Assertion: In circular motion, dot product of velocity vector `(v)` and acceleration vector `(a)` may be positive, negative or zero.
Reason: Dot product of angular velocity vector and linear velocity vector is always zero.

Options

A. If both Assertion 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, true but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understanding the Assertion
The assertion states that in circular motion, the dot product of the velocity vector \( \mathbf{v} \) and the acceleration vector \( \mathbf{a} \) may be positive, negative, or zero.

- In uniform circular motion, the acceleration (centripetal acceleration) is directed towards the center of the circle, while the velocity is tangential to the circle. Since these two vectors are perpendicular to each other, their dot product is zero:
\[ \mathbf{v} \cdot \mathbf{a} = |\mathbf{v}| |\mathbf{a}| \cos(90^\circ) = 0 \]

- In non-uniform circular motion, the acceleration has two components: centripetal (towards the center) and tangential (along the direction of motion). Depending on whether the particle is speeding up or slowing down, the angle between the velocity vector and the resultant acceleration vector can vary:
- If the particle is speeding up, the angle is acute, and the dot product is positive.
- If the particle is slowing down, the angle is obtuse, and the dot product is negative.

Thus, the assertion is true.

### Step 2: Understanding the Reason
The reason states that the dot product of the angular velocity vector \( \mathbf{\omega} \) and the linear velocity vector \( \mathbf{v} \) is always zero.

- The linear velocity \( \mathbf{v} \) is tangential to the circular path, while the angular velocity \( \mathbf{\omega} \) is directed along the axis of rotation (perpendicular to the plane of motion). Since these two vectors are perpendicular:
\[ \mathbf{\omega} \cdot \mathbf{v} = |\mathbf{\omega}| |\mathbf{v}| \cos(90^\circ) = 0 \]

Thus, the reason is also true.

### Step 3: Analyzing the Relationship
While both the assertion and the reason are true, they are not directly related to each other. The assertion discusses the relationship between velocity and acceleration in circular motion, while the reason discusses the relationship between angular velocity and linear velocity.

### Conclusion
Both the assertion and the reason are true, but the reason does not correctly explain the assertion. Therefore, the correct answer is:
- Both assertion and reason are true, but reason is not the correct explanation of assertion.

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