Assertion: A boy is rotating in a rotating chair with some angular speed. Initially arma of the boy are stretched out. When boy folds his hands then angular speed increases
Reason: Angular momentum of the system is conserved in absence of external torque.

Options

A. If both assertion and reason are correct and reason is the correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that a boy rotating in a chair with some angular speed increases his angular speed when he folds his arms. This implies that the folding of arms affects the moment of inertia of the boy.

### Step 2: Understand the Reason
The reason given is that angular momentum of the system is conserved in the absence of external torque. This is a fundamental principle in physics known as the conservation of angular momentum.

### Step 3: Apply the Conservation of Angular Momentum
According to the conservation of angular momentum:
\[ L = I \omega \]
where \( L \) is angular momentum, \( I \) is moment of inertia, and \( \omega \) is angular speed. If no external torque acts on the system, then:
\[ L_{\text{initial}} = L_{\text{final}} \]

### Step 4: Analyze the Moment of Inertia
When the boy has his arms stretched out, his moment of inertia \( I_i \) is larger because the mass is distributed further from the axis of rotation. When he folds his arms, his moment of inertia \( I_f \) decreases because the mass is now closer to the axis of rotation:
\[ I_f < I_i \]

### Step 5: Relate Moment of Inertia and Angular Speed
Since angular momentum is conserved:
\[ I_i \omega_i = I_f \omega_f \]
If \( I_f < I_i \), to keep the product \( I \omega \) constant, \( \omega_f \) must be greater than \( \omega_i \):
\[ \omega_f > \omega_i \]

### Step 6: Conclusion
Both the assertion and the reason are correct. The assertion is supported by the reason, which explains that the increase in angular speed when the boy folds his arms is due to the conservation of angular momentum.

### Final Answer
The correct option is: **Reason is the correct explanation of the assertion.**

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