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A : If angular momentum of an object is ...

A : If angular momentum of an object is constant about a point then net torque on it about that point is zero.
R : Torque is equal to the rate of change of angular momentum.

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion,

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion,

C

If Assertion is true statement but Reason is false,

D

If both Assertion and Reason are false statements,

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given problem, we need to analyze the statements A and R and determine their validity and relationship. ### Step-by-Step Solution: 1. **Understanding Statement A**: - Statement A claims that if the angular momentum of an object is constant about a point, then the net torque on it about that point is zero. - Angular momentum (L) is defined as \( L = I \omega \) for a rigid body, where \( I \) is the moment of inertia and \( \omega \) is the angular velocity. - If angular momentum is constant, it means that \( \frac{dL}{dt} = 0 \). 2. **Understanding Statement R**: - Statement R states that torque (\( \tau \)) is equal to the rate of change of angular momentum. - Mathematically, this is expressed as \( \tau = \frac{dL}{dt} \). - This means that if there is no change in angular momentum over time, the torque must be zero. 3. **Connecting A and R**: - From Statement R, we know that torque is the rate of change of angular momentum. - If angular momentum is constant (as stated in A), then \( \frac{dL}{dt} = 0 \). - Therefore, substituting this into the equation for torque gives us \( \tau = 0 \). 4. **Conclusion**: - Since both statements A and R are true, and R correctly explains why A is true, we conclude that the correct option is that both statements are true and R is the correct explanation for A. ### Final Answer: Both Statement A and Statement R are true, and R is the correct explanation of A. ---
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