A body is uniformly rotating bout an axis fixed in an inertial frame of reference. Let `vecA` be a unit vector along the axis of rotation and `vecB` be the unit vector along the resultant force on a particle P of the body away from the axis. The value of `vecA.vecB` is

Options

A. 1
B. -1
C. 0
D. none of these

Answer

To solve the problem, we need to determine the value of the dot product of two vectors: \(\vec{A}\), which is a unit vector along the axis of rotation, and \(\vec{B}\), which is a unit vector along the resultant force on a particle \(P\) of the body away from the axis.

### Step-by-Step Solution:

1. **Understanding the Vectors**:
- \(\vec{A}\) is a unit vector along the axis of rotation. This means it points in the direction of the axis around which the body is rotating.
- \(\vec{B}\) is a unit vector along the resultant force acting on a particle \(P\) of the body. Since the body is rotating uniformly, the only force acting on the particle \(P\) (assuming no other forces like friction) is the centripetal force, which is directed towards the center of the rotation.

2. **Direction of Forces**:
- The centripetal force acting on particle \(P\) is directed radially inward towards the center of the circular path. Therefore, \(\vec{B}\) points towards the center of the rotation.

3. **Angle Between the Vectors**:
- Since \(\vec{A}\) points along the axis of rotation (let's say vertically), and \(\vec{B}\) points radially inward (horizontally), the two vectors are perpendicular to each other.
- The angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) is \(90^\circ\).

4. **Dot Product Calculation**:
- The dot product of two vectors is given by the formula:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta) \]
- Since both \(\vec{A}\) and \(\vec{B}\) are unit vectors, their magnitudes are \(1\):
\[ |\vec{A}| = 1, \quad |\vec{B}| = 1 \]
- Therefore, the dot product simplifies to:
\[ \vec{A} \cdot \vec{B} = 1 \cdot 1 \cdot \cos(90^\circ) = \cos(90^\circ) \]
- We know that \(\cos(90^\circ) = 0\).

5. **Conclusion**:
- Thus, the value of \(\vec{A} \cdot \vec{B}\) is:
\[ \vec{A} \cdot \vec{B} = 0 \]

### Final Answer:
The value of \(\vec{A} \cdot \vec{B}\) is \(0\).