A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made 4 times, its angular momentum will become

Options

A. 4L
B. 16L
C. `sqrt(2)L`
D. 2L

Explanation

To solve the problem, we need to relate the angular momentum \( L \) of a rigid body to its rotational kinetic energy \( E \) and analyze how changes in kinetic energy affect angular momentum.

### Step-by-Step Solution:

1. **Understand the relationship between angular momentum and rotational kinetic energy**:
- The angular momentum \( L \) of a rigid body is given by:
\[ L = I \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.
- The rotational kinetic energy \( E \) is given by:
\[ E = \frac{1}{2} I \omega^2 \]

2. **Express \( \omega \) in terms of \( L \)**:
- From the equation for angular momentum, we can express \( \omega \):
\[ \omega = \frac{L}{I} \]

3. **Substitute \( \omega \) into the kinetic energy equation**:
- Substitute \( \omega \) into the kinetic energy equation:
\[ E = \frac{1}{2} I \left(\frac{L}{I}\right)^2 = \frac{1}{2} I \frac{L^2}{I^2} = \frac{L^2}{2I} \]

4. **Rearranging the equation for \( L \)**:
- Rearranging gives:
\[ L^2 = 2EI \]
- Taking the square root:
\[ L = \sqrt{2EI} \]

5. **Consider the change in kinetic energy**:
- If the rotational kinetic energy is increased to 4 times its original value, we have:
\[ E' = 4E \]

6. **Calculate the new angular momentum \( L' \)**:
- Substitute \( E' \) into the equation for \( L \):
\[ L' = \sqrt{2E'I} = \sqrt{2(4E)I} = \sqrt{8EI} = 2\sqrt{2EI} \]
- Since \( L = \sqrt{2EI} \), we can express \( L' \) in terms of \( L \):
\[ L' = 2L \]

### Final Answer:
Thus, if the rotational kinetic energy is made 4 times, the angular momentum will become:
\[ \boxed{2L} \]