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Assertion: A girl sits on a rolling chai...

Assertion: A girl sits on a rolling chair, when she stretch her arms horizontally, her speed is reduced.
Reason: Principle of conservation of angular momentum is applicable in this situation.

A

Both assertion and reason are true and reason is the correct explanation of assertion.

B

Both assertion and reason are true but reason is not the correct explanation of assertion

C

Assertion is true but reason is false.

D

Both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we will analyze the assertion and reason step by step. ### Step 1: Understanding the Assertion The assertion states that when a girl sitting on a rolling chair stretches her arms horizontally, her speed is reduced. - **Explanation**: When she stretches her arms, she increases her moment of inertia. In a rolling chair, her speed (angular speed) decreases as a result of this increase in moment of inertia. ### Step 2: Understanding the Reason The reason given is that the principle of conservation of angular momentum is applicable in this situation. - **Explanation**: The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. In this case, as the girl stretches her arms, the distribution of her mass changes, leading to an increase in her moment of inertia. ### Step 3: Applying the Conservation of Angular Momentum Let’s denote: - Initial moment of inertia as \( I_i \) - Final moment of inertia as \( I_f \) - Initial angular speed as \( \omega_i \) - Final angular speed as \( \omega_f \) According to the conservation of angular momentum: \[ I_i \omega_i = I_f \omega_f \] When the girl stretches her arms, \( I_f > I_i \). To keep the product \( I \omega \) constant, if \( I \) increases, \( \omega \) must decrease. Thus: \[ \omega_f < \omega_i \] ### Step 4: Conclusion Since the assertion is true (the girl's speed decreases when she stretches her arms) and the reason is also true (the principle of conservation of angular momentum applies), we conclude that both the assertion and reason are true, and the reason correctly explains the assertion. ### Final Answer Both assertion and reason are true, and the reason is the correct explanation of the assertion. ---
To solve the question, we will analyze the assertion and reason step by step. ### Step 1: Understanding the Assertion The assertion states that when a girl sitting on a rolling chair stretches her arms horizontally, her speed is reduced. - **Explanation**: When she stretches her arms, she increases her moment of inertia. In a rolling chair, her speed (angular speed) decreases as a result of this increase in moment of inertia. ### Step 2: Understanding the Reason ...
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