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 understand the relationship between angular momentum (L) and rotational kinetic energy (K) of a rigid body.

### Step-by-Step Solution:

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

2. **Relate Angular Momentum and Rotational Kinetic Energy**:
- We can express \(K\) in terms of \(L\):
\[ K = \frac{1}{2} I \omega^2 = \frac{1}{2} \frac{L^2}{I} \]
- From this, we can derive that:
\[ L^2 = 2K I \]
- Thus, we can express \(L\) in terms of \(K\):
\[ L = \sqrt{2KI} \]

3. **Determine the Effect of Increasing Kinetic Energy**:
- If the rotational kinetic energy is made 4 times, we denote the new kinetic energy as \(K' = 4K\).
- Substituting this into our expression for angular momentum:
\[ L' = \sqrt{2K'I} = \sqrt{2(4K)I} = \sqrt{8KI} = 2\sqrt{2KI} \]
- Since \(L = \sqrt{2KI}\), we can rewrite \(L'\) as:
\[ L' = 2L \]

4. **Conclusion**:
- Therefore, if the rotational kinetic energy is made 4 times, the new angular momentum \(L'\) becomes:
\[ L' = 2L \]

### Final Answer:
The angular momentum will become \(2L\).