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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 regarding angular momentum and torque. ### Step-by-Step Solution: 1. **Understanding Angular Momentum**: - Angular momentum (L) of an object about a point is defined as \( L = r \times p \), where \( r \) is the position vector from the point to the object, and \( p \) is the linear momentum of the object. - If the angular momentum is constant about a point, it means that \( \frac{dL}{dt} = 0 \). 2. **Relating Torque to Angular Momentum**: - Torque (\( \tau \)) is defined as the rate of change of angular momentum: \[ \tau = \frac{dL}{dt} \] - If the angular momentum is constant, then its rate of change is zero, which implies: \[ \tau = 0 \] - Therefore, if the angular momentum is constant about a point, the net torque about that point must also be zero. 3. **Evaluating Statement A**: - Statement A claims: "If angular momentum of an object is constant about a point, then net torque on it about that point is zero." - Based on our analysis, this statement is **true**. 4. **Evaluating Statement R**: - Statement R claims: "Torque is equal to the rate of change of angular momentum." - This is a direct definition of torque, which we have already established as \( \tau = \frac{dL}{dt} \). - Therefore, this statement is also **true**. 5. **Conclusion**: - Both statements A and R are true. ### Final Answer: - Statement A is true, and Statement R is true.
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