When a body is spinning on its axis in absence of any external torque, then choose the wrong statement

Options

A. `vec(omega)` can be changed by keeping `vec(L)` same
B. `vec(L)` can be changed by keeping `vec(omega)` same
C. l can be change by keeping `vec(L)` same
D. l and `vec(omega)` both can be changed by keeping `vec(L)` same

Answer

To solve the problem, we need to analyze the statements related to a body spinning on its axis in the absence of external torque. We will evaluate each statement to determine which one is incorrect.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
- Angular momentum (L) of a body is given by the formula \( L = I \cdot \omega \), where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.
- In the absence of external torque, the angular momentum of the system remains constant according to the law of conservation of angular momentum.

2. **Evaluating the Statements**:
- **Statement 1**: "If there is no external torque, the angular momentum remains constant."
- This statement is **correct** because, as mentioned, angular momentum is conserved in the absence of external torque.

- **Statement 2**: "L can be changed by keeping omega the same."
- This statement is **incorrect**. Since there is no external torque, the angular momentum \( L \) cannot change. Therefore, it is impossible to change \( L \) while keeping \( \omega \) constant.

- **Statement 3**: "I can be changed by keeping L the same."
- This statement is **correct**. If the moment of inertia \( I \) changes, the angular velocity \( \omega \) must adjust to maintain the same angular momentum \( L \).

- **Statement 4**: "I and omega both can be changed by keeping L constant."
- This statement is **correct**. If \( L \) is constant, then changes in \( I \) will result in corresponding changes in \( \omega \) to keep \( L \) the same.

3. **Conclusion**:
- The only statement that is incorrect is **Statement 2**: "L can be changed by keeping omega the same."

### Final Answer:
The wrong statement is: "L can be changed by keeping omega the same."