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The moment of the force F acting at a po...

The moment of the force F acting at a point P, about the point C is

A

`FtimesCP`

B

`CP*F`

C

a vector having the same direction as F

D

`CPtimesF`

Text Solution

AI Generated Solution

The correct Answer is:
To find the moment of the force \( \mathbf{F} \) acting at point \( P \) about point \( C \), we can follow these steps: ### Step 1: Understand the Concept of Moment The moment of a force about a point is defined as the vector product (cross product) of the position vector and the force vector. The formula for the moment \( \mathbf{M} \) is given by: \[ \mathbf{M} = \mathbf{r} \times \mathbf{F} \] where \( \mathbf{r} \) is the position vector from point \( C \) to point \( P \). ### Step 2: Define the Position Vector \( \mathbf{r} \) The position vector \( \mathbf{r} \) can be expressed in terms of the position vectors of points \( P \) and \( C \): \[ \mathbf{r} = \mathbf{P} - \mathbf{C} \] This means that \( \mathbf{r} \) is the vector that points from \( C \) to \( P \). ### Step 3: Substitute \( \mathbf{r} \) into the Moment Formula Now, we substitute \( \mathbf{r} \) into the moment formula: \[ \mathbf{M} = (\mathbf{P} - \mathbf{C}) \times \mathbf{F} \] ### Step 4: Calculate the Moment The moment \( \mathbf{M} \) can now be calculated using the cross product: \[ \mathbf{M} = \mathbf{P} \times \mathbf{F} - \mathbf{C} \times \mathbf{F} \] This expression gives us the moment of the force about point \( C \). ### Step 5: Analyze the Direction of the Moment The direction of the moment vector \( \mathbf{M} \) is perpendicular to the plane formed by \( \mathbf{r} \) and \( \mathbf{F} \). Therefore, the moment will not be in the same direction as \( \mathbf{F} \) or \( \mathbf{C} \). ### Conclusion Thus, the moment of the force \( \mathbf{F} \) acting at point \( P \) about point \( C \) is given by: \[ \mathbf{M} = (\mathbf{P} - \mathbf{C}) \times \mathbf{F} \]
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Knowledge Check

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