for \( \omega \)
From the equation above, we can solve for \( \omega \):
\[ \omega^2 = \frac{2E}{I} \]
Taking the square root of both sides, we get:
\[ \omega = \sqrt{\frac{2E}{I}} \]

### Step 3: Write the formula for angular momentum
The angular momentum \( L \) is defined as:
\[ L = I \omega \]

### Step 4: Substitute \( \omega \) into the angular momentum equation
Now we substitute the expression for \( \omega \) from Step 2 into the angular momentum equation:
\[ L = I \left( \sqrt{\frac{2E}{I}} \right) \]

### Step 5: Simplify the expression
Now we simplify the expression for \( L \):
\[ L = I \cdot \sqrt{\frac{2E}{I}} = \sqrt{2E \cdot I} \]

### Conclusion
Thus, the angular momentum \( L \) in terms of \( E \) and \( I \) is:
\[ L = \sqrt{2EI} \]

### Final Answer
The angular momentum is \( \sqrt{2EI} \).

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