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 question, we need to analyze the statements given in the context of rotational dynamics, particularly focusing on angular momentum and its relationship with moment of inertia and angular velocity.

### Step-by-Step Solution:

1. **Understanding the Given Conditions**:
- The body is spinning on its axis without any external torque acting on it.
- This means the net external torque (τ) is zero.

2. **Applying the Principle of Angular Momentum**:
- According to the rotational dynamics, when the external torque is zero, the angular momentum (L) of the system remains constant.
- Mathematically, this is expressed as:
\[ \frac{dL}{dt} = 0 \implies L = \text{constant} \]

3. **Relating Angular Momentum to Moment of Inertia and Angular Velocity**:
- Angular momentum (L) can be expressed as:
\[ L = I \omega \]
- Where \(I\) is the moment of inertia and \(\omega\) is the angular velocity.

4. **Analyzing the Options**:
- **Option A**: "ω can be changed by keeping L the same."
- This statement is **correct**. Since L is constant, if I changes, ω can change accordingly to keep L constant.

- **Option B**: "L can be changed by keeping ω the same."
- This statement is **incorrect**. Since L is constant (as established), it cannot be changed while keeping ω the same.

- **Option C**: "I can be changed by keeping L the same."
- This statement is **correct**. If L is constant, I can change, and ω will adjust accordingly.

- **Option D**: "I and ω both can be changed keeping L the same."
- This statement is **correct**. Both I and ω can vary as long as their product (L) remains constant.

5. **Identifying the Wrong Statement**:
- From the analysis, the wrong statement is **Option B**: "L can be changed by keeping ω the same."

### Final Answer:
The wrong statement is **Option B**.

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