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Moment of concurrent forces about any po...

Moment of concurrent forces about any point is constant.
If vector sum of all concurrent forces is zero, then moment of all the forces about any point is also zero.

A

If both Accertion and Reason are true and the reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true but reason is not the correct explanation of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

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The correct Answer is:
To solve the given question, we need to analyze the two statements provided in the assertion and reason: 1. **Assertion**: The moment of concurrent forces about any point is constant. 2. **Reason**: If the vector sum of all concurrent forces is zero, then the moment of all the forces about any point is also zero. ### Step-by-Step Solution: **Step 1: Understand the concept of moment (torque) of a force.** - The moment (or torque) of a force about a point is defined as the product of the force and the perpendicular distance from the line of action of the force to the point. Mathematically, it can be expressed as: \[ \tau = \vec{F} \cdot \vec{r} \] where \( \tau \) is the torque, \( \vec{F} \) is the force vector, and \( \vec{r} \) is the position vector from the point to the line of action of the force. **Step 2: Analyze the assertion.** - The assertion states that the moment of concurrent forces about any point is constant. - Concurrent forces are forces that meet at a single point. If we have multiple concurrent forces acting at a point, the moment about any point will depend on the magnitudes of the forces and their angles with respect to the position vector. - Since the forces are concurrent, the resultant force can be calculated, and the moment about any point will remain constant as long as the magnitudes and angles of the forces do not change. **Step 3: Analyze the reason.** - The reason states that if the vector sum of all concurrent forces is zero, then the moment of all the forces about any point is also zero. - If the vector sum of the forces is zero, it means that the forces are balanced and there is no net force acting on the system. In this case, the resultant torque (moment) about any point will also be zero because the sum of the individual moments will cancel out. **Step 4: Determine the relationship between assertion and reason.** - Both statements are true: - The assertion is true because the moment of concurrent forces about any point remains constant. - The reason is also true because if the vector sum of the forces is zero, the moment about any point will also be zero. - However, the reason does not serve as a direct explanation for the assertion since the assertion holds true for all concurrent forces, while the reason is a specific case when the forces balance out to zero. ### Conclusion: Based on the analysis: - The correct answer is **Option B**: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

To solve the given question, we need to analyze the two statements provided in the assertion and reason: 1. **Assertion**: The moment of concurrent forces about any point is constant. 2. **Reason**: If the vector sum of all concurrent forces is zero, then the moment of all the forces about any point is also zero. ### Step-by-Step Solution: **Step 1: Understand the concept of moment (torque) of a force.** ...
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